A few more ux refinements, and added the ability to hide captions

is making large objects like the 120-cell noticeably stuttery

README.md

@@ -4,7 +4,12 @@ FourDjs
 Visualisations of four-dimensional polytopes projected into 3-space, rendered
 with three.js
 
+[Basic interactive demo](https://etc.mikelynch.org/fourjs/)
+
+<img src="https://raw.githubusercontent.com/spikelynch/fourdjs/main/docs/screenshot-24cell.png" width="612" /><br />
+
+<img src="https://raw.githubusercontent.com/spikelynch/fourdjs/main/docs/screenshot-120cell.png" width="612" /><br />
+
+<img src="https://raw.githubusercontent.com/spikelynch/fourdjs/main/docs/screenshot-600cell.png" width="612" />
 
-<img src="https://raw.githubusercontent.com/spikelynch/fourdjs/main/docs/screenshot-24cell.png" width="445" />
 
-[Basic interactive demo](https://etc.mikelynch.org/fourjs/)

cell120.js

@@ -0,0 +1,137 @@
+// trying to go from faces to dodecahedra
+
+
+function shared_vertices(f1, f2) {
+	return f1.nodes.filter((f) => f2.nodes.includes(f));	
+}
+
+
+function adjacent_faces(f1, f2) {
+	// adjacent faces which share an edge, not just a vertex
+	const intersect = shared_vertices(f1, f2);
+	if( intersect.length < 2 ) {
+		return false;
+	}
+	if( intersect.length > 2 ) {
+		console.log(`warning: faces ${f1.id} and ${f2.id} have too many common vertices`);
+	}
+	return true;
+}
+
+
+function find_adjacent_faces(faces, face) {
+	const neighbours = faces.filter((f) => f.id !== face.id && adjacent_faces(f, face));
+	return neighbours;
+}
+
+
+
+
+function find_dodeca_mutuals(faces, f1, f2) {
+	// for any two adjacent faces, find their common neighbours where
+	// all three share exactly one vertex (this, I think, guarantees that
+	// all are on the same dodecahedron)
+
+	const n1 = find_adjacent_faces(faces, f1);
+	const n2 = find_adjacent_faces(faces, f2);
+	const common =  n1.filter((f1) => n2.filter((f2) => f1.id === f2.id).length > 0 );
+	// there's one extra here - the third which has two nodes in common with
+	// both f1 and f2 - filter it out 
+	const mutuals = common.filter((cf) => {
+		const shared = cf.nodes.filter((n) => f1.nodes.includes(n) && f2.nodes.includes(n));
+		return shared.length === 1
+	});
+	return mutuals;
+}
+
+function find_dodeca_next(faces, dodeca, f1, f2) {
+	// of a pair of mutuals, return the one we haven't already got
+	const m = find_dodeca_mutuals(faces, f1, f2);
+	if( dodeca.filter((f) => f.id === m[0].id ).length > 0 ) {
+		m.shift();
+	}
+	return m[0];
+}
+
+// from any two mutual faces, return all the faces in their dodecahedron
+
+function make_dodecahedron(faces, f1, f2) {
+	const dodecahedron = [ f1, f2 ];
+
+	// take f1 as the 'center', get the other four around it from f2
+	const fs = find_dodeca_mutuals(faces, f1, f2);
+	const f3 = fs[0];
+	const f6 = fs[1];
+	dodecahedron.push(f3);
+	const f4 = find_dodeca_next(faces, dodecahedron, f1, f3);
+	dodecahedron.push(f4);
+	const f5 = find_dodeca_next(faces, dodecahedron, f1, f4);
+	dodecahedron.push(f5);
+	dodecahedron.push(f6);
+
+	// get the next ring
+
+	const f7 = find_dodeca_next(faces, dodecahedron, f6, f2);
+	dodecahedron.push(f7);
+	const f8 = find_dodeca_next(faces, dodecahedron, f2, f3);
+	dodecahedron.push(f8);
+	const f9 = find_dodeca_next(faces, dodecahedron, f3, f4);
+	dodecahedron.push(f9);
+	const f10 = find_dodeca_next(faces, dodecahedron, f4, f5);
+	dodecahedron.push(f10);
+	const f11 = find_dodeca_next(faces, dodecahedron, f5, f6);
+	dodecahedron.push(f11);
+
+	// get the last
+
+	const f12 = find_dodeca_next(faces, dodecahedron, f7, f8);
+	dodecahedron.push(f12);
+
+	return dodecahedron;
+}
+
+
+// for a face, pick an edge, and then find the other two faces which
+// share this edge. These can be used as the starting points for the
+// first face's two dodecahedra 
+
+function find_edge_neighbours(faces, face) {
+	const n1 = face.nodes[0];
+	const n2 = face.nodes[1];
+	return faces.filter((f) => f.id !== face.id && f.nodes.includes(n1) && f.nodes.includes(n2));
+}
+
+
+// each face is in two dodecahedra: this returns them both
+
+function face_to_dodecahedra(faces, f) {
+	const edge_friends = find_edge_neighbours(faces, f);
+	const d1 = make_dodecahedron(faces, f, edge_friends[0]);
+	const d2 = make_dodecahedron(faces, f, edge_friends[1]);
+	return [ d1, d2 ];
+}
+
+// brute-force calculation of all dodecahedra 
+
+function dd_fingerprint(dodecahedron) {
+	const ids = dodecahedron.map((face) => face.id);
+	ids.sort()
+	return ids.join(',');
+}
+
+export function make_120cell_dodecahedra(faces) {
+	const dodecas = [];
+	const seen = {};
+	for( const face of faces ) {
+		const dds = face_to_dodecahedra(faces, face);
+		for( const dd of dds ) {
+			const fp = dd_fingerprint(dd);
+			if( ! (fp in seen) ) {
+				console.log(`added dodeca ${fp}`);
+				dodecas.push(dd);
+				seen[fp] = 1;
+			}
+		}
+	}
+	return dodecas;
+}

cellindex.js

@@ -0,0 +1,188 @@
+
+export const LAYER_NAMES = {
+	0: "North pole",
+	1: "Arctic circle",
+	2: "North temperate",
+	3: "Tropic of Cancer",
+	4: "Equator",
+	5: "Tropic of Capricorn",
+	6: "South temperate",
+	7: "Antarctic circle (all)"
+};
+
+
+export const INDEX120 = {
+	"1": [
+		27,38,48,49,61,68,74,87,95,98,105,120, 126,131,140,149,156,165,174,
+		179,185,200,207,210,218,223,226,231,234,239,241,248,252,253,258,263,
+		265,272,274,279,284,285,289,296,300,301,306,311,313,320,324,325,331,
+		334,339,342,347,350,356,357,362,367,369,376,378,383,388,389,393,400,
+		403,406,413,414,419,420,425,427,438,440,444,448,449,453,458,460,469,
+		471,473,474,487,488,490,494,499,503,511,512,513,514,525,527,530,532,
+		539,543,546,550,555,558,563,566,572,573,580,581,585,592,593,600
+	],
+	"2":[
+		1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,28,
+		30,31,34,35,37,40,41,44,46,47,50,51,53,56,57,60,62,63,66,67,69,72,73,
+		76,78,79,82,83,85,88,90,91,93,96,97,100,102,103,106,107,109,112,113,
+		116,118,119,122,123,125,128,129,132,134,135,138,139,141,144,145,148,
+		150,151,154,155,157,160,161,164,166,167,170,171,173,176,177,180,182,
+		183,186,187,189,192,193,196,198,199,202,203,205,208,209,212,214,215
+		],
+	"3":[
+		26,39,45,52,64,65,75,86,94,99,108,117,127,130,137,152,153,168,175,
+		178,188,197,206,211,219,222,227,230,235,238,244,245,251,254,257,264,
+		268,269,273,280,283,286,292,293,299,302,305,312,316,317,321,328,330,
+		335,338,343,348,349,355,358,363,366,370,375,377,384,385,392,394,399,
+		404,405,415,416,417,418,426,428,437,439,441,445,452,456,457,459,470,
+		472,475,476,485,486,491,495,498,502,509,510,515,516,526,528,529,531,
+		538,542,547,551,554,559,562,567,569,576,577,584,588,589,596,597
+		],
+	"4":[
+		32,33,43,54,58,71,77,84,92,101,110,115,121,136,143,146,159,162,169,
+		184,190,195,204,213,220,221,228,229,236,237,242,247,249,256,260,261,
+		266,271,276,277,281,288,290,295,297,304,308,309,315,318,322,327,329,
+		336,340,341,346,351,354,359,361,368,371,374,379,382,387,390,396,397,
+		401,408,409,410,423,424,430,432,433,435,443,447,450,454,461,463,466,
+		468,477,478,483,484,489,493,500,504,507,508,517,518,522,524,533,535,
+		540,544,545,549,553,560,561,568,570,575,578,583,587,590,595,598
+		],
+	"5":[
+		29,36,42,55,59,70,80,81,89,104,111,114,124,133,142,147,158,163,172,
+		181,191,194,201,216,217,224,225,232,233,240,243,246,250,255,259,262,
+		267,270,275,278,282,287,291,294,298,303,307,310,314,319,323,326,332,
+		333,337,344,345,352,353,360,364,365,372,373,380,381,386,391,395,398,
+		402,407,411,412,421,422,429,431,434,436,442,446,451,455,462,464,465,
+		467,479,480,481,482,492,496,497,501,505,506,519,520,521,523,534,536,
+		537,541,548,552,556,557,564,565,571,574,579,582,586,591,594,599
+		]
+};
+
+
+export const LAYERS120 =  {
+	"0": [154,266,158,222,218,250,254,162,268,156,160,252,256,166,270,272,
+		164,220,224,168],
+	"1": [2,318,314,30,414,510,362,26,506,410,338,458,462,110,
+		 106,6,350,346,34,482,418,474,330,442,450,98,90,14,
+		 364,28,508,476,394,570,572,124,122,478,348,32,480,
+		 512,396,576,574,126,128,8,352,38,422,486,334,454,
+		 446,94,102,514,366,518,342,470,466,114,118,16,368,
+		 36,484,516,398,580,578,130,132,412,316,420,332,452,
+		 444,92,100,4,320,416,340,464,460,108,112,40,488,424,
+		 336,448,456,104,96,520,400,582,584,136,134,344,468,472,120,116],
+	"2":[246,242,42,170,426,50,434,178,226,322,46,430,174,54,182,438,326,
+		230,78,558,526,62,494,542,590,142,74,554,386,300,298,202,290,206,
+		522,58,538,490,138,586,236,234,186,60,540,188,282,378,66,546,194,
+		68,196,548,382,286,498,82,562,530,146,594,76,556,204,80,208,560,
+		388,292,588,44,428,492,140,524,64,544,380,238,190,240,192,284,
+		592,496,432,48,528,144,70,198,550,72,552,200,288,384,502,534,566,
+		86,598,150,390,302,210,304,214,294,84,212,564,88,568,216,296,392,
+		596,500,436,52,532,148,324,244,172,248,180,228,176,56,440,184,232,
+		328,504,536,152,600],
+	"3":[369,273,275,371,17,353,257,261,357,9,401,305,306,402,21,307,308,
+		403,22,404,259,263,355,11,359,277,279,373,19,375,309,310,405,23,
+		406,258,262,354,10,358,274,276,370,18,372,356,260,264,360,12,407,
+		311,312,408,24,374,278,280,376,20],"4":[229,325,173,45,429,493,
+		141,525,589,289,385,557,77,205,201,137,521,553,73,585,285,381,
+		193,65,545,593,145,497,529,225,321,433,49,177,139,587,491,281,377,
+		539,59,187,283,379,189,61,541,197,287,199,237,239,191,293,389,213,
+		149,533,565,85,597,295,391,211,147,531,563,83,595,227,323,171,43,
+		427,523,151,503,535,231,327,439,55,183,599,383,551,71,87,215,567,
+		169,241,245,181,489,425,41,185,233,235,195,537,57,591,543,63,495,
+		143,549,69,501,179,499,435,51,175,431,47,527,203,291,387,555,75,
+		207,299,297,559,79,437,53,209,561,81,301,303,547,67,243,247],
+	"5":[457,337,461,105,109,469,341,465,117,113,89,97,441,449,329,93,445,
+		101,453,333,573,395,125,127,575,121,569,393,123,571,451,331,443,
+		99,91,129,577,131,579,397,107,459,111,339,463,95,447,335,103,455,
+		133,135,581,583,399,115,119,467,471,343
+		],
+	"6":[1,417,313,409,413,317,421,5,475,345,473,481,349,483,33,513,507,
+		13,363,511,7,487,351,485,37,517,15,519,367,515,3,423,319,415,39,
+		25,505,509,477,29,411,27,479,347,31,365,419,35,315,361
+		],
+	"7":[217,153,221,157,265,161,165,269,249,253,251,255,267,159,155,
+		163,219,271,223,167]
+};
+
+// Schoute's partition via https://arxiv.org/abs/1010.4353
+
+export const PARTITION600 = {
+
+	"2,0,0,0": 1,
+	"0,2,0,0": 1,
+	"0,0,2,0": 1,
+	"0,0,0,2": 1,
+	"1,1,1,1": 1,
+	"1,1,-1,-1": 1,
+	"1,-1,1,-1": 1,
+	"1,-1,-1,1": 1,
+	"1,-1,-1,-1": 1,
+	"1,-1,1,1": 1,
+	"1,1,-1,1": 1,
+	"1,1,1,-1": 1,
+
+	"k,0,-t,-1": 2,
+	"0,k,1,-t": 2,
+	"t,-1,k,0": 2,
+	"1,t,0,k": 2,
+	"t,k,0,-1": 2,
+	"1,0,k,t": 2,
+	"k,-t,-1,0": 2,
+	"0,1,-t,k": 2,
+	"1,k,t,0": 2,
+	"t,0,-1,k": 2,
+	"0,t,-k,-1": 2,
+	"k,-1,0,-t": 2,
+
+	"t,0,1,k": 3,
+	"0,t,-k,1": 3,
+	"1,-k,-t,0": 3,
+	"k,1,0,-t": 3,
+	"0,k,1,t": 3,
+	"t,1,-k,0": 3,
+	"k,0,t,-1": 3,
+	"1,-t,0,k": 3,
+	"t,-k,0,-1": 3,
+	"0,1,-t,-k": 3,
+	"1,0,-k,t": 3,
+	"k,t,1,0": 3,
+
+	"t,0,-1,-k": 4,
+	"0,t,k,-1": 4,
+	"1,-k,t,0": 4,
+	"k,1,0,t": 4,
+	"t,1,k,0": 4,
+	"0,k,-1,-t": 4,
+	"1,-t,0,-k": 4,
+	"k,0,-t,1": 4,
+	"0,1,t,k": 4,
+	"t,-k,0,1": 4,
+	"k,t,-1,0": 4,
+	"1,0,k,-t": 4,
+
+	"k,0,t,1": 5,
+	"0,k,-1,t": 5,
+	"t,-1,-k,0": 5,
+	"1,t,0,-k": 5,
+	"1,0,-k,-t": 5,
+	"t,k,0,1": 5,
+	"0,1,t,-k": 5,
+	"k,-t,1,0": 5,
+	"t,0,1,-k": 5,
+	"1,k,-t,0": 5,
+	"k,-1,0,t": 5,
+	"0,t,k,1": 5
+};
+
+
+
+export const LAYERS600 = {
+	"0":[2,42,46,50,54,106,110,44,48,52,56,108,112],
+	"1":[10,12,14,16,18,20,22,24,34,36,38,40,98,102,100,104,90,92,94,96],
+	"2":[26,58,74,28,76,30,60,32,62,78,80,64],
+	"3":[3,4,5,6,7,8,65,113,81,66,114,82,67,115,83,68,116,84,69,117,85,70,118,86,71,119,87,72,120,88],
+	"4":[25,29,27,31,57,61,59,63,73,75,77,79],
+	"5":[97,101,99,103,33,35,37,39,89,91,93,95,9,11,13,15,17,19,21,23],
+	"6":[41,105,49,43,51,45,107,47,109,53,55,111],
+	"7":[1]
+};

colours.js

@@ -0,0 +1,37 @@
+import ColorScheme from 'color-scheme';
+import Color from 'color';
+
+export const get_colours = (basis) => {
+	const basis_c = Color(basis);
+	const hslb = basis_c.hsl();
+	const hue = hslb['color'][0];
+	const saturation = hslb['color'][1];
+	const luminance = hslb['color'][2];
+	const scheme = new ColorScheme;
+	scheme.from_hue(hue).scheme("tetrade").distance(0.75);
+	const colours = scheme.colors().slice(1, 9);
+	colours.reverse();
+	const hsl = colours.map((c) => Color("#" + c).hsl());
+	const resaturated = hsl.map((hslc) => hslc.saturationl(saturation).rgbNumber()); 
+	resaturated.unshift(basis);
+	return resaturated;
+}
+
+// basic colours where 0 = blue
+// 1 - dark blue
+// 2 - white
+// 3 - light cyan
+// 4 - light orange
+// 5 - dark orange
+
+export const get_plain_colours = (basis) => {
+	return [
+		basis,
+		0xffffff,
+		0x00ff00,
+		0xff0000,
+		0x0000ff,
+		0xff9900,
+		0x000000,
+		]
+}

docs/manual_index_ideas.md

@@ -0,0 +1,12 @@
+# Indexing manually ideas
+
+- a list of all the faces (and maybe dodecahedra) which lets me assign
+  labels to them and lights up the interface
+
+- where faces / vertices are repeated in the table, assigning a vertex in one
+  spot changes it everywhere else
+
+
+
+separately - take the links generated by this codebase and apply them to
+the d3.js forcemap code I wrote for the 24-cell

docs/notes_120_cell.md

@@ -0,0 +1,244 @@
+
+Steps forward -
+
+1. algorithm which, given a face, finds the two dodecahedra it belongs to
+
+2. using this, generate a list of all 120 dodecahedra:
+
+
+
+1.
+
+For a face: there are five edges, and ten other faces sharing an edge.
+
+These edges are in two sets: one for each dodecahedron. The sets are defined
+by them sharing vertices which aren't in the first face.
+
+Go around a set of five, by pairs: for each pair, find the other neighbour - 
+
+this gives the next five faces.
+
+There's only one face left, which is defined by the shared other vertices of 
+the last five.
+
+
+
+2. have tried manual labelling and it will drive me crazy before I finish
+
+3. Automated approach based on what I've got so far:
+
+- should be possible to colour a single dodecahedron from a single face and
+  one other vertex (to pick a chirality)
+
+- write a function to do this - the compound-of-four-tetrahedra map can be
+  more or less hard coded: follow the pattern 1-2-3-4-5, 3-4-5-1-2, etc out
+  from the inner ring, and map the original face's permutation
+
+From this:
+
+- colour the first dodecahedron, picking a chirality
+
+- the next vertices from each of this dodecahedron's vertices have colours
+  which come from the first dodeca
+
+- these can be used to colour the next layer of dodecahedra 
+
+- and so on 
+
+Alternatively:
+
+- do it by the discrete Hopf fibration, one fibre at a time
+
+
+
+
+
+/// old shit below that didn't work VVVV
+
+
+Chords: 1.74806 - the 120-cell has 7200 chords of this length
+
+Looking for a way to partition the 600 vertices of the 120 cell into five
+disjoint 600-cells, each of which has 120 vertices.
+
+(there are 10 such 600-cells so two ways to do the partition I guess)
+
+a 600-cell has 720 edges! optimistically this means that each chord in the
+collection of 7200 belongs to one and only one of the 600-cells.
+
+
+the way forward:
+
+I need to take the 7200 chords (pairs of nodes) and divide them into sets
+which are connected to one another - with any luck, each of these will be
+one of the 10 600-cells
+
+Then need to sort these 10 sets of 120 vertices into the two sets of 5
+
+
+collate chords by node
+
+Each 120-cell vertex has 24 of the chord3s from it - as a 600-cell has 12
+edges to each vertex, this suggests that each 120-vertex belongs to two 
+600-cells with a disjoint set of vertices
+
+Next algorithm - gather each 600-cell
+
+use the chords as the basis for this.
+
+n1 -> 24 chords -> add these 24 neighbours
+
+bad luck - traversing chord3s from the first vertex reaches all 600 vertices-
+which isn't suprising as the two 5 disjoint sets overlap. Sigh.
+
+Use the angles between the chords? seems a bit complex
+
+Get the angles from the 600-cell model. Use these to separate out the sets of
+24 chords from a point on the 120-cell.
+
+Notes from dinner:
+
+- all of the 60-degree angles are chords joining the vertices of the tetrahedra
+  - there should be two sets of these
+
+for eg - this works for the chords from 1!
+
+    [ 25, 41 ],
+    [ 25, 97 ],
+    [ 25, 109 ],
+    [ 25, 157 ],
+    [ 25, 161 ],  
+    [ 41, 97 ],
+    [ 41, 109 ],
+    [ 41, 173 ],
+    [ 41, 177 ],
+ 	[ 97, 113 ],
+ 	[ 97, 161 ],
+    [ 97, 177 ],
+    [ 37, 53 ],
+    [ 37, 93 ],
+    [ 37, 113 ],
+    [ 37, 157 ],
+    [ 37, 161 ],
+    [ 53, 93 ],
+    [ 53, 113 ],
+    [ 53, 173 ],
+    [ 53, 177 ],
+	[ 173, 177 ]
+    [ 93, 109 ],
+	[ 93, 157 ],
+	[ 93, 173 ],   
+ 	[ 109, 157 ],
+ 	[ 109, 173 ],
+	[ 113, 161 ],
+	[ 113, 177 ],
+    [ 157, 161 ],  
+
+
+    [ 29, 45 ],     5
+    [ 29, 101 ],    101
+    [ 29, 105 ],    105
+    [ 29, 153 ],    153
+    [ 29, 165 ],    165
+    [ 45, 101 ],    
+    [ 45, 105 ],
+    [ 45, 169 ],    169
+    [ 45, 181 ],    181
+	[ 101, 117 ],   117
+	[ 101, 165 ],   
+	[ 101, 181 ],
+    [ 105, 153 ],  
+    [ 105, 169 ],
+    [ 33, 49 ],     33 49
+    [ 33, 89 ],     89
+    [ 33, 117 ],
+    [ 33, 153 ],
+    [ 33, 165 ],
+    [ 49, 89 ],
+    [ 49, 117 ],
+    [ 49, 169 ],
+    [ 49, 181 ],
+	[ 169, 181 ],
+    [ 89, 105 ],
+    [ 89, 153 ],
+    [ 89, 169 ],
+    [ 117, 165 ],
+    [ 117, 181 ],
+	[ 153, 165 ], 
+    
+
+So each of these is one of the two icosahedral pyramids from node 1.
+
+Doing this manually for the rest of the partition is possible, but could it
+be automated based on angles?
+
+
+
+Plan for Sunday:
+
+* use the existing label_subgraph to make a function which partitions the
+  60-angle chords into two groups (like I did manually above)
+
+  // this is done and seems to work
+
+* test this labelling manually (ie colour one set of 60-angle vertices)
+
+  // done this with the manual labels and it looks good
+
+* make another labeling routine which can fill out the rest of the 600-cell
+  from the starting dodecahedron, by only following chords which are at 60
+  to the entering chord
+
+Then the big algorithm does the following:
+
+- start from node 1, find 60-angles, pick one partition at random, label that 600-cell
+
+- find the next unlabelled node
+
+- find 60-angles, partition them, pick a partition with no unlabelled cells and label that 600-cell
+
+- repeat the previous step for the remaining three 600-cells
+
+Alternative, more manual option: just write the second labelling routine and
+do the rest by hand
+
+
+    [ 25, 41 ],
+    [ 25, 97 ],
+    [ 25, 109 ],
+    [ 25, 157 ],
+    [ 25, 161 ],  
+    [ 41, 97 ],
+    [ 41, 109 ],
+    [ 41, 173 ],
+    [ 41, 177 ],
+ 	[ 97, 113 ],
+ 	[ 97, 161 ],
+    [ 97, 177 ],
+    [ 37, 53 ],
+    [ 37, 93 ],
+    [ 37, 113 ],
+    [ 37, 157 ],
+    [ 37, 161 ],
+    [ 53, 93 ],
+    [ 53, 113 ],
+    [ 53, 173 ],
+    [ 53, 177 ],
+	[ 173, 177 ]
+    [ 93, 109 ],
+	[ 93, 157 ],
+	[ 93, 173 ],   
+ 	[ 109, 157 ],
+ 	[ 109, 173 ],
+	[ 113, 161 ],
+	[ 113, 177 ],
+    [ 157, 161 ],  
+25 41 97 109
+157 161 173 177
+113 37 53 93
+
+
+Another idea - look at colouring the vertices of a dodecahedron according to
+the four compound tetrahedra and see if this can be repeated automatically to
+neighbouring cells
+

fourDShape.js

@@ -1,23 +1,24 @@
 import * as THREE from 'three';
 
 
-const HYPERPLANE = 2;
+const HYPERPLANE = 2.0;
-
+const W_FORESHORTENING = 0.04;
-const NODE_SIZE = 0.01;
-const LINK_SIZE = 0.01;
-
-
 
 class FourDShape extends THREE.Group {
 
-	constructor(node_ms, link_ms, structure) {
+	constructor(node_ms, link_ms, face_ms, structure) {
 		super();
 		this.node_ms = node_ms;
 		this.link_ms = link_ms;
+		this.face_ms = face_ms;
 		this.nodes4 = structure.nodes;
 		this.nodes3 = {};
 		this.links = structure.links;
+		this.faces = ( "faces" in structure ) ? structure.faces : [];
+		this.node_scale = 1;
+		this.link_scale = 1;
 		this.hyperplane = HYPERPLANE;
+		this.foreshortening = W_FORESHORTENING;
 		this.initShapes();
 	}
 
@@ -33,8 +34,8 @@ class FourDShape extends THREE.Group {
 		}
 	}
 
-	makeNode(material, v3) {
+	makeNode(material, v3, scale) {
-		const geometry = new THREE.SphereGeometry(NODE_SIZE);
+		const geometry = new THREE.SphereGeometry(this.node_size);
 		const sphere = new THREE.Mesh(geometry, material);
 		sphere.position.copy(v3);
 		this.add(sphere);
@@ -42,75 +43,145 @@ class FourDShape extends THREE.Group {
 	}
 
 	makeLink(material, link) {
-		const n1 = this.nodes3[link.source].v3;
+		const n1 = this.nodes3[link.source];
-		const n2 = this.nodes3[link.target].v3;
+		const n2 = this.nodes3[link.target];
-		const length = n1.distanceTo(n2);
+		const s1 = n1.scale;
+		const s2 = n2.scale;
+		const length = n1.v3.distanceTo(n2.v3);
 		const centre = new THREE.Vector3();
-		centre.lerpVectors(n1, n2, 0.5);
+		centre.lerpVectors(n1.v3, n2.v3, 0.5);
-		const geometry = new THREE.CylinderGeometry(LINK_SIZE, LINK_SIZE, 1);
+		const geometry = new THREE.CylinderGeometry(
+			this.link_scale * s2, this.link_scale * s1, 1,
+			16, 1, true
+		);
 		const cyl = new THREE.Mesh(geometry, material);
 		const edge = new THREE.Group();
 		edge.add(cyl);
 		edge.position.copy(centre);
 		edge.scale.copy(new THREE.Vector3(1, 1, length));
-		edge.lookAt(n2);
+		edge.lookAt(n2.v3);
 		cyl.rotation.x = Math.PI / 2.0;
 		this.add(edge);
 		return edge;
 	}
 
-	updateLink(link) {
+	updateLink(link, links_show) {
-		const n1 = this.nodes3[link.source].v3;
+		const n1 = this.nodes3[link.source];
-		const n2 = this.nodes3[link.target].v3;
+		const n2 = this.nodes3[link.target];
-		const length = n1.distanceTo(n2);
+		const s1 = n1.scale;
+		const s2 = n2.scale;
+		const length = n1.v3.distanceTo(n2.v3);
 		const centre = new THREE.Vector3();
-		centre.lerpVectors(n1, n2, 0.5);
+		centre.lerpVectors(n1.v3, n2.v3, 0.5);
-		link.object.scale.copy(new THREE.Vector3(1, 1, length));
+		// take the average of the ends as the thickness - as a workaround,
+		// because I haven't worked out how to reshape tapered links without
+		// having to reassign a new geometry to every link
+		const link_mean = this.link_scale * (s1 + s2) * 0.5;		
+		link.object.scale.copy(new THREE.Vector3(link_mean, link_mean, length));
 		link.object.position.copy(centre);
-		link.object.lookAt(n2);
+		link.object.lookAt(n2.v3);
 		link.object.children[0].rotation.x = Math.PI / 2.0;
+		link.object.visible = (!links_show || link.label in links_show); 
 	}
 
-	fourDtoV3(x, y, z, w, rotations) {
+
+	setFaceGeometry(face, geometry) {
+		const values = [];
+		for( const f of face.nodes ) {
+			const v3 = this.nodes3[f].v3;
+			values.push(v3.x);
+			values.push(v3.y);
+			values.push(v3.z);
+		}
+		const v3 = this.nodes3[face.nodes[0]].v3;
+		values.push(v3.x);
+		values.push(v3.y);
+		values.push(v3.z);
+		const vertices = new Float32Array(values);
+		geometry.setAttribute( 'position', new THREE.BufferAttribute( vertices, 3 ) );
+	}
+
+	makeFace(material, face) {
+		const geometry = new THREE.BufferGeometry();
+		this.setFaceGeometry(face, geometry)
+		const mesh = new THREE.Mesh( geometry, material );
+		this.add(mesh);
+		return mesh;
+	}
+
+
+	fourDtoV3_old(x, y, z, w, rotations) {
 		const v4 = new THREE.Vector4(x, y, z, w);
 		for ( const m4 of rotations ) {
 			v4.applyMatrix4(m4);
 		}
-		const k = this.hyperplane / (this.hyperplane + v4.w);
+		const k = this.fourDscale(v4.w);
 		return new THREE.Vector3(v4.x * k, v4.y * k, v4.z * k);
 	}
 
+	fourDscale(w) {
+		return this.hyperplane / ( this.hyperplane + w );
+	}
+	
+	fourDrotate(x, y, z, w, rotations) {
+		const v4 = new THREE.Vector4(x, y, z, w);
+		for ( const m4 of rotations ) {
+			v4.applyMatrix4(m4);
+		}
+		return v4;
+	}
+
+	fourDtoV3(v4) {
+		const k = this.fourDscale(v4.w);
+		return new THREE.Vector3(v4.x * k, v4.y * k, v4.z * k);		
+	}
 
 	initShapes() {
 		for( const n of this.nodes4 ) {
-			const v3 = this.fourDtoV3(n.x, n.y, n.z, n.w, []);
+			const k = this.fourDscale(n.w);
+			const v3 = new THREE.Vector3(n.x * k, n.y * k, n.z * k);
 			const material = this.getMaterial(n, this.node_ms);
 			this.nodes3[n.id] = {
 				v3: v3,
-				object: this.makeNode(material, v3)
+				scale: k,
+				label: n.label,
+				object: this.makeNode(material, v3, k)
 			};
 		}
 		for( const l of this.links ) {
 			const material = this.getMaterial(l, this.link_ms);
 			l.object = this.makeLink(material, l);
 		}
+		for( const f of this.faces ) {
+			const material = this.getMaterial(f, this.face_ms);
+			f.object = this.makeFace(material, f);
+		}
 	}
 
 
-	render3(rotations) {
+	render3(rotations, nodes_show, links_show) {
+		this.scalev3 = new THREE.Vector3(this.node_scale, this.node_scale, this.node_scale);
 		for( const n of this.nodes4 ) {
-			const v3 = this.fourDtoV3(n.x, n.y, n.z, n.w, rotations);
+			const v4 = this.fourDrotate(n.x, n.y, n.z, n.w,  rotations);
+			const k = this.fourDscale(v4.w);
+			const v3 = new THREE.Vector3(v4.x * k, v4.y * k, v4.z * k);
+			const s4 = k * this.node_scale * this.foreshortening;
+			const s3 = new THREE.Vector3(s4, s4, s4);
 			this.nodes3[n.id].v3 = v3;
+			this.nodes3[n.id].scale = k * this.foreshortening;
 			this.nodes3[n.id].object.position.copy(v3);
-			// could do scaling here
+			this.nodes3[n.id].object.scale.copy(s3);
+			this.nodes3[n.id].object.visible = ( !nodes_show || n.label in nodes_show );
+		}
+		for( const l of this.links ) {
+			this.updateLink(l, links_show);
 		}
 
-		for( const l of this.links ) {
+		for( const f of this.faces ) {
-			this.updateLink(l);
+			this.setFaceGeometry(f, f.object.geometry);
 		}
 	}
 
-
 }
 
-export { FourDShape };
+export { FourDShape };

gui.js

@@ -0,0 +1,220 @@
+import { GUI } from 'lil-gui';
+
+
+const DEFAULTS = {
+	nodesize: 0.25,
+	nodeopacity: 1,
+	linksize: 0.2,
+	linkopacity: 0.75,
+	link2opacity: 0.75,
+	shape: '120-cell',
+	option: 'none',
+	visibility: 5,
+	inscribed: false,
+	inscribe_all: false,
+	color: 0x3293a9,
+	background: 0xd4d4d4,
+	hyperplane: 0.93,
+	zoom: 1,
+	xRotate: 'YW',
+	yRotate: 'XW',
+	dtheta: 0,
+	damping: false,
+	captions: true,
+	dpsi: 0,
+}
+
+
+
+class FourDGUI {
+
+	constructor(shapes, changeShape, setColor, setBackground, setNodeOpacity,setLinkOpacity, setVisibility, showDocs) {
+		this.gui = new GUI();
+		const SHAPE_NAMES = shapes.map((s) => s.name);
+
+		this.parseLinkParams();
+		const guiObj = this;
+		this.params = {
+			shape: this.link['shape'],
+			option: this.link['option'],
+			inscribed: this.link['inscribed'],
+			inscribe_all: this.link['inscribe_all'],
+			linksize: this.link['linksize'],
+			linkopacity: this.link['linkopacity'],
+			link2opacity: this.link['linkopacity'],
+			nodesize: this.link['nodesize'],
+			nodeopacity: this.link['nodeopacity'],
+			depth: this.link['depth'],
+			color: this.link['color'],
+			background: this.link['background'],
+			hyperplane: this.link['hyperplane'],
+			zoom: this.link['zoom'],
+			xRotate: this.link['xRotate'],
+			yRotate: this.link['yRotate'],
+			damping: false,
+			captions: true,
+			dtheta: this.link['dtheta'],
+			dpsi: this.link['dpsi'],
+			"copy link": function () { guiObj.copyUrl() }
+		};
+		let options_ctrl;
+		this.gui.add(this.params, 'shape', SHAPE_NAMES).onChange((shape) => {
+			const options = this.getShapeOptions(shapes, shape);
+			options_ctrl = options_ctrl.options(options).onChange((option) => {
+				setVisibility(option)
+			});
+			options_ctrl.setValue(options[0])
+			changeShape(shape)
+		});
+		const options = this.getShapeOptions(shapes, this.params['shape']);
+		options_ctrl = this.gui.add(this.params, 'option').options(options).onChange((option) => {
+			setVisibility(option)
+		});
+		this.gui.add(this.params, 'hyperplane', 0.5, 1 / 0.8);
+		this.gui.add(this.params, 'zoom', 0.1, 2.0);
+		this.gui.add(this.params, 'nodesize', 0, 1);
+		this.gui.add(this.params, 'nodeopacity', 0, 1).onChange(setNodeOpacity);
+		this.gui.add(this.params, 'linksize', 0, 1);
+		this.gui.add(this.params, 'linkopacity', 0, 1).onChange(
+			(v) => setLinkOpacity(v, true)
+		);
+		this.gui.add(this.params, 'link2opacity', 0, 1).onChange(
+			(v) => setLinkOpacity(v, false)
+		);
+		this.gui.addColor(this.params, 'color').onChange(setColor);
+		this.gui.addColor(this.params, 'background').onChange(setBackground);
+		this.gui.add(this.params, 'xRotate', [ 'YW', 'YZ', 'ZW' ]);
+		this.gui.add(this.params, 'yRotate', [ 'XZ', 'XY', 'XW' ]);
+		this.gui.add(this.params, 'captions').onChange(showDocs);
+		this.gui.add(this.params, 'damping');
+		this.gui.add(this.params, 'copy link');
+
+	}
+
+	getShapeOptions(shapes, shape) {
+		const spec = shapes.filter((s) => s.name === shape);
+		if( spec && spec[0].options ) {
+			return spec[0].options.map((o) => o.name);
+		} else {
+			return [];
+		}
+	}
+
+
+	numParam(param, parser) {
+		const value = this.urlParams.get(param);
+		if( value ) {
+			const n = parser(value);
+			if( n !== NaN ) {
+				return n;
+			}
+		}
+		return DEFAULTS[param];
+	}
+
+	stringToHex(cstr) {
+		return parseInt('0x' + cstr.substr(1));
+	}
+
+	hexToString(hex) {
+		return '#' + hex.toString(16);
+	}
+
+
+
+	parseLinkParams() {
+		this.linkUrl = new URL(window.location.toLocaleString());
+		this.link = {};
+		const guiObj = this;
+
+		this.urlParams = this.linkUrl.searchParams;
+		for( const param of [ "shape", "xRotate", "yRotate", "option" ]) {
+			const value = this.urlParams.get(param);
+			if( value ) {
+				this.link[param] = value;
+			} else {
+				this.link[param] = DEFAULTS[param];
+			}
+		}
+		for( const param of [ "inscribed", "inscribe_all"] ) {
+			this.link[param] = ( this.urlParams.get(param) === 'y' );
+		}
+		this.link['hyperplane'] = this.numParam('hyperplane', parseFloat);
+		this.link['zoom'] = this.numParam('zoom', parseFloat);
+		this.link['linksize'] = this.numParam('linksize', parseFloat);
+		this.link['linkopacity'] = this.numParam('linkopacity', parseFloat);
+		this.link['link2opacity'] = this.numParam('link2opacity', parseFloat);
+		this.link['nodesize'] = this.numParam('nodesize', parseFloat);
+		this.link['nodeopacity'] = this.numParam('nodeopacity', parseFloat);
+		this.link['color'] = this.numParam('color', (s) => guiObj.stringToHex(s));
+		this.link['background'] = this.numParam('background', (s) => guiObj.stringToHex(s));
+		this.link['dpsi'] = this.numParam('dpsi', parseFloat);
+		this.link['dtheta'] = this.numParam('dtheta', parseFloat);
+	}
+
+
+	copyUrl() {
+		const url = new URL(this.linkUrl.origin + this.linkUrl.pathname);
+		url.searchParams.append("shape", this.params.shape);
+		url.searchParams.append("option", this.params.option);
+		url.searchParams.append("inscribed", this.params.inscribed ? 'y': 'n');
+		url.searchParams.append("inscribe_all", this.params.inscribe_all ? 'y': 'n');
+		url.searchParams.append("linksize", this.params.linksize.toString());
+		url.searchParams.append("nodesize", this.params.nodesize.toString());
+		url.searchParams.append("nodeopacity", this.params.nodesize.toString());
+		url.searchParams.append("linkopacity", this.params.nodeopacity.toString());
+		url.searchParams.append("link2opacity", this.params.link2opacity.toString());
+		url.searchParams.append("color", this.hexToString(this.params.color));
+		url.searchParams.append("background", this.hexToString(this.params.background));
+		url.searchParams.append("hyperplane", this.params.hyperplane.toString());
+		url.searchParams.append("zoom", this.params.zoom.toString());
+		url.searchParams.append("xRotate", this.params.xRotate);
+		url.searchParams.append("yRotate", this.params.yRotate);
+		url.searchParams.append("dtheta", this.params.dtheta.toString());
+		url.searchParams.append("dpsi", this.params.dpsi.toString());
+		this.copyTextToClipboard(url);
+	}
+
+
+	copyTextToClipboard(text) {
+ 		if (!navigator.clipboard) {
+    		this.fallbackCopyTextToClipboard(text);
+    		return;
+  		}
+  		navigator.clipboard.writeText(text).then(function() {
+    		console.log('Async: Copying to clipboard was successful!');
+  		}, function(err) {
+    	console.error('Async: Could not copy text: ', err);
+  		});
+	}
+
+
+	fallbackCopyTextToClipboard(text) {
+		var textArea = document.createElement("textarea");
+		textArea.value = text;
+		  
+		// Avoid scrolling to bottom
+		textArea.style.top = "0";
+		textArea.style.left = "0";
+		textArea.style.position = "fixed";
+
+		document.body.appendChild(textArea);
+		textArea.focus();
+		textArea.select();
+
+		try {
+		    var successful = document.execCommand('copy');
+		    var msg = successful ? 'successful' : 'unsuccessful';
+		    console.log('Fallback: Copying text command was ' + msg);
+		} catch (err) {
+		    console.error('Fallback: Oops, unable to copy', err);
+		}
+
+		document.body.removeChild(textArea);
+	}
+
+
+}
+
+
+export { FourDGUI, DEFAULTS };

index.html

@@ -5,9 +5,28 @@
 		<title>FourD</title>
 		<style>
 			body { margin: 0; }
+			div#description {
+				position: fixed;
+				top: 0;
+				left: 0;
+				width: 20%;
+				z-index: 2;
+				font-family: sans-serif;
+				padding: 1em;
+			}
+			div#info {
+				position: fixed;
+				bottom:0;
+				right: 0;
+				z-index: 2;
+				border:0.5em;
+				font-family: sans-serif }
 		</style>
 	</head>
 	<body>
 		<script type="module" src="/main.js"></script>
+		<div id="description"></div>
+		<div id="info">by <a target="_blank" href="https://mikelynch.org/">Mike Lynch</a> -
+			<a target="_blank" href="https://git.tilde.town/bombinans/fourdjs">source</a></div>
 	</body>
 </html>

indexing_attempts/complicated_vectors.js

@@ -0,0 +1,294 @@
+// bad stuff
+
+function find_chords(chords, n) {
+	return chords.filter((c) => c[0].id === n.id || c[1].id === n.id);
+}
+
+function find_neighbours(chords, n) {
+	const c = find_chords(chords, n);
+	return c.map((c) => c[0].id === n.id ? c[1] : c[0])
+}
+
+
+
+// for a list of pairs [n1, n2] (these are nodes which share a common angle
+// from a center), find all the groups of nodes which don't appear in a pair
+// together
+
+function partition_nodes(pairs) {
+	let groups = [];
+	const seen = new Set();
+	for( const pair of pairs ) {
+		// both nodes are in a group already
+		if( seen.has(pair[0]) && seen.has(pair[1]) ) {
+			continue;
+		}
+		let already = false;
+		// check if either node is already in a group
+		for( const group of groups ) {
+			if( group.has(pair[0]) ) {
+				group.add(pair[1]);
+				seen.add(pair[1]);
+				already = true;
+				continue;
+			} else if( group.has(pair[1]) ) {
+				group.has(pair[0]);
+				seen.has(pair[0]);
+				already = true;
+				continue;
+			}
+		}
+		// if neither of the pair was in a former group, start a new group
+		if( !already ) {
+			groups.push(new Set(pair));
+		}
+		// collapse any groups which now have common elements
+		groups = collapse_groups(groups);
+	}
+	return groups;
+}
+
+// given a list of groups, if any have common elements, collapse them
+
+function collapse_groups(groups) {
+	const new_groups = [ ];
+	for( group of groups ) {
+		let collapsed = false;
+		for( new_group of new_groups ) {
+			const i = intersection(group, new_group);
+			if( i.size > 0 ) {
+				for( const e of group ) {
+					new_group.add(e);
+				}
+				collapsed = true;
+				break;
+			}
+		}
+		if( !collapsed ) {
+			new_groups.push(new Set(group));
+		}
+	}
+	return new_groups;
+}
+
+
+function intersection(s1, s2) {
+	const i = new Set();
+	for( const e of s1 ) {
+		if( s2.has(e) ) {
+			i.add(e)
+		}
+	}
+	return i;
+}
+
+function union(s1, s2) {
+	const u = new Set(s1);
+	for( const e of s2 ) {
+		u.add(e);
+	}
+	return u;
+}
+
+
+function vector_angle(n1, n2, n3) {
+	const v1 = new THREE.Vector4(n1.x, n1.y, n1.z, n1.w);
+	const v2 = new THREE.Vector4(n2.x, n2.y, n2.z, n2.w);
+	const v3 = new THREE.Vector4(n3.x, n3.y, n3.z, n3.w);
+	v2.sub(v1);
+	v3.sub(v1);
+	const dp = v2.dot(v3);
+	return Math.acos(dp / ( v2.length() * v3.length()));
+}
+
+function neighbour_angles_orig(chords, n) {
+	const ns = find_neighbours(chords, n);
+	const angles = {};
+	for( let i = 0; i < ns.length - 1; i++ ) {
+		for( let j = i + 1; j < ns.length; j++ ) {
+			const n2 = ns[i];
+			const n3 = ns[j];
+			const a = THREE.MathUtils.radToDeg(vector_angle(n, n2, n3));
+			const af = (a).toFixed(3);
+			if( ! (af in angles) ) {
+				angles[af] = [];
+			}
+			angles[af].push([n2.id, n3.id]);
+		}
+	}
+	return angles;
+}
+
+function neighbour_angles(chords, n, angle) {
+	const ns = find_neighbours(chords, n);
+	const pairs = [];
+	for( let i = 0; i < ns.length - 1; i++ ) {
+		for( let j = i + 1; j < ns.length; j++ ) {
+			const n2 = ns[i];
+			const n3 = ns[j];
+			const a = THREE.MathUtils.radToDeg(vector_angle(n, n2, n3));
+			const af = (a).toFixed(3);
+			if( af === angle ) {
+				pairs.push([n2.id, n3.id]);
+			}
+		}
+	}
+	return pairs;
+}
+
+
+function make_120_partition(nodes, n) {
+	const chords = find_all_chords(nodes);
+	const chord3 = chords["1.74806"];  // these are edges of the 600-cells;
+	const pairs60 = neighbour_angles(chord3, n, "60.000");
+	const icosas = partition_nodes(pairs60);
+
+	n.label = 1;
+	const angles = icosa_nodes(nodes, icosas[0]);
+	label_120_partition_r(nodes, chord3, 1, n, angles);
+}
+
+// recursive function to label a single 600-cell vertex partition of the 
+// 120-cell by following icosahedral nets
+// this doesn't work! completely - labels only 108-112
+
+function label_120_partition_r(nodes, chords, label, origin, neighbours) {
+	console.log(`label_120_partition_r ${origin.id}`);
+	console.log(neighbours.map((n) => n.id).join(', '));
+
+	// first try to label everything
+	const unlabelled = [];
+	for( const n of neighbours ) {
+		if( n.label === 0 ) {
+			console.log(`Labelled ${n.id} ${label}`);
+			n.label = label;
+			unlabelled.push(n);
+		} else if( n.label !== label ) {
+			console.log(`node ${n.id} is already in group ${n.label}`);
+			//return false;
+		}
+	}
+	for( const n of unlabelled ) { 
+		// the angles represent two icosahedral pyramids - partition them and
+		// pick the one which is at 60 to the edge we arrived on
+		//console.log(`looking for more neighbors for ${n}`);
+		const pairs60 = neighbour_angles(chords, n, "60.000");
+		const icosas = partition_nodes(pairs60);
+		const icosa = choose_icosa(nodes, origin, n, icosas);
+		const icosa_n = icosa_nodes(nodes, icosa);
+		console.log(`recursing to ${nice_icosa(nodes,icosa)}`);
+		return label_120_partition_r(nodes, chords, label, n, icosa_n);
+	}
+}
+
+// given a pair of icosa-sets, pick the one which is at the right angle to
+// the incoming vector
+
+function choose_icosa(nodes, origin, n1, icosas) {
+	for( const icosa of icosas ) {
+		const inodes = icosa_nodes(nodes, icosa);
+		const a60 = inodes.map((ni) => {
+			const a = THREE.MathUtils.radToDeg(vector_angle(n1, origin, ni));
+			return a.toFixed(3);
+		});
+		if( a60.filter((a) => a === "60.000").length > 0 ) {
+			return icosa;
+		}
+	}
+	console.log("No icosa found!");
+	return undefined;
+}
+
+function icosa_nodes(nodes, icosa) {
+	return Array.from(icosa).map((nid) => node_by_id(nodes, nid)).sort((a, b) => a.id - b.id);
+}
+
+function node_by_id(nodes, nid) {
+	const ns = nodes.filter((n) => n.id === nid);
+	return ns[0];
+}
+
+
+function enumerate_icosas(nodes) {
+	const chords = find_all_chords(nodes);
+	const chord3 = chords["1.74806"];  // these are edges of the 600-cells;
+
+	for( const n of nodes ) {
+		const pairs60 = neighbour_angles(chord3, n, "60.000");
+		const icosas = partition_nodes(pairs60);
+		for( const icosa of icosas ) {
+			const inodes = icosa_nodes(nodes, icosa);
+			console.log(icosa_to_csv(n.id, inodes).join(','));
+		}
+	}
+}
+
+
+function icosa_to_csv(nid, icosa) {
+	const cols = [ nid ];
+	const ia = icosa.map((n) => n.id);
+	for( let i = 1; i < 601; i++ ) {
+		if( ia.includes(i) ) {
+			cols.push(i);
+		} else {
+			cols.push('')
+		}
+	}
+	return cols;
+}
+
+
+function start_icosas(nodes, chords, origin) {
+	const pairs60 = neighbour_angles(chords, origin, "60.000");
+	return partition_nodes(pairs60).map((i) => nice_icosa(nodes, i));
+}
+
+
+
+function next_icosa(nodes, chords, origin, nid) {
+	const n = node_by_id(nodes, nid);
+	const pairs60 = neighbour_angles(chords, n, "60.000");
+	const icosas = partition_nodes(pairs60);
+	const icosa = choose_icosa(nodes, origin, n, icosas);
+
+	return nice_icosa(nodes, icosa);
+}
+
+function nice_icosa(nodes, icosa) {
+	return icosa_nodes(nodes, icosa).map((n) => n.id).join(', ');
+}
+
+
+function find_by_chord(nodesid, n, d) {
+	const EPSILON = 0.02;
+	return Object.keys(nodesid).filter((n1) => {
+		const d2 = dist2(nodesid[n1], nodesid[n]);
+		return Math.abs(d2 - d ** 2) < EPSILON;
+	});
+}
+
+
+function has_chord(n1, n2, d) {
+	const d2 = dist2(n1, n2);
+	const EPSILON = 0.01;
+	return Math.abs(d2 - d ** 2) < EPSILON;
+}
+
+
+function find_all_chords(nodes) {
+	const chords = {};
+	for( let i = 0; i < nodes.length - 1; i++ ) {
+		for( let j = i + 1; j < nodes.length; j++ ) {
+			const n1 = nodes[i];
+			const n2 = nodes[j];
+			const chord = Math.sqrt(dist2(n1, n2)).toFixed(5);
+			if( !(chord in chords) ) {
+				chords[chord] = [];
+			} 
+			chords[chord].push([n1, n2]);
+		}
+	}
+	return chords;
+}
+
+

indexing_attempts/graph_traversal.js

@@ -0,0 +1,78 @@
+// New approach with tetrahedral coloring
+
+function find_edges(links, nid) {
+	return links.filter((l) => l.source === nid || l.target === nid );
+}
+
+
+function find_adjacent(links, nid) {
+	return find_edges(links, nid).map((l) => {
+		if( l.source === nid ) {
+			return l.target;
+		} else {
+			return l.source;
+		}
+	});
+}
+
+function iterate_graph(nodes, links, n, fn) {
+	const queue = [];
+	const seen = {};
+	const nodes_id = {};
+	nodes.map((n) => nodes_id[n.id] = n);
+
+	queue.push(n.id);
+	seen[n.id] = true;
+	fn(n);
+
+	while( queue.length > 0 ) {
+		const v = queue.shift();
+		find_adjacent(links, v).map((aid) => {
+			if( !(aid in seen) ) {
+				seen[aid] = true;
+				queue.push(aid);
+				fn(nodes_id[aid]);
+			}
+		})
+	}
+}
+
+
+
+
+// stupid tetrahedral labelling
+// keeps getting stuck
+
+
+function naive_label_120cell(nodes, links, n) {
+	const nodes_id = {};
+	nodes.map((n) => nodes_id[n.id] = n);
+	iterate_graph(nodes, links, nodes[0], (n) => {
+		const cols = new Set();
+		const nbors = find_adjacent(links, n.id);
+		for( const nb of nbors ) {
+			if( nodes_id[nb].label > 0 ) {
+				cols.add(nodes_id[nb].label);
+			}
+			for( const nb2 of find_adjacent(links, nb) ) {
+				if( nb2 !== n.id && nodes_id[nb].label > 0 ) {
+					cols.add(nodes_id[nb2].label);
+				}
+			}
+		}
+		const pcols = [ 1, 2, 3, 4, 5 ].filter((c) => !cols.has(c));
+		if( pcols.length < 1 ) {
+			console.log(`Got stuck, no options at ${n.id}`);
+			return false;
+		} else {
+			n.label = pcols[0];
+			console.log(`found ${pcols.length} colors for node ${n.id}`);
+			console.log(`applied ${pcols[0]} to node ${n.id}`);
+			return true;
+		}
+	});
+}
+
+
+
+

layer600cell.js

@@ -0,0 +1,173 @@
+
+
+import * as POLYTOPES from './polytopes.js';
+
+// face detection for the 600-cell
+
+
+export function nodes_links(links, nodeid) {
+	return links.filter((l) => l.source === nodeid || l.target === nodeid);
+}
+
+
+export function linked(links, n1, n2) {
+	const ls = nodes_links(nodes_links(links, n1), n2);
+	if( ls.length ) {
+		return ls[0]
+	} else {
+		return false;
+	}
+}
+
+
+function fingerprint(ids) {
+	const sids = [...ids];
+	sids.sort();
+	return sids.join(',');
+}
+
+
+export function make_600cell() {
+	const nodes = POLYTOPES.make_600cell_vertices();
+	const links = POLYTOPES.auto_detect_edges(nodes, 12);
+	return {
+		nodes: nodes,
+		links: links
+	}
+}
+
+export function link_to_tetras(nodes, links, link) {
+	const n1 = link.source;
+	const n2 = link.target;
+	const nl1 = nodes_links(links, n1).filter((l) => l.id !== link.id);
+	const nl2 = nodes_links(links, n2).filter((l) => l.id !== link.id);
+	const p1 = new Set();
+	const p = new Set();
+	for( const nl of nl1 ) {
+		if( nl.source !== n1 ) {
+			p1.add(nl.source);
+		}
+		if( nl.target !== n1 ) {
+			p1.add(nl.target);
+		}
+	}
+	for( const nl of nl2 ) {
+		if( nl.source !== n2 && p1.has(nl.source) ) {
+			p.add(nl.source);
+		}
+		if( nl.target !== n2 && p1.has(nl.target) ) {
+			p.add(nl.target);
+		}
+	}
+	const lp = Array.from(p);
+	const seen = {};
+	const tetras = [];
+	for( const p1 of lp ) {
+		for( const p2 of lp ) {
+			if( p1 != p2 ) {
+				if( linked(links, p1, p2) ) {
+					const fp = fingerprint([n1, n2, p1, p2]);
+					if( !seen[fp] ) {
+						seen[fp] = true;
+						tetras.push({fingerprint: fp, nodes: [n1, n2, p1, p2]})
+					}
+				}
+			}
+		}
+	}
+	return tetras;
+}
+
+
+export function auto_600cell_cells(nodes, links) {
+	const seen = {};
+	const tetras = [];
+	links.map((link) => {
+		link_to_tetras(nodes, links, link).map((lt) => {
+			if( !seen[lt.fingerprint] ) {
+				seen[lt.fingerprint] = true;
+				tetras.push(lt.nodes);
+			}
+		})
+	});
+
+	return tetras;
+}
+
+
+function node_by_id(nodes, nid) {
+	const ns = nodes.filter((n) => n.id === nid);
+	return ns[0];
+}
+
+
+export function tetra_w(nodes, tetra) {
+	let w = 0;
+	for( const nid of tetra ) {
+		const node = node_by_id(nodes, nid);
+		w += node.w;
+	}
+	return w / 4;
+}
+
+export function sorted_600cells() {
+	const cell600 = make_600cell();
+	const tetras = auto_600cell_cells(cell600.nodes, cell600.links);
+	const layers = tetras.map((t) => { return { "nodes": t, w: tetra_w(cell600.nodes, t) } });
+	layers.sort((a, b) => b.w - a.w);
+	return layers;
+}
+
+// const cell600 = make_600cell();
+
+// const layers = sorted_600cells(cell600.nodes, cell600.links);
+// for( const cell of layers ) {
+// //	const fp = fingerprint(cell.nodes);
+// 	console.log(`${cell.w} ${cell.nodes}`);
+// }
+
+export function make_layered_600cell() {
+	const tetras = sorted_600cells()
+
+	const LAYERS = [
+		[ "00", 20 ],
+		[ "01", 20 ], 
+		[ "02", 30 ], 
+		[ "03", 60 ], 
+		[ "04", 60 ], 
+		[ "05", 60 ], 
+		[ "06", 20 ],
+		[ "07", 60 ], 
+		[ "08", 20 ],
+		[ "09", 60 ], 
+		[ "10", 60 ], 
+		[ "11", 60 ], 
+		[ "12", 30 ], 
+		[ "13", 20 ], 
+		[ "14", 20 ]
+	];
+
+	const vertices = {};
+	const seen = {};
+	let i = 0;
+
+	for( const layer of LAYERS ) {
+		const label = layer[0];
+		const n = layer[1];
+		vertices[label] = [];
+		console.log(`Layer ${label} starting at ${i}`);
+		for( const t of tetras.slice(i, i + n) ) {
+			console.log(t);
+			for( const n of t.nodes ) {
+				if( !seen[n] ) {
+					vertices[label].push(n);
+					seen[n] = true;
+				}
+			}
+		}
+		i += n;
+	}
+	return JSON.stringify(vertices);
+}
+
+

main.js

@@ -1,238 +1,252 @@
 import * as THREE from 'three';
 
+
+
 import * as POLYTOPES from './polytopes.js';
-
+import { rotfn } from './rotation.js';
+import { FourDGUI, DEFAULTS } from './gui.js';
 import { FourDShape } from './fourDShape.js';
+import { get_colours } from './colours.js';
 
-import { GUI } from 'lil-gui';
+const FACE_OPACITY = 0.3;
-
+const CAMERA_K = 5;
-
-const DEFAULT_SHAPE = '5-cell';
-
-// hacky stuff for 4d rotations
-
-// see https://math.stackexchange.com/questions/1402362/can-rotations-in-4d-be-given-an-explicit-matrix-form#1402376
-
-
-
-function rotZW(theta) {
-	const ctheta = Math.cos(theta);
-	const stheta = Math.sin(theta);
-	return new THREE.Matrix4(
-		ctheta, -stheta, 0, 0,
-		stheta, ctheta, 0, 0,
-		0, 0, 1, 0,
-		0, 0, 0, 1
-		);
-}
-
-function rotYW(theta) {
-	const ctheta = Math.cos(theta);
-	const stheta = Math.sin(theta);
-	return new THREE.Matrix4(
-		ctheta, 0, -stheta, 0,
-		0, 1, 0, 0,
-		stheta, 0, ctheta, 0,
-		0, 0, 0, 1,
-		);
-}
-
-function rotYZ(theta) {
-	const ctheta = Math.cos(theta);
-	const stheta = Math.sin(theta);
-	return new THREE.Matrix4(
-		ctheta, 0, 0, -stheta,
-		0, 1, 0, 0,
-		0, 0, 1, 0,
-		stheta, 0, 0, ctheta, 
-		);
-}
-
-function rotXW(theta) {
-	const ctheta = Math.cos(theta);
-	const stheta = Math.sin(theta);
-	return new THREE.Matrix4(
-		1, 0, 0, 0,
-		0, ctheta, -stheta, 0,
-		0, stheta, ctheta, 0,
-		0, 0, 0, 1
-		);
-}
-
-function rotXZ(theta) {
-	const ctheta = Math.cos(theta);
-	const stheta = Math.sin(theta);
-	return new THREE.Matrix4(
-		1, 0, 0, 0,
-		0, ctheta, 0, -stheta,
-		0, 0, 1, 0,
-		0, stheta, 0, ctheta,
-		);
-}
-
-function rotXY(theta) {
-	const ctheta = Math.cos(theta);
-	const stheta = Math.sin(theta);
-	return new THREE.Matrix4(
-		1, 0, 0, 0,
-		0, 1, 0, 0,
-		0, 0, ctheta, -stheta,
-		0, 0, stheta, ctheta,
-		);
-}
-
-
-
-
-
 
+// scene, lights and camera
 
 const scene = new THREE.Scene();
 const camera = new THREE.PerspectiveCamera( 75, window.innerWidth / window.innerHeight, 0.1, 1000 );
-
 const light = new THREE.PointLight(0xffffff, 2);
 light.position.set(10, 10, 10);
 scene.add(light);
-
+const light2 = new THREE.PointLight(0xffffff, 2);
-
+light2.position.set(-10, 5, 10);
+scene.add(light);
 const amblight = new THREE.AmbientLight(0xffffff, 0.5);
 scene.add(amblight);
 
-scene.background = new THREE.Color(0xdddddd);
+camera.position.set(0, 0, CAMERA_K / 2);
 
+camera.lookAt(0, 0, 0);
+//camera.position.z = 4;
 
 const renderer = new THREE.WebGLRenderer({antialias: true});
 renderer.setSize( window.innerWidth, window.innerHeight );
 document.body.appendChild( renderer.domElement );
 
+// set up colours and materials for gui callbacks
 
-const NODE_OPACITY = 1.0;
+scene.background = new THREE.Color(DEFAULTS.background);
-const LINK_OPACITY = 1.0;
+const material = new THREE.MeshStandardMaterial({ color: DEFAULTS.color });
+const node_colours = get_colours(DEFAULTS.color);
 
-const node_ms = [
-	new THREE.MeshStandardMaterial( { color: 0x90ebff } )
-];
 
-for( const node_m of node_ms ) {
+material.transparent = true;
-	node_m.roughness = 0.9;
+material.opacity = 0.5;
 
-	if( NODE_OPACITY < 1.0 ) {
+
-		node_m.transparent = true;	
+const node_ms = node_colours.map((c) => new THREE.MeshStandardMaterial({color: c}));
-		node_m.opacity = NODE_OPACITY;
+const link_ms = node_colours.map((c) => new THREE.MeshStandardMaterial({color: c}));
+
+node_ms.map((m) => {
+	m.transparent =  true;
+	m.opacity = 1.0;
 	}
-}
+);
 
-const link_ms = [
+link_ms.map((m) => {
-	new THREE.MeshStandardMaterial( { color: 0x90ebff } )
+	m.transparent =  true;
+	m.opacity = 0.5;
+	}
+);
+
+
+
+const face_ms = [
+	new THREE.MeshLambertMaterial( { color: 0x44ff44 } )
 	];
 
-for( const link_m of link_ms ) {
+for( const face_m of face_ms ) {
-	link_m.metalness = 0.8;
+	face_m.transparent = true;	
-	link_m.roughness = 0.1;
+	face_m.opacity = FACE_OPACITY;
-
-	if( LINK_OPACITY < 1.0 ) {
-		link_m.transparent = true;	
-		link_m.opacity = LINK_OPACITY;
-	}
 }
 
-const STRUCTURES = {
-	'5-cell': POLYTOPES.cell5(),
-	'16-cell': POLYTOPES.cell16(),
-	'tesseract': POLYTOPES.tesseract(),
-	'24-cell': POLYTOPES.cell24(),
-	'120-cell': POLYTOPES.cell120(),
-	'600-cell': POLYTOPES.cell600()
-};
 
+const STRUCTURES = POLYTOPES.build_all();
+
+const STRUCTURES_BY_NAME = {};
+
+STRUCTURES.map((s) => STRUCTURES_BY_NAME[s.name] = s);
 
 let shape = false;
+let structure = false;
+let node_show = [];
+let link_show = []; 
 
-function createShape(name) {
+
+function createShape(name, option) {
 	if( shape ) {
 		scene.remove(shape);
 	}
-	shape = new FourDShape(node_ms, link_ms, STRUCTURES[name]);
+	structure = STRUCTURES_BY_NAME[name];
+	shape = new FourDShape(node_ms, link_ms, face_ms, structure);
 	scene.add(shape);
+	setVisibility(option ? option : structure.options[0].name);
+}
 
+function displayDocs(name) {
+	const docdiv = document.getElementById("description");
+	const description = STRUCTURES_BY_NAME[name].description;
+	if( description ) {
+		docdiv.innerHTML =`<p>${name}</p><p>${description}</p>`;
+	} else {
+		docdiv.innerHTML =`<p>${name}</p>`;
+	}
+}
+
+function showDocs(visible) {
+	console.log(`showDocs ${visible}`);
+	const docdiv = document.getElementById("description");
+	if( visible ) {
+		docdiv.style.display = '';
+	} else {
+		docdiv.style.display = 'none';
+	}
+}
+
+// initialise gui and read params from URL
+
+// callbacks to do things which are triggered by controls: reset the shape,
+// change the colors.  Otherwise we just read stuff from gui.params.
+
+function setColors(c) {
+	const nc = get_colours(c);
+	for( let i = 0; i < node_ms.length; i++ ) {
+		node_ms[i].color = new THREE.Color(nc[i]);
+		link_ms[i].color = new THREE.Color(nc[i]);
+	}
+	material.color = new THREE.Color(c);
+}
+
+function setBackground(c) {
+	scene.background = new THREE.Color(c)
+}
+
+function setLinkOpacity(o, primary) {
+	if( structure.nolink2opacity ) {
+		link_ms.map((lm) => lm.opacity = o);
+	} else {
+		if( primary ) {
+			link_ms[0].opacity = o;
+		} else {
+			link_ms.slice(1).map((lm) => lm.opacity = o);
+		}
+	}
+}
+
+function setNodeOpacity(o) {
+	node_ms.map((nm) => nm.opacity = o);
 }
 
 
+let gui; 
 
 
-createShape(DEFAULT_SHAPE);
+function changeShape() {
+	createShape(gui.params.shape);
+	displayDocs(gui.params.shape);
+}
+
+function setVisibility(option_name) {
+	const option = structure.options.filter((o) => o.name === option_name);
+	if( option.length ) {
+		node_show = option[0].nodes;
+		link_show = option[0].links;
+	} else {
+		console.log(`Error: option '${option_name}' not found`);
+	}
+}
 
 
-camera.position.z = 4;
+gui = new FourDGUI(
+	STRUCTURES,
+	changeShape,
+	setColors,
+	setBackground,
+	setNodeOpacity,
+	setLinkOpacity,
+	setVisibility,
+	showDocs
+);
+
+// these are here to pick up colour settings from the URL params
+setColors(gui.params.color);
+setBackground(gui.params.background);
 
 const dragK = 0.005;
+const damping = 0.99;
 
 let theta = 0;
 let psi = 0;
-let startX = 0;
+let theta0 = 0;
-let startY = 0;
+let psi0 = 0;
-let startX0 = 0;
+let dragx0 = 0;
-let startY0 = 0;
+let dragy0 = 0;
+let dragging = false;
 
-renderer.domElement.addEventListener("mousedown", (event) => {
+
+renderer.domElement.addEventListener("pointerdown", (event) => {
 	if( event.buttons === 1 ) {
-		startX = event.clientX;
+		theta0 = theta;
-		startY = event.clientY;
+		psi0 = psi;
-		startX0 = theta / dragK;
+		dragx0 = event.clientX;
-		startY0 = theta / dragK;
+		dragy0 = event.clientY;
+		dragging = true;
 	}
 })
 
-
+renderer.domElement.addEventListener("pointermove", (event) => {
-renderer.domElement.addEventListener("mousemove", (event) => {
 	if( event.buttons === 1 ) {
-		theta = (event.clientX - startX + startX0) * dragK;
+		const theta1 = theta0 + (event.clientX - dragx0) * dragK;
-		psi = (event.clientY - startY + startY0) * dragK;
+		const psi1 = psi0 + (event.clientY - dragy0) * dragK;
+		gui.params.dtheta = theta1 - theta;
+		gui.params.dpsi = psi1 - psi;
+		theta = theta1;
+		psi = psi1;
 	}
 })
 
-// set up GUI
+renderer.domElement.addEventListener("pointerup", (event) => {
+	dragging = false;
+})
 
-const gui = new GUI();
+createShape(gui.params.shape, gui.params.option);
-
+displayDocs(gui.params.shape);
-const gui_params = {
-	shape: DEFAULT_SHAPE,
-	hyperplane: 2,
-	xRotate: 'YW',
-	yRotate: 'XZ',
-};
-
-gui.add(gui_params, 'shape',
-	[ '5-cell', '16-cell', 'tesseract', '24-cell', '120-cell', '600-cell' ]
-	).onChange(createShape)
-
-gui.add(gui_params, 'hyperplane', 1.5, 4);
-gui.add(gui_params, 'xRotate', [ 'YW', 'YZ', 'ZW' ]);
-gui.add(gui_params, 'yRotate', [ 'XZ', 'XY', 'XW' ]);
-
-const ROTFN = {
-	XY: rotXY,
-	XZ: rotXZ,
-	XW: rotXW,
-	YZ: rotYZ,
-	YW: rotYW,
-	ZW: rotZW,
-};
-
-
-
-const rotation = new THREE.Matrix4();
 
 function animate() {
 	requestAnimationFrame( animate );
 
+	if( ! dragging ) {
+		theta += gui.params.dtheta;
+		psi += gui.params.dpsi;
+		if( gui.params.damping ) {
+			gui.params.dtheta = gui.params.dtheta * damping;
+			gui.params.dpsi = gui.params.dpsi * damping;
+		}
+	}
+
 	const rotations = [
-		ROTFN[gui_params.xRotate](theta), 
+		rotfn[gui.params.xRotate](theta), 
-		ROTFN[gui_params.yRotate](psi)
+		rotfn[gui.params.yRotate](psi)
 	];
-	shape.hyperplane = gui_params.hyperplane;
+	shape.hyperplane = 1 / gui.params.hyperplane;
-	shape.render3(rotations);
+	camera.position.set(0, 0, gui.params.zoom * CAMERA_K * gui.params.hyperplane);
+
+	shape.node_scale = gui.params.nodesize;
+	shape.link_scale = gui.params.linksize * gui.params.nodesize * 0.5;
+	shape.render3(rotations, node_show, link_show);
+
+
 
 	renderer.render( scene, camera );
 }
-animate();
+animate();

package-lock.json

@@ -4,8 +4,11 @@
   "requires": true,
   "packages": {
     "": {
+      "name": "fourdjs",
       "dependencies": {
-        "lil-gui": "^0.18.2",
+        "color": "^4.2.3",
+        "color-scheme": "^1.0.1",
+        "lil-gui": "^0.19.0",
         "three": "^0.154.0"
       },
       "devDependencies": {
@@ -13,9 +16,9 @@
       }
     },
     "node_modules/@esbuild/android-arm": {
-      "version": "0.18.15",
+      "version": "0.18.20",
-      "resolved": "https://registry.npmjs.org/@esbuild/android-arm/-/android-arm-0.18.15.tgz",
+      "resolved": "https://registry.npmjs.org/@esbuild/android-arm/-/android-arm-0.18.20.tgz",
-      "integrity": "sha512-wlkQBWb79/jeEEoRmrxt/yhn5T1lU236OCNpnfRzaCJHZ/5gf82uYx1qmADTBWE0AR/v7FiozE1auk2riyQd3w==",
+      "integrity": "sha512-fyi7TDI/ijKKNZTUJAQqiG5T7YjJXgnzkURqmGj13C6dCqckZBLdl4h7bkhHt/t0WP+zO9/zwroDvANaOqO5Sw==",
       "cpu": [
         "arm"
       ],
@@ -29,9 +32,9 @@
       }
     },
     "node_modules/@esbuild/android-arm64": {
-      "version": "0.18.15",
+      "version": "0.18.20",
-      "resolved": "https://registry.npmjs.org/@esbuild/android-arm64/-/android-arm64-0.18.15.tgz",
+      "resolved": "https://registry.npmjs.org/@esbuild/android-arm64/-/android-arm64-0.18.20.tgz",
-      "integrity": "sha512-NI/gnWcMl2kXt1HJKOn2H69SYn4YNheKo6NZt1hyfKWdMbaGadxjZIkcj4Gjk/WPxnbFXs9/3HjGHaknCqjrww==",
+      "integrity": "sha512-Nz4rJcchGDtENV0eMKUNa6L12zz2zBDXuhj/Vjh18zGqB44Bi7MBMSXjgunJgjRhCmKOjnPuZp4Mb6OKqtMHLQ==",
       "cpu": [
         "arm64"
       ],
@@ -45,9 +48,9 @@
       }
     },
     "node_modules/@esbuild/android-x64": {
-      "version": "0.18.15",
+      "version": "0.18.20",
-      "resolved": "https://registry.npmjs.org/@esbuild/android-x64/-/android-x64-0.18.15.tgz",
+      "resolved": "https://registry.npmjs.org/@esbuild/android-x64/-/android-x64-0.18.20.tgz",
-      "integrity": "sha512-FM9NQamSaEm/IZIhegF76aiLnng1kEsZl2eve/emxDeReVfRuRNmvT28l6hoFD9TsCxpK+i4v8LPpEj74T7yjA==",
+      "integrity": "sha512-8GDdlePJA8D6zlZYJV/jnrRAi6rOiNaCC/JclcXpB+KIuvfBN4owLtgzY2bsxnx666XjJx2kDPUmnTtR8qKQUg==",
       "cpu": [
         "x64"
       ],
@@ -61,9 +64,9 @@
       }
     },
     "node_modules/@esbuild/darwin-arm64": {
-      "version": "0.18.15",
+      "version": "0.18.20",
-      "resolved": "https://registry.npmjs.org/@esbuild/darwin-arm64/-/darwin-arm64-0.18.15.tgz",
+      "resolved": "https://registry.npmjs.org/@esbuild/darwin-arm64/-/darwin-arm64-0.18.20.tgz",
-      "integrity": "sha512-XmrFwEOYauKte9QjS6hz60FpOCnw4zaPAb7XV7O4lx1r39XjJhTN7ZpXqJh4sN6q60zbP6QwAVVA8N/wUyBH/w==",
+      "integrity": "sha512-bxRHW5kHU38zS2lPTPOyuyTm+S+eobPUnTNkdJEfAddYgEcll4xkT8DB9d2008DtTbl7uJag2HuE5NZAZgnNEA==",
       "cpu": [
         "arm64"
       ],
@@ -77,9 +80,9 @@
       }
     },
     "node_modules/@esbuild/darwin-x64": {
-      "version": "0.18.15",
+      "version": "0.18.20",
-      "resolved": "https://registry.npmjs.org/@esbuild/darwin-x64/-/darwin-x64-0.18.15.tgz",
+      "resolved": "https://registry.npmjs.org/@esbuild/darwin-x64/-/darwin-x64-0.18.20.tgz",
-      "integrity": "sha512-bMqBmpw1e//7Fh5GLetSZaeo9zSC4/CMtrVFdj+bqKPGJuKyfNJ5Nf2m3LknKZTS+Q4oyPiON+v3eaJ59sLB5A==",
+      "integrity": "sha512-pc5gxlMDxzm513qPGbCbDukOdsGtKhfxD1zJKXjCCcU7ju50O7MeAZ8c4krSJcOIJGFR+qx21yMMVYwiQvyTyQ==",
       "cpu": [
         "x64"
       ],
@@ -93,9 +96,9 @@
       }
     },
     "node_modules/@esbuild/freebsd-arm64": {
-      "version": "0.18.15",
+      "version": "0.18.20",
-      "resolved": "https://registry.npmjs.org/@esbuild/freebsd-arm64/-/freebsd-arm64-0.18.15.tgz",
+      "resolved": "https://registry.npmjs.org/@esbuild/freebsd-arm64/-/freebsd-arm64-0.18.20.tgz",
-      "integrity": "sha512-LoTK5N3bOmNI9zVLCeTgnk5Rk0WdUTrr9dyDAQGVMrNTh9EAPuNwSTCgaKOKiDpverOa0htPcO9NwslSE5xuLA==",
+      "integrity": "sha512-yqDQHy4QHevpMAaxhhIwYPMv1NECwOvIpGCZkECn8w2WFHXjEwrBn3CeNIYsibZ/iZEUemj++M26W3cNR5h+Tw==",
       "cpu": [
         "arm64"
       ],
@@ -109,9 +112,9 @@
       }
     },
     "node_modules/@esbuild/freebsd-x64": {
-      "version": "0.18.15",
+      "version": "0.18.20",
-      "resolved": "https://registry.npmjs.org/@esbuild/freebsd-x64/-/freebsd-x64-0.18.15.tgz",
+      "resolved": "https://registry.npmjs.org/@esbuild/freebsd-x64/-/freebsd-x64-0.18.20.tgz",
-      "integrity": "sha512-62jX5n30VzgrjAjOk5orYeHFq6sqjvsIj1QesXvn5OZtdt5Gdj0vUNJy9NIpjfdNdqr76jjtzBJKf+h2uzYuTQ==",
+      "integrity": "sha512-tgWRPPuQsd3RmBZwarGVHZQvtzfEBOreNuxEMKFcd5DaDn2PbBxfwLcj4+aenoh7ctXcbXmOQIn8HI6mCSw5MQ==",
       "cpu": [
         "x64"
       ],
@@ -125,9 +128,9 @@
       }
     },
     "node_modules/@esbuild/linux-arm": {
-      "version": "0.18.15",
+      "version": "0.18.20",
-      "resolved": "https://registry.npmjs.org/@esbuild/linux-arm/-/linux-arm-0.18.15.tgz",
+      "resolved": "https://registry.npmjs.org/@esbuild/linux-arm/-/linux-arm-0.18.20.tgz",
-      "integrity": "sha512-dT4URUv6ir45ZkBqhwZwyFV6cH61k8MttIwhThp2BGiVtagYvCToF+Bggyx2VI57RG4Fbt21f9TmXaYx0DeUJg==",
+      "integrity": "sha512-/5bHkMWnq1EgKr1V+Ybz3s1hWXok7mDFUMQ4cG10AfW3wL02PSZi5kFpYKrptDsgb2WAJIvRcDm+qIvXf/apvg==",
       "cpu": [
         "arm"
       ],
@@ -141,9 +144,9 @@
       }
     },
     "node_modules/@esbuild/linux-arm64": {
-      "version": "0.18.15",
+      "version": "0.18.20",
-      "resolved": "https://registry.npmjs.org/@esbuild/linux-arm64/-/linux-arm64-0.18.15.tgz",
+      "resolved": "https://registry.npmjs.org/@esbuild/linux-arm64/-/linux-arm64-0.18.20.tgz",
-      "integrity": "sha512-BWncQeuWDgYv0jTNzJjaNgleduV4tMbQjmk/zpPh/lUdMcNEAxy+jvneDJ6RJkrqloG7tB9S9rCrtfk/kuplsQ==",
+      "integrity": "sha512-2YbscF+UL7SQAVIpnWvYwM+3LskyDmPhe31pE7/aoTMFKKzIc9lLbyGUpmmb8a8AixOL61sQ/mFh3jEjHYFvdA==",
       "cpu": [
         "arm64"
       ],
@@ -157,9 +160,9 @@
       }
     },
     "node_modules/@esbuild/linux-ia32": {
-      "version": "0.18.15",
+      "version": "0.18.20",
-      "resolved": "https://registry.npmjs.org/@esbuild/linux-ia32/-/linux-ia32-0.18.15.tgz",
+      "resolved": "https://registry.npmjs.org/@esbuild/linux-ia32/-/linux-ia32-0.18.20.tgz",
-      "integrity": "sha512-JPXORvgHRHITqfms1dWT/GbEY89u848dC08o0yK3fNskhp0t2TuNUnsrrSgOdH28ceb1hJuwyr8R/1RnyPwocw==",
+      "integrity": "sha512-P4etWwq6IsReT0E1KHU40bOnzMHoH73aXp96Fs8TIT6z9Hu8G6+0SHSw9i2isWrD2nbx2qo5yUqACgdfVGx7TA==",
       "cpu": [
         "ia32"
       ],
@@ -173,9 +176,9 @@
       }
     },
     "node_modules/@esbuild/linux-loong64": {
-      "version": "0.18.15",
+      "version": "0.18.20",
-      "resolved": "https://registry.npmjs.org/@esbuild/linux-loong64/-/linux-loong64-0.18.15.tgz",
+      "resolved": "https://registry.npmjs.org/@esbuild/linux-loong64/-/linux-loong64-0.18.20.tgz",
-      "integrity": "sha512-kArPI0DopjJCEplsVj/H+2Qgzz7vdFSacHNsgoAKpPS6W/Ndh8Oe24HRDQ5QCu4jHgN6XOtfFfLpRx3TXv/mEg==",
+      "integrity": "sha512-nXW8nqBTrOpDLPgPY9uV+/1DjxoQ7DoB2N8eocyq8I9XuqJ7BiAMDMf9n1xZM9TgW0J8zrquIb/A7s3BJv7rjg==",
       "cpu": [
         "loong64"
       ],
@@ -189,9 +192,9 @@
       }
     },
     "node_modules/@esbuild/linux-mips64el": {
-      "version": "0.18.15",
+      "version": "0.18.20",
-      "resolved": "https://registry.npmjs.org/@esbuild/linux-mips64el/-/linux-mips64el-0.18.15.tgz",
+      "resolved": "https://registry.npmjs.org/@esbuild/linux-mips64el/-/linux-mips64el-0.18.20.tgz",
-      "integrity": "sha512-b/tmngUfO02E00c1XnNTw/0DmloKjb6XQeqxaYuzGwHe0fHVgx5/D6CWi+XH1DvkszjBUkK9BX7n1ARTOst59w==",
+      "integrity": "sha512-d5NeaXZcHp8PzYy5VnXV3VSd2D328Zb+9dEq5HE6bw6+N86JVPExrA6O68OPwobntbNJ0pzCpUFZTo3w0GyetQ==",
       "cpu": [
         "mips64el"
       ],
@@ -205,9 +208,9 @@
       }
     },
     "node_modules/@esbuild/linux-ppc64": {
-      "version": "0.18.15",
+      "version": "0.18.20",
-      "resolved": "https://registry.npmjs.org/@esbuild/linux-ppc64/-/linux-ppc64-0.18.15.tgz",
+      "resolved": "https://registry.npmjs.org/@esbuild/linux-ppc64/-/linux-ppc64-0.18.20.tgz",
-      "integrity": "sha512-KXPY69MWw79QJkyvUYb2ex/OgnN/8N/Aw5UDPlgoRtoEfcBqfeLodPr42UojV3NdkoO4u10NXQdamWm1YEzSKw==",
+      "integrity": "sha512-WHPyeScRNcmANnLQkq6AfyXRFr5D6N2sKgkFo2FqguP44Nw2eyDlbTdZwd9GYk98DZG9QItIiTlFLHJHjxP3FA==",
       "cpu": [
         "ppc64"
       ],
@@ -221,9 +224,9 @@
       }
     },
     "node_modules/@esbuild/linux-riscv64": {
-      "version": "0.18.15",
+      "version": "0.18.20",
-      "resolved": "https://registry.npmjs.org/@esbuild/linux-riscv64/-/linux-riscv64-0.18.15.tgz",
+      "resolved": "https://registry.npmjs.org/@esbuild/linux-riscv64/-/linux-riscv64-0.18.20.tgz",
-      "integrity": "sha512-komK3NEAeeGRnvFEjX1SfVg6EmkfIi5aKzevdvJqMydYr9N+pRQK0PGJXk+bhoPZwOUgLO4l99FZmLGk/L1jWg==",
+      "integrity": "sha512-WSxo6h5ecI5XH34KC7w5veNnKkju3zBRLEQNY7mv5mtBmrP/MjNBCAlsM2u5hDBlS3NGcTQpoBvRzqBcRtpq1A==",
       "cpu": [
         "riscv64"
       ],
@@ -237,9 +240,9 @@
       }
     },
     "node_modules/@esbuild/linux-s390x": {
-      "version": "0.18.15",
+      "version": "0.18.20",
-      "resolved": "https://registry.npmjs.org/@esbuild/linux-s390x/-/linux-s390x-0.18.15.tgz",
+      "resolved": "https://registry.npmjs.org/@esbuild/linux-s390x/-/linux-s390x-0.18.20.tgz",
-      "integrity": "sha512-632T5Ts6gQ2WiMLWRRyeflPAm44u2E/s/TJvn+BP6M5mnHSk93cieaypj3VSMYO2ePTCRqAFXtuYi1yv8uZJNA==",
+      "integrity": "sha512-+8231GMs3mAEth6Ja1iK0a1sQ3ohfcpzpRLH8uuc5/KVDFneH6jtAJLFGafpzpMRO6DzJ6AvXKze9LfFMrIHVQ==",
       "cpu": [
         "s390x"
       ],
@@ -253,9 +256,9 @@
       }
     },
     "node_modules/@esbuild/linux-x64": {
-      "version": "0.18.15",
+      "version": "0.18.20",
-      "resolved": "https://registry.npmjs.org/@esbuild/linux-x64/-/linux-x64-0.18.15.tgz",
+      "resolved": "https://registry.npmjs.org/@esbuild/linux-x64/-/linux-x64-0.18.20.tgz",
-      "integrity": "sha512-MsHtX0NgvRHsoOtYkuxyk4Vkmvk3PLRWfA4okK7c+6dT0Fu4SUqXAr9y4Q3d8vUf1VWWb6YutpL4XNe400iQ1g==",
+      "integrity": "sha512-UYqiqemphJcNsFEskc73jQ7B9jgwjWrSayxawS6UVFZGWrAAtkzjxSqnoclCXxWtfwLdzU+vTpcNYhpn43uP1w==",
       "cpu": [
         "x64"
       ],
@@ -269,9 +272,9 @@
       }
     },
     "node_modules/@esbuild/netbsd-x64": {
-      "version": "0.18.15",
+      "version": "0.18.20",
-      "resolved": "https://registry.npmjs.org/@esbuild/netbsd-x64/-/netbsd-x64-0.18.15.tgz",
+      "resolved": "https://registry.npmjs.org/@esbuild/netbsd-x64/-/netbsd-x64-0.18.20.tgz",
-      "integrity": "sha512-djST6s+jQiwxMIVQ5rlt24JFIAr4uwUnzceuFL7BQT4CbrRtqBPueS4GjXSiIpmwVri1Icj/9pFRJ7/aScvT+A==",
+      "integrity": "sha512-iO1c++VP6xUBUmltHZoMtCUdPlnPGdBom6IrO4gyKPFFVBKioIImVooR5I83nTew5UOYrk3gIJhbZh8X44y06A==",
       "cpu": [
         "x64"
       ],
@@ -285,9 +288,9 @@
       }
     },
     "node_modules/@esbuild/openbsd-x64": {
-      "version": "0.18.15",
+      "version": "0.18.20",
-      "resolved": "https://registry.npmjs.org/@esbuild/openbsd-x64/-/openbsd-x64-0.18.15.tgz",
+      "resolved": "https://registry.npmjs.org/@esbuild/openbsd-x64/-/openbsd-x64-0.18.20.tgz",
-      "integrity": "sha512-naeRhUIvhsgeounjkF5mvrNAVMGAm6EJWiabskeE5yOeBbLp7T89tAEw0j5Jm/CZAwyLe3c67zyCWH6fsBLCpw==",
+      "integrity": "sha512-e5e4YSsuQfX4cxcygw/UCPIEP6wbIL+se3sxPdCiMbFLBWu0eiZOJ7WoD+ptCLrmjZBK1Wk7I6D/I3NglUGOxg==",
       "cpu": [
         "x64"
       ],
@@ -301,9 +304,9 @@
       }
     },
     "node_modules/@esbuild/sunos-x64": {
-      "version": "0.18.15",
+      "version": "0.18.20",
-      "resolved": "https://registry.npmjs.org/@esbuild/sunos-x64/-/sunos-x64-0.18.15.tgz",
+      "resolved": "https://registry.npmjs.org/@esbuild/sunos-x64/-/sunos-x64-0.18.20.tgz",
-      "integrity": "sha512-qkT2+WxyKbNIKV1AEhI8QiSIgTHMcRctzSaa/I3kVgMS5dl3fOeoqkb7pW76KwxHoriImhx7Mg3TwN/auMDsyQ==",
+      "integrity": "sha512-kDbFRFp0YpTQVVrqUd5FTYmWo45zGaXe0X8E1G/LKFC0v8x0vWrhOWSLITcCn63lmZIxfOMXtCfti/RxN/0wnQ==",
       "cpu": [
         "x64"
       ],
@@ -317,9 +320,9 @@
       }
     },
     "node_modules/@esbuild/win32-arm64": {
-      "version": "0.18.15",
+      "version": "0.18.20",
-      "resolved": "https://registry.npmjs.org/@esbuild/win32-arm64/-/win32-arm64-0.18.15.tgz",
+      "resolved": "https://registry.npmjs.org/@esbuild/win32-arm64/-/win32-arm64-0.18.20.tgz",
-      "integrity": "sha512-HC4/feP+pB2Vb+cMPUjAnFyERs+HJN7E6KaeBlFdBv799MhD+aPJlfi/yk36SED58J9TPwI8MAcVpJgej4ud0A==",
+      "integrity": "sha512-ddYFR6ItYgoaq4v4JmQQaAI5s7npztfV4Ag6NrhiaW0RrnOXqBkgwZLofVTlq1daVTQNhtI5oieTvkRPfZrePg==",
       "cpu": [
         "arm64"
       ],
@@ -333,9 +336,9 @@
       }
     },
     "node_modules/@esbuild/win32-ia32": {
-      "version": "0.18.15",
+      "version": "0.18.20",
-      "resolved": "https://registry.npmjs.org/@esbuild/win32-ia32/-/win32-ia32-0.18.15.tgz",
+      "resolved": "https://registry.npmjs.org/@esbuild/win32-ia32/-/win32-ia32-0.18.20.tgz",
-      "integrity": "sha512-ovjwoRXI+gf52EVF60u9sSDj7myPixPxqzD5CmkEUmvs+W9Xd0iqISVBQn8xcx4ciIaIVlWCuTbYDOXOnOL44Q==",
+      "integrity": "sha512-Wv7QBi3ID/rROT08SABTS7eV4hX26sVduqDOTe1MvGMjNd3EjOz4b7zeexIR62GTIEKrfJXKL9LFxTYgkyeu7g==",
       "cpu": [
         "ia32"
       ],
@@ -349,9 +352,9 @@
       }
     },
     "node_modules/@esbuild/win32-x64": {
-      "version": "0.18.15",
+      "version": "0.18.20",
-      "resolved": "https://registry.npmjs.org/@esbuild/win32-x64/-/win32-x64-0.18.15.tgz",
+      "resolved": "https://registry.npmjs.org/@esbuild/win32-x64/-/win32-x64-0.18.20.tgz",
-      "integrity": "sha512-imUxH9a3WJARyAvrG7srLyiK73XdX83NXQkjKvQ+7vPh3ZxoLrzvPkQKKw2DwZ+RV2ZB6vBfNHP8XScAmQC3aA==",
+      "integrity": "sha512-kTdfRcSiDfQca/y9QIkng02avJ+NCaQvrMejlsB3RRv5sE9rRoeBPISaZpKxHELzRxZyLvNts1P27W3wV+8geQ==",
       "cpu": [
         "x64"
       ],
@@ -364,10 +367,52 @@
         "node": ">=12"
       }
     },
+    "node_modules/color": {
+      "version": "4.2.3",
+      "resolved": "https://registry.npmjs.org/color/-/color-4.2.3.tgz",
+      "integrity": "sha512-1rXeuUUiGGrykh+CeBdu5Ie7OJwinCgQY0bc7GCRxy5xVHy+moaqkpL/jqQq0MtQOeYcrqEz4abc5f0KtU7W4A==",
+      "dependencies": {
+        "color-convert": "^2.0.1",
+        "color-string": "^1.9.0"
+      },
+      "engines": {
+        "node": ">=12.5.0"
+      }
+    },
+    "node_modules/color-convert": {
+      "version": "2.0.1",
+      "resolved": "https://registry.npmjs.org/color-convert/-/color-convert-2.0.1.tgz",
+      "integrity": "sha512-RRECPsj7iu/xb5oKYcsFHSppFNnsj/52OVTRKb4zP5onXwVF3zVmmToNcOfGC+CRDpfK/U584fMg38ZHCaElKQ==",
+      "dependencies": {
+        "color-name": "~1.1.4"
+      },
+      "engines": {
+        "node": ">=7.0.0"
+      }
+    },
+    "node_modules/color-name": {
+      "version": "1.1.4",
+      "resolved": "https://registry.npmjs.org/color-name/-/color-name-1.1.4.tgz",
+      "integrity": "sha512-dOy+3AuW3a2wNbZHIuMZpTcgjGuLU/uBL/ubcZF9OXbDo8ff4O8yVp5Bf0efS8uEoYo5q4Fx7dY9OgQGXgAsQA=="
+    },
+    "node_modules/color-scheme": {
+      "version": "1.0.1",
+      "resolved": "https://registry.npmjs.org/color-scheme/-/color-scheme-1.0.1.tgz",
+      "integrity": "sha512-4x+ya6+z6g9DaTFSfVzTZc8TSjxHuDT40NB43N3XPUkQlF6uujhwH8aeMeq8HBgoQQog/vrYgJ16mt/eVTRXwQ=="
+    },
+    "node_modules/color-string": {
+      "version": "1.9.1",
+      "resolved": "https://registry.npmjs.org/color-string/-/color-string-1.9.1.tgz",
+      "integrity": "sha512-shrVawQFojnZv6xM40anx4CkoDP+fZsw/ZerEMsW/pyzsRbElpsL/DBVW7q3ExxwusdNXI3lXpuhEZkzs8p5Eg==",
+      "dependencies": {
+        "color-name": "^1.0.0",
+        "simple-swizzle": "^0.2.2"
+      }
+    },
     "node_modules/esbuild": {
-      "version": "0.18.15",
+      "version": "0.18.20",
-      "resolved": "https://registry.npmjs.org/esbuild/-/esbuild-0.18.15.tgz",
+      "resolved": "https://registry.npmjs.org/esbuild/-/esbuild-0.18.20.tgz",
-      "integrity": "sha512-3WOOLhrvuTGPRzQPU6waSDWrDTnQriia72McWcn6UCi43GhCHrXH4S59hKMeez+IITmdUuUyvbU9JIp+t3xlPQ==",
+      "integrity": "sha512-ceqxoedUrcayh7Y7ZX6NdbbDzGROiyVBgC4PriJThBKSVPWnnFHZAkfI1lJT8QFkOwH4qOS2SJkS4wvpGl8BpA==",
       "dev": true,
       "hasInstallScript": true,
       "bin": {
@@ -377,34 +422,34 @@
         "node": ">=12"
       },
       "optionalDependencies": {
-        "@esbuild/android-arm": "0.18.15",
+        "@esbuild/android-arm": "0.18.20",
-        "@esbuild/android-arm64": "0.18.15",
+        "@esbuild/android-arm64": "0.18.20",
-        "@esbuild/android-x64": "0.18.15",
+        "@esbuild/android-x64": "0.18.20",
-        "@esbuild/darwin-arm64": "0.18.15",
+        "@esbuild/darwin-arm64": "0.18.20",
-        "@esbuild/darwin-x64": "0.18.15",
+        "@esbuild/darwin-x64": "0.18.20",
-        "@esbuild/freebsd-arm64": "0.18.15",
+        "@esbuild/freebsd-arm64": "0.18.20",
-        "@esbuild/freebsd-x64": "0.18.15",
+        "@esbuild/freebsd-x64": "0.18.20",
-        "@esbuild/linux-arm": "0.18.15",
+        "@esbuild/linux-arm": "0.18.20",
-        "@esbuild/linux-arm64": "0.18.15",
+        "@esbuild/linux-arm64": "0.18.20",
-        "@esbuild/linux-ia32": "0.18.15",
+        "@esbuild/linux-ia32": "0.18.20",
-        "@esbuild/linux-loong64": "0.18.15",
+        "@esbuild/linux-loong64": "0.18.20",
-        "@esbuild/linux-mips64el": "0.18.15",
+        "@esbuild/linux-mips64el": "0.18.20",
-        "@esbuild/linux-ppc64": "0.18.15",
+        "@esbuild/linux-ppc64": "0.18.20",
-        "@esbuild/linux-riscv64": "0.18.15",
+        "@esbuild/linux-riscv64": "0.18.20",
-        "@esbuild/linux-s390x": "0.18.15",
+        "@esbuild/linux-s390x": "0.18.20",
-        "@esbuild/linux-x64": "0.18.15",
+        "@esbuild/linux-x64": "0.18.20",
-        "@esbuild/netbsd-x64": "0.18.15",
+        "@esbuild/netbsd-x64": "0.18.20",
-        "@esbuild/openbsd-x64": "0.18.15",
+        "@esbuild/openbsd-x64": "0.18.20",
-        "@esbuild/sunos-x64": "0.18.15",
+        "@esbuild/sunos-x64": "0.18.20",
-        "@esbuild/win32-arm64": "0.18.15",
+        "@esbuild/win32-arm64": "0.18.20",
-        "@esbuild/win32-ia32": "0.18.15",
+        "@esbuild/win32-ia32": "0.18.20",
-        "@esbuild/win32-x64": "0.18.15"
+        "@esbuild/win32-x64": "0.18.20"
       }
     },
     "node_modules/fsevents": {
-      "version": "2.3.2",
+      "version": "2.3.3",
-      "resolved": "https://registry.npmjs.org/fsevents/-/fsevents-2.3.2.tgz",
+      "resolved": "https://registry.npmjs.org/fsevents/-/fsevents-2.3.3.tgz",
-      "integrity": "sha512-xiqMQR4xAeHTuB9uWm+fFRcIOgKBMiOBP+eXiyT7jsgVCq1bkVygt00oASowB7EdtpOHaaPgKt812P9ab+DDKA==",
+      "integrity": "sha512-5xoDfX+fL7faATnagmWPpbFtwh/R77WmMMqqHGS65C3vvB0YHrgF+B1YmZ3441tMj5n63k0212XNoJwzlhffQw==",
       "dev": true,
       "hasInstallScript": true,
       "optional": true,
@@ -415,10 +460,15 @@
         "node": "^8.16.0 || ^10.6.0 || >=11.0.0"
       }
     },
+    "node_modules/is-arrayish": {
+      "version": "0.3.2",
+      "resolved": "https://registry.npmjs.org/is-arrayish/-/is-arrayish-0.3.2.tgz",
+      "integrity": "sha512-eVRqCvVlZbuw3GrM63ovNSNAeA1K16kaR/LRY/92w0zxQ5/1YzwblUX652i4Xs9RwAGjW9d9y6X88t8OaAJfWQ=="
+    },
     "node_modules/lil-gui": {
-      "version": "0.18.2",
+      "version": "0.19.0",
-      "resolved": "https://registry.npmjs.org/lil-gui/-/lil-gui-0.18.2.tgz",
+      "resolved": "https://registry.npmjs.org/lil-gui/-/lil-gui-0.19.0.tgz",
-      "integrity": "sha512-DgdrLy3/KGC0PiQLKgOcJMPItP4xY4iWgJ9+91Zaxfr8GCTmMps05QS9w9jW7yspILlbscbquwjOwxmWnSx5Uw=="
+      "integrity": "sha512-02/Z7rPng3GXWFwkQVj1hQaJYo2fIEYctqe0ima5uI/N2HEagB9ZGCQKkVWr3UuKfTr0arto3Q9prTB8sxtJJw=="
     },
     "node_modules/nanoid": {
       "version": "3.3.6",
@@ -445,9 +495,9 @@
       "dev": true
     },
     "node_modules/postcss": {
-      "version": "8.4.27",
+      "version": "8.4.31",
-      "resolved": "https://registry.npmjs.org/postcss/-/postcss-8.4.27.tgz",
+      "resolved": "https://registry.npmjs.org/postcss/-/postcss-8.4.31.tgz",
-      "integrity": "sha512-gY/ACJtJPSmUFPDCHtX78+01fHa64FaU4zaaWfuh1MhGJISufJAH4cun6k/8fwsHYeK4UQmENQK+tRLCFJE8JQ==",
+      "integrity": "sha512-PS08Iboia9mts/2ygV3eLpY5ghnUcfLV/EXTOW1E2qYxJKGGBUtNjN76FYHnMs36RmARn41bC0AZmn+rR0OVpQ==",
       "dev": true,
       "funding": [
         {
@@ -473,9 +523,9 @@
       }
     },
     "node_modules/rollup": {
-      "version": "3.26.3",
+      "version": "3.29.4",
-      "resolved": "https://registry.npmjs.org/rollup/-/rollup-3.26.3.tgz",
+      "resolved": "https://registry.npmjs.org/rollup/-/rollup-3.29.4.tgz",
-      "integrity": "sha512-7Tin0C8l86TkpcMtXvQu6saWH93nhG3dGQ1/+l5V2TDMceTxO7kDiK6GzbfLWNNxqJXm591PcEZUozZm51ogwQ==",
+      "integrity": "sha512-oWzmBZwvYrU0iJHtDmhsm662rC15FRXmcjCk1xD771dFDx5jJ02ufAQQTn0etB2emNk4J9EZg/yWKpsn9BWGRw==",
       "dev": true,
       "bin": {
         "rollup": "dist/bin/rollup"
@@ -488,6 +538,14 @@
         "fsevents": "~2.3.2"
       }
     },
+    "node_modules/simple-swizzle": {
+      "version": "0.2.2",
+      "resolved": "https://registry.npmjs.org/simple-swizzle/-/simple-swizzle-0.2.2.tgz",
+      "integrity": "sha512-JA//kQgZtbuY83m+xT+tXJkmJncGMTFT+C+g2h2R9uxkYIrE2yy9sgmcLhCnw57/WSD+Eh3J97FPEDFnbXnDUg==",
+      "dependencies": {
+        "is-arrayish": "^0.3.1"
+      }
+    },
     "node_modules/source-map-js": {
       "version": "1.0.2",
       "resolved": "https://registry.npmjs.org/source-map-js/-/source-map-js-1.0.2.tgz",
@@ -503,14 +561,14 @@
       "integrity": "sha512-Uzz8C/5GesJzv8i+Y2prEMYUwodwZySPcNhuJUdsVMH2Yn4Nm8qlbQe6qRN5fOhg55XB0WiLfTPBxVHxpE60ug=="
     },
     "node_modules/vite": {
-      "version": "4.4.6",
+      "version": "4.5.3",
-      "resolved": "https://registry.npmjs.org/vite/-/vite-4.4.6.tgz",
+      "resolved": "https://registry.npmjs.org/vite/-/vite-4.5.3.tgz",
-      "integrity": "sha512-EY6Mm8vJ++S3D4tNAckaZfw3JwG3wa794Vt70M6cNJ6NxT87yhq7EC8Rcap3ahyHdo8AhCmV9PTk+vG1HiYn1A==",
+      "integrity": "sha512-kQL23kMeX92v3ph7IauVkXkikdDRsYMGTVl5KY2E9OY4ONLvkHf04MDTbnfo6NKxZiDLWzVpP5oTa8hQD8U3dg==",
       "dev": true,
       "dependencies": {
         "esbuild": "^0.18.10",
-        "postcss": "^8.4.26",
+        "postcss": "^8.4.27",
-        "rollup": "^3.25.2"
+        "rollup": "^3.27.1"
       },
       "bin": {
         "vite": "bin/vite.js"

package.json

@@ -1,9 +1,12 @@
 {
   "dependencies": {
-    "lil-gui": "^0.18.2",
+    "color": "^4.2.3",
+    "color-scheme": "^1.0.1",
+    "lil-gui": "^0.19.0",
     "three": "^0.154.0"
   },
   "devDependencies": {
     "vite": "^4.4.6"
-  }
+  },
+  "type": "module"
 }

polytopes.js

@@ -1,23 +1,28 @@
-
 import * as PERMUTE from './permute.js';
 
-function scale_and_index(nodes, scale) {
+import * as CELLINDEX from './cellindex.js';
+
+function index_nodes(nodes, scale) {
 	let i = 1;
 	for( const n of nodes ) {
 		n["id"] = i;
 		i++;
+	}
+}
+
+function scale_nodes(nodes, scale) {
+	for( const n of nodes ) {
 		for( const a of [ 'x', 'y', 'z', 'w' ] ) {
 			n[a] = scale * n[a];
 		}
 	}
-	return nodes;
 }
 
 function dist2(n1, n2) {
 	return (n1.x - n2.x) ** 2 + (n1.y - n2.y) ** 2 + (n1.z - n2.z) ** 2 + (n1.w - n2.w) ** 2;
 }
 
-function auto_detect_edges(nodes, neighbours) {
+export function auto_detect_edges(nodes, neighbours, debug=false) {
 	const seen = {};
 	const nnodes = nodes.length;
 	const links = [];
@@ -29,6 +34,10 @@ function auto_detect_edges(nodes, neighbours) {
 		}
 		d2.sort((a, b) => a.d2 - b.d2);
 		const closest = d2.slice(1, neighbours + 1);
+		if( debug ) {
+			console.log(`closest = ${closest.length}`);
+			console.log(closest);
+		}
 		for( const e of closest ) {
 			const ids = [ n1.id, e.id ];
 			ids.sort();
@@ -40,21 +49,24 @@ function auto_detect_edges(nodes, neighbours) {
 			}
 		}
 	}
+	if( debug ) {
+		console.log(`Found ${links.length} edges`)
+	}
 	return links;
 }
 
 // too small and simple to calculate
 
 export const cell5 = () => {
-	const r5 = Math.sqrt(5);
+	const c1 = Math.sqrt(5) / 4;
-	const r2 = Math.sqrt(2) / 2;
 	return {
+		name: '5-cell',
 		nodes: [
-	      {id:1, x: r2, y: r2, z: r2, w: -r2 / r5 },
+	      {id:1, label: 1, x: c1, y: c1, z: c1, w: -0.25 },
-	      {id:2, x: r2, y: -r2, z: -r2, w: -r2 / r5 },
+	      {id:2, label: 2, x: c1, y: -c1, z: -c1, w: -0.25 },
-	      {id:3, x: -r2, y: r2, z: -r2, w: -r2 / r5 },
+	      {id:3, label: 3, x: -c1, y: c1, z: -c1, w: -0.25 },
-	      {id:4, x: -r2, y: -r2, z: r2, w: -r2 / r5 },
+	      {id:4, label: 4, x: -c1, y: -c1, z: c1, w: -0.25 },
-	      {id:5, x: 0, y: 0, z: 0, w: 4 * r2 / r5 },
+	      {id:5, label: 5, x: 0, y: 0, z: 0, w: 1 },
 		],
 		links: [
 			{ id:1, source:1, target: 2},
@@ -67,7 +79,13 @@ export const cell5 = () => {
 			{ id:8, source:3, target: 4},
 			{ id:9, source:3, target: 5},
 			{ id:10, source:4, target: 5},
-		]
+		],
+		options: [ { name: '--' }],
+		description: `Five tetrahedra joined at ten faces with three
+		tetrahedra around each edge. The 5-cell is the simplest regular
+		four-D polytope and the four-dimensional analogue of the tetrahedron.
+		A corresponding polytope, or simplex, exists for every n-dimensional
+		space.`,
 	};
 };
 
@@ -75,46 +93,218 @@ export const cell5 = () => {
 export const cell16 = () => {
 	let nodes = PERMUTE.coordinates([1, 1, 1, 1],  0);
 	nodes = nodes.filter((n) => n.x * n.y * n.z * n.w > 0);
-	scale_and_index(nodes, 0.75);
+
-	console.log('cell16 auto_detect_edges');
+	nodes[0].label = 1;
-	console.log(nodes);
+	nodes[3].label = 2;
-	const links = auto_detect_edges(nodes, 8);
+	nodes[5].label = 3;
+	nodes[6].label = 4;
+	nodes[7].label = 1;
+	nodes[4].label = 2;
+	nodes[2].label = 3;
+	nodes[1].label = 4;
+
+	index_nodes(nodes);
+	scale_nodes(nodes, 0.5);
+	const links = auto_detect_edges(nodes, 6);
 
 	return {
+		name: '16-cell',
 		nodes: nodes,
-		links: links
+		links: links,
+		options: [ { name: '--' }],
+		description: `Sixteen tetrahedra joined at 32 faces with four
+		tetrahedra around each edge. The 16-cell is the four-dimensional
+		analogue of the octahedron and is dual to the tesseract. Every
+		n-dimensional space has a corresponding polytope in this family.`,
 	};
 };
 
 
 
 export const tesseract = () => {
-	const nodes = scale_and_index(PERMUTE.coordinates([1, 1, 1, 1],  0), Math.sqrt(2) / 2);
+	const nodes = PERMUTE.coordinates([1, 1, 1, 1],  0);
+	index_nodes(nodes);
+
+	for( const n of nodes ) {
+		if( n.x * n.y * n.z * n.w > 0 ) {
+			n.label = 2;
+		} else {
+			n.label = 1;
+		}
+	}
+
+	scale_nodes(nodes, 0.5);
 	const links = auto_detect_edges(nodes, 4);
+	links.map((l) => { l.label = 0 });
+
+	for( const p of [ 1, 2 ] ) {
+		const nodes16 = nodes.filter((n) => n.label === p);
+		const links16 = auto_detect_edges(nodes16, 6);
+		links16.map((l) => l.label = p);
+		links.push(...links16);
+	}
+
 
 	return {
+		name: 'Tesseract',
 		nodes: nodes,
-		links: links
+		links: links,
+		options: [
+			{ name: 'none', links: [ 0 ] },
+			{ name: 'one 16-cell', links: [ 0, 1 ] },
+			{ name: 'both 16-cells', links: [ 0, 1, 2 ] },
+		],
+		description: `The most well-known four-dimensional shape, the
+		tesseract is analogous to the cube, and is constructed by placing two
+		cubes in parallel hyperplanes and joining their corresponding
+		vertices. It consists of eight cubes joined at 32 face with three 
+		cubes around each edge, and is dual to the 16-cell. Every
+		n-dimensional space has a cube analogue or measure polytope.`,
 	};
 }
 
 
+const CELL24_INDEXING = {
+	x: { y: 1, z: 3, w: 2 },
+	y: { z: 2, w: 3 },
+	z: { w: 1 } 
+};
+
+
+function node_by_id(nodes, nid) {
+	const ns = nodes.filter((n) => n.id === nid);
+	return ns[0];
+}
 
 
 export const cell24 = () => {
-	const nodes = scale_and_index(PERMUTE.coordinates([0, 0, 1, 1],  0), 1);
+	const nodes = PERMUTE.coordinates([0, 0, 1, 1], 0);
-	const links = auto_detect_edges(nodes, 6);
+	
+	for( const n of nodes ) {
+		const axes = ['x', 'y', 'z', 'w'].filter((a) => n[a] !== 0);
+		n.label = CELL24_INDEXING[axes[0]][axes[1]];
+	}
+
+	scale_nodes(nodes, Math.sqrt(2) / 2);
+	index_nodes(nodes);
+	const links = auto_detect_edges(nodes, 8);
+	links.map((l) => l.label = 0);
+
+	for( const p of [ 1, 2, 3 ] ) {
+		const nodes16 = nodes.filter((n) => n.label === p);
+		const links16 = auto_detect_edges(nodes16, 6);
+		links16.map((l) => l.label = p);
+		links.push(...links16);
+	}
+	// links.map((l) => {
+	// 	const ls = [ l.source, l.target ].map((nid) => node_by_id(nodes, nid).label);
+	// 	for ( const c of [1, 2, 3] ) {
+	// 		if( ! ls.includes(c) ) {
+	// 			l.label = c
+	// 		}
+	// 	}
+	// });
 
 	return {
+		name: '24-cell',
 		nodes: nodes,
-		links: links
+		links: links,
+		base: {},
+		options: [
+			{ name: 'none', links: [ 0 ] },
+			{ name: 'one 16-cell', links: [ 0, 1 ] },
+			{ name: 'three 16-cells', links: [ 0, 1, 2, 3 ] }
+		],
+		description: `A unique object without an exact analogue in higher
+		or lower dimensions, the 24-cell is made of twenty-four octahedra
+		joined at 96 faces, with three around each edge. The 24-cell is
+		self-dual.`,
 	};
 }
 
 
 
 
-function make_120cell_vertices() {
+
+// face detection for the 120-cell
+
+// NOTE: all of these return node ids, not nodes
+
+// return all the links which connect to a node
+
+function nodes_links(links, nodeid) {
+	return links.filter((l) => l.source === nodeid || l.target === nodeid);
+}
+
+// filter to remove a link to a given id from a set of links
+
+function not_to_this(link, nodeid) {
+	return !(link.source === nodeid || link.target === nodeid);
+}
+
+// given nodes n1, n2, return all neighbours of n2 which are not n1
+
+function unmutuals(links, n1id, n2id) {
+	const nlinks = nodes_links(links, n2id).filter((l) => not_to_this(l, n1id));
+	return nlinks.map((l) => {
+		if( l.source === n2id ) {
+			return l.target;
+		} else {
+			return l.source;
+		}
+	})
+}
+
+
+function fingerprint(ids) {
+	const sids = [...ids];
+	sids.sort();
+	return sids.join(',');
+}
+
+
+
+function auto_120cell_faces(links) {
+	const faces = [];
+	const seen = {};
+	let id = 1;
+	for( const edge of links ) {
+		const v1 = edge.source;
+		const v2 = edge.target;
+		const n1 = unmutuals(links, v2, v1);
+		const n2 = unmutuals(links, v1, v2);
+		const shared = [];
+		for( const a of n1 ) {
+			const an = unmutuals(links, v1, a);
+			for( const d of n2 ) {
+				const dn = unmutuals(links, v2, d);
+				for( const x of an ) {
+					for( const y of dn ) {
+						if( x == y ) {
+							shared.push([v1, a, x, d, v2])
+						}
+					}
+				}
+			}
+		}
+		if( shared.length !== 3 ) {
+			console.log(`Bad shared faces for ${edge.id} ${v1} ${v2}`);
+		}
+		for( const face of shared ) {
+			const fp = fingerprint(face);
+			if( !seen[fp] ) {
+				faces.push({ id: id, nodes: face });
+				id++;
+				seen[fp] = true;
+			}
+		}
+	}
+	return faces;
+}
+
+
+
+export function make_120cell_vertices() {
 	const phi = 0.5 * (1 + Math.sqrt(5));  
 	const r5 = Math.sqrt(5);   
 	const phi2 = phi * phi;    
@@ -131,42 +321,546 @@ function make_120cell_vertices() {
 		PERMUTE.coordinates([r5, phiinv, phi, 0], 0, true),
 		PERMUTE.coordinates([2, 1, phi, phiinv], 0, true),
 		].flat();
-	return scale_and_index(nodes, 0.5);
+	index_nodes(nodes);
+	scale_nodes(nodes, 0.25 * Math.sqrt(2));
+	return nodes;
 }
 
 
-export const cell120 = () => {
+
+
+
+function label_nodes(nodes, ids, label) {
+	nodes.filter((n) => ids.includes(n.id)).map((n) => n.label = label);
+}
+
+
+
+
+function label_faces_120cell(nodes, faces, cfaces, label) {
+	const ns = new Set();
+	for( const fid of cfaces ) {
+		const face = faces.filter((f)=> f.id === fid );
+		if( face.length > 0 ) {
+			for ( const nid of face[0].nodes ) {
+				ns.add(nid);
+			}
+		}
+	}
+	label_nodes(nodes, Array.from(ns), label);
+}
+
+
+function link_labels(nodes, link) {
+	const n1 = nodes.filter((n) => n.id === link.source);
+	const n2 = nodes.filter((n) => n.id === link.target);
+	return [ n1[0].label, n2[0].label ];
+}
+
+
+// version of the 120-cell where nodes are partitioned by 
+// layer and the links follow that
+
+export const cell120_layered = (max) => {
 	const nodes  = make_120cell_vertices();
 	const links = auto_detect_edges(nodes, 4);
+
+	nodes.map((n) => n.label = 9); // make all invisible by default
+
+	for (const cstr in CELLINDEX.LAYERS120 ) {
+		label_nodes(nodes, CELLINDEX.LAYERS120[cstr], Number(cstr));
+	}
+
+	links.map((l) => {
+		const labels = link_labels(nodes, l);
+		if( labels[0] >= labels[1] ) {
+			l.label = labels[0];
+		} else {
+			l.label = labels[1];
+		}
+	});
+
+	const options = [];
+	const layers = [];
+
+	for( const i of [ 0, 1, 2, 3, 4, 5, 6, 7 ] ) {
+		layers.push(i);
+		options.push({
+			name: CELLINDEX.LAYER_NAMES[i],
+			links: [...layers],
+			nodes: [...layers]
+		})
+	}
+
 	return {
+		name: '120-cell layered',
 		nodes: nodes,
-		links: links
+		links: links,
+		nolink2opacity: true,
+		options: options,
+		description: `This version of the 120-cell lets you explore its
+		structure by building each layer from the 'north pole' onwards.`,
 	}
 }
 
 
-function make_600cell_vertices() {
+
-	const phi = 0.5 * (1 + Math.sqrt(5));  
+
+export const cell120_inscribed = () => {
+	const nodes  = make_120cell_vertices();
+	const links = auto_detect_edges(nodes, 4);
+
+  	for( const cstr in CELLINDEX.INDEX120 ) {
+		label_nodes(nodes, CELLINDEX.INDEX120[cstr], Number(cstr));
+	}
+
+	links.map((l) => l.label = 0);
+
+	for( const p of [ 1, 2, 3, 4, 5 ]) {
+		const nodes600 = nodes.filter((n) => n.label === p);
+		const links600 = auto_detect_edges(nodes600, 12);
+		links600.map((l) => l.label = p);
+		links.push(...links600);
+	}
+
+	return {
+		name: '120-cell',
+		nodes: nodes,
+		links: links,
+		options: [
+			{ name: "none", links: [ 0 ]},
+			{ name: "one inscribed 600-cell", links: [ 0, 1 ] },
+			{ name: "five inscribed 600-cells", links: [ 0, 1, 2, 3, 4, 5 ] }
+		],
+		description: `The 120-cell is the four-dimensional analogue of the
+		dodecahedron, and consists of 120 dodecahedra joined at 720 faces,
+		with three dodecahedra around each edge. It is dual to the 600-cell,
+		and five 600-cells can be inscribed in its vertices.`,
+	}
+}
+
+
+
+
+
+function partition_coord(i, coords, invert) {
+	const j = invert ? -i : i;
+	if( j >= 0 ) {
+		return coords[j];
+	}
+	return "-" + coords[-j];
+}
+
+function partition_fingerprint(n, coords, invert) {
+	const p = ['x','y','z','w'].map((a) => partition_coord(n[a], coords, invert));
+	const fp = p.join(',');
+	return fp;
+}
+
+
+function label_vertex(n, coords, partition) {
+	const fp = partition_fingerprint(n, coords, false);
+	if( fp in partition ) {
+		return partition[fp];
+	} else {
+		const ifp = partition_fingerprint(n, coords, true);
+		if( ifp in partition ) {
+			return partition[ifp];
+		}
+		console.log(`Map for ${fp} ${ifp} not found`);
+		return 0;
+	}
+}
+
+
+function map_coord(i, coords, values) {
+	if( i >= 0 ) {
+		return values[coords[i]];
+	}
+	return -values[coords[-i]];
+}
+
+
+export function make_600cell_vertices() {
+	const coords = {
+		0: '0',
+		1: '1',
+		2: '2',
+		3: 't',
+		4: 'k'
+	};
+	const t = 0.5 * (1 + Math.sqrt(5));
+	const values = {
+		'0': 0,
+		'1': 1,
+		'2': 2,
+		't': t,
+		'k': 1 / t 
+	};
 
 	const nodes = [
 		PERMUTE.coordinates([0, 0, 0, 2],  0),
 		PERMUTE.coordinates([1, 1, 1, 1],  0),
+		PERMUTE.coordinates([3, 1, 4, 0],  0, true)
+	].flat();
 
-		PERMUTE.coordinates([phi, 1, 1 / phi, 0], 0, true)
+	for( const n of nodes ) {
-		].flat();
+		n.label = label_vertex(n, coords, CELLINDEX.PARTITION600);
-	return scale_and_index(nodes, 0.75);
+	}
+
+	for( const n of nodes ) {
+		for( const a of [ 'x', 'y', 'z', 'w'] ) {
+			n[a] = map_coord(n[a], coords, values);
+		}
+	}
+
+
+	index_nodes(nodes);
+	scale_nodes(nodes, 0.5);
+	return nodes;
 }
 
+function get_node(nodes, id) {
+	const ns = nodes.filter((n) => n.id === id);
+	if( ns ) {
+		return ns[0]
+	} else {
+		return undefined;
+	}
+}
 
-export const cell600 = () => {
+function audit_link_labels(nodes, links) {
-	const nodes  = make_600cell_vertices();
+	for( const l of links ) {
-	const links = auto_detect_edges(nodes, 20);
+		const n1 = get_node(nodes, l.source);
-	return {
+		const n2 = get_node(nodes, l.target);
-		nodes: nodes,
+		if( n1.label === n2.label ) {
-		links: links
+			console.log(`link ${l.id} joins ${n1.id} ${n2.id} with label ${n2.label}`);
+		}
 	}
 }
 
 
 
+export const cell600 = () => {
+	const nodes  = make_600cell_vertices();
+	const links = auto_detect_edges(nodes, 12);
 
+	links.map((l) => l.label = 0);
+
+	for( const p of [1, 2, 3, 4, 5]) {
+		const nodes24 = nodes.filter((n) => n.label === p);
+		const links24 = auto_detect_edges(nodes24, 8);
+		links24.map((l) => l.label = p);
+		links.push(...links24);
+	}
+
+	return {
+		name: '600-cell',
+		nodes: nodes,
+		links: links,
+		options: [
+			{ name: "none", links: [ 0 ]},
+			{ name: "one 24-cell", links: [ 0, 1 ] },
+			{ name: "five 24-cells", links: [ 0, 1, 2, 3, 4, 5 ] }
+		],
+		description: `The 600-cell is the four-dimensional analogue of the
+		icosahedron, and consists of 600 tetrahedra joined at 1200 faces
+		with five tetrahedra around each edge. It is dual to the 120-cell.
+		Its 120 vertices can be partitioned into five sets which form the
+		vertices of five inscribed 24-cells.`,
+	}
+}
+
+
+export const cell600_layered = () => {
+	const nodes  = make_600cell_vertices();
+	const links = auto_detect_edges(nodes, 12);
+
+	nodes.map((n) => n.label = 9); // make all invisible by default
+
+	for (const cstr in CELLINDEX.LAYERS600 ) {
+		label_nodes(nodes, CELLINDEX.LAYERS600[cstr], Number(cstr));
+	}
+
+	links.map((l) => {
+		const labels = link_labels(nodes, l);
+		if( labels[0] >= labels[1] ) {
+			l.label = labels[0];
+		} else {
+			l.label = labels[1];
+		}
+	});
+
+	const options = [];
+	const layers = [];
+
+	for( const i of [ 0, 1, 2, 3, 4, 5, 6, 7 ] ) {
+		layers.push(i);
+		options.push({
+			name: CELLINDEX.LAYER_NAMES[i],
+			links: [...layers],
+			nodes: [...layers]
+		})
+	}
+
+	return {
+		name: '600-cell layered',
+		nodes: nodes,
+		links: links,
+		nolink2opacity: true,
+		options: options,
+		description: `This version of the 600-cell lets you explore its
+		structure by building each layer from the 'north pole' onwards.`,
+	}
+
+
+}
+
+
+export const snub24cell = () => {
+	const nodes600  = make_600cell_vertices();
+	const links600 = auto_detect_edges(nodes600, 12);
+
+	const nodes = nodes600.filter((n) => n.label != 1);
+	const links = links600.filter((l) => {
+		const sn = node_by_id(nodes, l.source);
+		const tn = node_by_id(nodes, l.target);
+		return sn && tn;
+	});
+
+	links.map((l) => l.label = 0);
+
+	return {
+		name: 'Snub 24-cell',
+		nodes: nodes,
+		links: links,
+		options: [ { name: "--" } ],
+		description: `The snub 24-cell is a semiregular polytope which
+		connects the 24-cell with the 600-cell. It consists of 24 icosahedra
+		and 120 tetrahedra, and is constructed by removing one of the
+		five inscribed 24-cells from a 600-cell.`
+
+	}
+
+
+}
+
+
+
+
+
+function make_dodecahedron_vertices() {
+	const phi = 0.5 * (1 + Math.sqrt(5));  
+	const phiinv = 1 / phi;    
+
+	const nodes = [
+			{ x: 1, y: 1, z: 1, w: 0, 			label: 4 },
+			{ x: 1, y: 1, z: -1, w: 0, 			label: 3 },
+			{ x: 1, y: -1, z: 1, w: 0, 			label: 3 },
+			{ x: 1, y: -1, z: -1, w: 0, 		label: 2 },
+
+			{ x: -1, y: 1, z: 1, w: 0, 			label: 3 },
+			{ x: -1, y: 1, z: -1, w: 0, 		label: 1 },
+			{ x: -1, y: -1, z: 1, w: 0, 		label: 5 },
+			{ x: -1, y: -1, z: -1, w: 0, 		label: 3 },
+
+			{ x: 0, y: phi, z: phiinv, w: 0, 	label: 5 },
+			{ x: 0, y: phi, z: -phiinv, w: 0 , 	label: 2 },
+			{ x: 0, y: -phi, z: phiinv, w: 0, 	label: 4 },
+			{ x: 0, y: -phi, z: -phiinv, w: 0 , label: 1 },
+
+			{ x: phiinv, y: 0, z: phi, w: 0 , 	label: 2},
+			{ x: phiinv, y: 0, z: -phi, w: 0 , 	label: 4},
+			{ x: -phiinv, y: 0, z: phi, w: 0 , 	label: 1},
+			{ x: -phiinv, y: 0, z: -phi, w: 0 , label: 5},
+
+			{ x: phi, y: phiinv, z:0, w: 0 , 	label: 1},
+			{ x: phi, y: -phiinv, z:0, w: 0 , 	label: 5},
+			{ x: -phi, y: phiinv, z:0, w: 0 , 	label: 4},
+			{ x: -phi, y: -phiinv, z:0, w: 0 , 	label: 2},
+		];
+	scale_nodes(nodes, 1 / Math.sqrt(3));
+	index_nodes(nodes);
+	return nodes;
+}
+
+export const dodecahedron = () => {
+	const nodes  = make_dodecahedron_vertices();
+	const links = auto_detect_edges(nodes, 3);
+	links.map((l) => l.label = 0);
+
+	for( const p of [ 1, 2, 3, 4, 5 ]) {
+		const tetran = nodes.filter((n) => n.label === p);
+		const tetral = auto_detect_edges(tetran, 3);
+		tetral.map((l) => l.label = p);
+		links.push(...tetral);
+	}
+
+	return {
+		name: 'Dodecahedron',
+		nodes: nodes,
+		links: links,
+		options: [
+			{ name: "none", links: [ 0 ]},
+			{ name: "one tetrahedron", links: [ 0, 1 ] },
+			{ name: "five tetrahedra", links: [ 0, 1, 2, 3, 4, 5 ] }
+		],
+		description: `The dodecahedron is a three-dimensional polyhedron
+		which is included here so that you can see the partition of its
+		vertices into five interlocked tetrahedra. This structure is the
+		basis for the partition of the 120-cell's vertices into five
+		600-cells.`
+
+	}
+}
+
+
+export const tetrahedron = () => {
+	const r2 = Math.sqrt(2);
+	const r3 = Math.sqrt(3);
+	return {
+		name: 'Tetrahedron',
+		nodes: [
+	      {id:1, label: 1, x: 2 * r2 / 3, y: 0, z: -1/3, w: 0 },
+	      {id:2, label: 2, x: -r2 / 3, y: r2 / r3, z: -1/3, w: 0 },
+	      {id:3, label: 3, x: -r2 / 3, y: -r2 / r3, z: -1/3, w: 0 },
+	      {id:4, label: 4, x: 0, y: 0, z: 1, w: 0 },
+		],
+		links: [
+			{ id:1, source:1, target: 2},
+			{ id:2, source:1, target: 3},
+			{ id:3, source:1, target: 4},
+			{ id:4, source:2, target: 3},
+			{ id:5, source:2, target: 4},
+			{ id:6, source:3, target: 4},
+		],
+		options: [ { name: '--' }],
+		description: `The simplest three-dimensional polytope, consisting of four triangles joined at six edges. The 5-cell is its four-dimensional analogue.`,
+	};
+};
+
+export const octahedron = () => {
+	const nodes = [
+		{id: 1, label: 1, x: 1, y: 0, z: 0, w: 0},
+		{id: 2, label: 1, x: -1, y: 0, z: 0, w: 0},
+		{id: 3, label: 2, x: 0, y: 1, z: 0, w: 0},
+		{id: 4, label: 2, x: 0, y: -1, z: 0, w: 0},
+		{id: 5, label: 3, x: 0, y: 0, z: 1, w: 0},
+		{id: 6, label: 3, x: 0, y: 0, z: -1, w: 0},
+	];
+	const links = [
+		{id:1, source: 1, target: 3},
+		{id:2, source: 1, target: 4},
+		{id:3, source: 1, target: 5},
+		{id:4, source: 1, target: 6},
+		{id:5, source: 2, target: 3},
+		{id:6, source: 2, target: 4},
+		{id:7, source: 2, target: 5},
+		{id:8, source: 2, target: 6},
+		{id:9, source: 3, target: 5},
+		{id:10, source: 3, target: 6},
+		{id:11, source: 4, target: 5},
+		{id:12, source: 4, target: 6},
+	]
+	links.map((l) => { l.label = 0 });
+	return {
+		name: 'Octahedron',
+		nodes: nodes,
+		links: links,
+		options: [ { name: '--' }],
+		description: `The three-dimensional cross-polytope, the 16-cell is its four-dimensional analogue.`,
+	};
+
+}
+
+export const cube = () => {
+	const nodes = [
+		{id: 1, label: 1, x: 1, y: 1, z: 1, w: 0},
+		{id: 2, label: 2, x: -1, y: 1, z: 1, w: 0},
+		{id: 3, label: 2, x: 1, y: -1, z: 1, w: 0},
+		{id: 4, label: 1, x: -1, y: -1, z: 1, w: 0},
+		{id: 5, label: 2, x: 1, y: 1, z: -1, w: 0},
+		{id: 6, label: 1, x: -1, y: 1, z: -1, w: 0},
+		{id: 7, label: 1, x: 1, y: -1, z: -1, w: 0},
+		{id: 8, label: 2, x: -1, y: -1, z: -1, w: 0},
+	];
+	scale_nodes(nodes, 1/Math.sqrt(3));
+	const links = auto_detect_edges(nodes, 3);
+	links.map((l) => { l.label = 0 });
+	return {
+		name: 'Cube',
+		nodes: nodes,
+		links: links,
+		options: [ { name: '--' }],
+		description: `The three-dimensional measure polytope, the tesseract is its four-dimensional analogue.`,
+	};
+
+}
+
+
+
+function make_icosahedron_vertices() {
+	const phi = 0.5 * (1 + Math.sqrt(5));  
+
+	const nodes = [
+		{ x: 0, y: 1, z: phi, w: 0, label: 1 },
+		{ x: 0, y: -1, z: phi, w: 0, label: 1 },
+		{ x: 0, y: 1, z: -phi, w: 0, label: 1 },
+		{ x: 0, y: -1, z: -phi, w: 0, label: 1 },
+		{ x: 1, y: phi, z: 0, w: 0, label: 2 },
+		{ x: -1, y: phi, z: 0, w: 0, label: 2 },
+		{ x: 1, y: -phi, z: 0, w: 0, label: 2 },
+		{ x: -1, y: -phi, z: 0, w: 0, label: 2 },
+		{ x: phi, y: 0, z: 1, w: 0, label: 3},
+		{ x: phi, y: 0, z: -1, w: 0, label: 3},
+		{ x: -phi, y: 0, z: 1, w: 0, label: 3},
+		{ x: -phi, y: 0, z: -1, w: 0, label: 3},
+		];
+
+   	scale_nodes(nodes, 1/Math.sqrt((5 + Math.sqrt(5)) / 2));
+	index_nodes(nodes);
+	return nodes;
+}
+
+
+
+export const icosahedron = () => {
+	const nodes  = make_icosahedron_vertices();
+	const links = auto_detect_edges(nodes, 5);
+	links.map((l) => l.label = 0);
+
+	return {
+		name: 'Icosahedron',
+		nodes: nodes,
+		links: links,
+		options: [
+			{ name: "--"},
+		],
+		description: `The icosahedron is a twenty-sided polyhedron and is dual to the dodecahedron. Its four-dimensional analogue is the 600-cell.`
+
+	}
+}
+
+
+export const build_all = () => {
+	return [
+		tetrahedron(),
+		octahedron(),
+		cube(),
+		icosahedron(),
+	 	dodecahedron(),
+	 	cell5(),
+		cell16(),
+		tesseract(),
+		cell24(),
+		snub24cell(),
+		cell600(),
+		cell600_layered(),
+	 	cell120_inscribed(),
+	 	cell120_layered()
+	 	];
+}
+
+export const radii = (shape) => {
+	return shape.nodes.map(n => Math.sqrt(n.x * n.x + n.y * n.y + n.z * n.z + n.w * n.w))
+}

rotation.js

@@ -0,0 +1,85 @@
+// hacky stuff for 4d rotations
+
+// see https://math.stackexchange.com/questions/1402362/can-rotations-in-4d-be-given-an-explicit-matrix-form#1402376
+
+import * as THREE from 'three';
+
+
+function rotZW(theta) {
+	const ctheta = Math.cos(theta);
+	const stheta = Math.sin(theta);
+	return new THREE.Matrix4(
+		ctheta, -stheta, 0, 0,
+		stheta, ctheta, 0, 0,
+		0, 0, 1, 0,
+		0, 0, 0, 1
+		);
+}
+
+function rotYW(theta) {
+	const ctheta = Math.cos(theta);
+	const stheta = Math.sin(theta);
+	return new THREE.Matrix4(
+		ctheta, 0, -stheta, 0,
+		0, 1, 0, 0,
+		stheta, 0, ctheta, 0,
+		0, 0, 0, 1,
+		);
+}
+
+function rotYZ(theta) {
+	const ctheta = Math.cos(theta);
+	const stheta = Math.sin(theta);
+	return new THREE.Matrix4(
+		ctheta, 0, 0, -stheta,
+		0, 1, 0, 0,
+		0, 0, 1, 0,
+		stheta, 0, 0, ctheta, 
+		);
+}
+
+function rotXW(theta) {
+	const ctheta = Math.cos(theta);
+	const stheta = Math.sin(theta);
+	return new THREE.Matrix4(
+		1, 0, 0, 0,
+		0, ctheta, -stheta, 0,
+		0, stheta, ctheta, 0,
+		0, 0, 0, 1
+		);
+}
+
+function rotXZ(theta) {
+	const ctheta = Math.cos(theta);
+	const stheta = Math.sin(theta);
+	return new THREE.Matrix4(
+		1, 0, 0, 0,
+		0, ctheta, 0, -stheta,
+		0, 0, 1, 0,
+		0, stheta, 0, ctheta,
+		);
+}
+
+function rotXY(theta) {
+	const ctheta = Math.cos(theta);
+	const stheta = Math.sin(theta);
+	return new THREE.Matrix4(
+		1, 0, 0, 0,
+		0, 1, 0, 0,
+		0, 0, ctheta, -stheta,
+		0, 0, stheta, ctheta,
+		);
+}
+
+
+export const rotfn = {
+	XY: rotXY,
+	XZ: rotXZ,
+	XW: rotXW,
+	YZ: rotYZ,
+	YW: rotYW,
+	ZW: rotZW,
+};
+
+
+

vite.config.js

@@ -3,5 +3,14 @@
 import { defineConfig, loadEnv } from 'vite';
 
 export default defineConfig({
-	base: '/fourjs/'	
+	base: '/fourjs/',
+	build: {
+		rollupOptions: {
+			output: {
+				manualChunks: {
+					threejs: [ 'three' ]
+				}
+			}		
+		}
+	}	
 })