cellindex.js

@@ -1 +1,92 @@
-export const INDEX = {"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 INDEX = {
+	"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 LAYERS =  {
+	"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]
+};

colours.js

@@ -5,7 +5,7 @@ export const get_colours = (basis) => {
 	const hexbasis = basis.toString(16).padStart(6, "0");
 	scheme.from_hex(hexbasis).scheme("tetrade").variation("hard").distance(0.5);
 	const colours = scheme.colors().map((cs) => parseInt('0x' + cs));
-	const set = colours.slice(1, 6);
+	const set = colours.slice(1, 9);
 	set.reverse();
 	set.unshift(colours[0]);
 	return set;

fourDShape.js

@@ -61,7 +61,7 @@ class FourDShape extends THREE.Group {
 		return edge;
 	}
 
-	updateLink(link) {
+	updateLink(link, links_show) {
 		const n1 = this.nodes3[link.source].v3;
 		const n2 = this.nodes3[link.target].v3;
 		const length = n1.distanceTo(n2);
@@ -71,6 +71,7 @@ class FourDShape extends THREE.Group {
 		link.object.position.copy(centre);
 		link.object.lookAt(n2);
 		link.object.children[0].rotation.x = Math.PI / 2.0;
+		link.object.visible = (!links_show || link.label in links_show); 
 	}
 
 
@@ -115,6 +116,7 @@ class FourDShape extends THREE.Group {
 			const material = this.getMaterial(n, this.node_ms);
 			this.nodes3[n.id] = {
 				v3: v3,
+				label: n.label,
 				object: this.makeNode(material, v3)
 			};
 		}
@@ -129,17 +131,17 @@ class FourDShape extends THREE.Group {
 	}
 
 
-	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);
 			this.nodes3[n.id].v3 = v3;
 			this.nodes3[n.id].object.position.copy(v3);
 			this.nodes3[n.id].object.scale.copy(this.scalev3);
+			this.nodes3[n.id].object.visible = ( !nodes_show || n.label in nodes_show );
 		}
-
 		for( const l of this.links ) {
-			this.updateLink(l);
+			this.updateLink(l, links_show);
 		}
 
 		for( const f of this.faces ) {
@@ -147,7 +149,6 @@ class FourDShape extends THREE.Group {
 		}
 	}
 
-
 }
 
 export { FourDShape };

gui.js

@@ -1,13 +1,14 @@
 import { GUI } from 'lil-gui';
 
 
-
 const DEFAULTS = {
 	thickness: 0.25,
 	nodesize: 1.25,
 	linkopacity: 0.5,
 	link2opacity: 0.5,
-	shape: '120-cell',
+	shape: '',
+	option: '',
+	visibility: 5,
 	inscribed: false,
 	inscribe_all: false,
 	color: 0x3293a9,
@@ -22,18 +23,25 @@ const DEFAULTS = {
 
 class FourDGUI {
 
-	constructor(changeShape, setColor, setBackground, setLinkOpacity) {
+	constructor(shapes, changeShape, setColor, setBackground, setLinkOpacity, setVisibility) {
 		this.gui = new GUI();
+		const SHAPE_NAMES = shapes.map((s) => s.name);
+		// set default shape + option from the first shape
+		DEFAULTS.shape = shapes[0].name;
+		DEFAULTS.option = shapes[0].options[0].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'],
 			thickness: this.link['thickness'],
 			linkopacity: this.link['linkopacity'],
 			link2opacity: this.link['linkopacity'],
 			nodesize: this.link['nodesize'],
+			depth: this.link['depth'],
 			color: this.link['color'],
 			background: this.link['background'],
 			hyperplane: this.link['hyperplane'],
@@ -43,13 +51,19 @@ class FourDGUI {
 			dpsi: this.link['dpsi'],
 			"copy link": function () { guiObj.copyUrl() }
 		};
-
+		let options_ctrl;
-		this.gui.add(this.params, 'shape',
+		this.gui.add(this.params, 'shape', SHAPE_NAMES).onChange((shape) => {
-			[ 'dodecahedron', '5-cell', '16-cell', 'tesseract',
+			const options = this.getShapeOptions(shapes, shape);
-				'24-cell', '600-cell', '120-cell' ]
+			options_ctrl = options_ctrl.options(options).onChange((option) => {
-		).onChange(changeShape)
+				setVisibility(option)
-		this.gui.add(this.params, 'inscribed').onChange(changeShape);
+			});
-		this.gui.add(this.params, 'inscribe_all').onChange(changeShape);
+			options_ctrl.setValue(options[0])
+			changeShape(shape)
+		});
+		const options = this.getShapeOptions(shapes, this.params['shape']);
+		options_ctrl = this.gui.add(this.params, 'option', options).onChange((option) => {
+			setVisibility(option)
+		});
 		this.gui.add(this.params, 'hyperplane', 1.5, 2.25);
 		this.gui.add(this.params, 'thickness', 0.1, 2);
 		this.gui.add(this.params, 'linkopacity', 0, 1).onChange(
@@ -67,6 +81,15 @@ class FourDGUI {
 
 	}
 
+	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);
@@ -95,7 +118,7 @@ class FourDGUI {
 		const guiObj = this;
 
 		this.urlParams = this.linkUrl.searchParams;
-		for( const param of [ "shape", "rotation" ]) {
+		for( const param of [ "shape", "rotation", "option" ]) {
 			const value = this.urlParams.get(param);
 			if( value ) {
 				this.link[param] = value;
@@ -121,6 +144,7 @@ class FourDGUI {
 	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("thickness", this.params.thickness.toString());

label120cell.js

@@ -1,7 +1,8 @@
 
-//testbed for playing with stuff in node repl
+// code for generating the 120-cell labels
+// has some overlap with permute - FIXME
 
-const THREE =require('three');
+const THREE = require('three');
 
 function pandita(a) {
 	const n = a.length;
@@ -133,7 +134,7 @@ 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, debug=false) {
+export function auto_detect_edges(nodes, neighbours, debug=false) {
 	const seen = {};
 	const nnodes = nodes.length;
 	const links = [];
@@ -168,7 +169,7 @@ function auto_detect_edges(nodes, neighbours, debug=false) {
 
 
 
-function make_120cell_vertices() {
+export function make_120cell_vertices() {
 	const phi = 0.5 * (1 + Math.sqrt(5));  
 	const r5 = Math.sqrt(5);   
 	const phi2 = phi * phi;    
@@ -230,7 +231,7 @@ function fingerprint(ids) {
 
 
 
-function auto_120cell_faces(links) {
+export function auto_120cell_faces(links) {
 	const faces = [];
 	const seen = {};
 	let id = 1;
@@ -486,7 +487,7 @@ function colour_next_dodeca_maybe(nodes, links, faces, colours, dd, nextf, nextd
 	const nextvs = dodecahedron_vertices(nextdd);
 	// get the initial colour permutations from the existing labels;
 	const p = [];
-	for( i = 0; i < 5; i ++ ) {
+	for( let i = 0; i < 5; i ++ ) {
 		p[i] = colours[nextvs[i]];
 	}
 	const nlabels = colour_dodecahedron_from_face(nextdd, p);
@@ -529,6 +530,33 @@ function meridian(nodes, links, faces, startf, startn, dir=11, max=10) {
 }
 
 
+function meridian_bump(nodes, links, faces, startf, startn, bumpdir=6) {
+	const o =  face_plus_to_dodecahedron(faces, startf, startn);
+	const dir = 11;
+	const max = 10;
+
+	const colours = colour_dodecahedron_from_face(o, [ 1, 2, 3, 4, 5 ] );
+
+	const dds = follow_meridian(nodes, links, faces, colours, o, dir, max);
+
+	const dd4 = dds[4];
+	const nextf = dd4[bumpdir];
+	const bump = follow_face_to_dodeca(faces, dd4, nextf);
+	const ncolours = colour_next_dodeca_maybe(nodes, links, faces, colours, dd4, nextf, bump);
+
+	add_colours(colours, ncolours);
+
+	const labels = { 1: [], 2:[], 3:[], 4:[], 5:[] };
+	for( const vstr in colours ) {
+		labels[colours[vstr]].push(Number(vstr));
+	}
+
+	return { dodecahedra: dds, labels: labels };
+
+}
+
+
+
 function all_meridians(nodes, links, faces, startf, startn) {
 	const o =  face_plus_to_dodecahedron(faces, startf, startn);
 
@@ -668,8 +696,9 @@ function arctic(nodes, links, faces, startf, startn, max) {
 
 
 
+// this is the final one that works for the whole 120-cell
 
-function arctic_two(nodes, links, faces, startf, startn) {
+export function label_120cell(nodes, links, faces, startf, startn) {
 	const pole = face_plus_to_dodecahedron(faces, startf, startn);
 	const dds = [ pole ];
 
@@ -688,10 +717,6 @@ function arctic_two(nodes, links, faces, startf, startn) {
 		seen[dd_fingerprint(nextdd)] = true;
 	}
 
-	// go around all of the arctic circle and grow all faces
-
-    // 1, 12, 20, 12, 30 = 75
-    // 0  1   13, 33, 45
 
 	for( const a of dds.slice(1, 13) ) {
 		for( const i of [ 6, 7, 8, 9, 10 ] ) {
@@ -722,6 +747,8 @@ function arctic_two(nodes, links, faces, startf, startn) {
 	}
 
 	// the 30 equatorials?
+
+
 	for( const a of dds.slice(13, 46) ) {
 		for( const i of [ 6, 7, 8, 9, 10 ] ) {
 			const [ nextdd, ncolours ] = follow_and_colour(
@@ -750,7 +777,10 @@ function arctic_two(nodes, links, faces, startf, startn) {
 		}
 	}
 
+
 	// this should get the rest or explode!
+
+
 	for( const a of dds ) {
 		for( const i of [ 6, 7, 8, 9, 10 ] ) {
 			const [ nextdd, ncolours ] = follow_and_colour(
@@ -778,6 +808,124 @@ function arctic_two(nodes, links, faces, startf, startn) {
 
 
 
+export function cell120_layers(nodes, links, faces, startf, startn, max_layer) {
+	const pole = face_plus_to_dodecahedron(faces, startf, startn);
+	const dds = [ pole ];
+	const dd_families = { "0": [ pole ] }
+
+	const seen = {};
+	seen[dd_fingerprint(pole)] = true;
+
+	const colours = colour_dodecahedron_from_face(dds[0], [ 1, 2, 3, 4, 5 ] );
+	const vs = dodecahedron_vertices(dds[0]);
+
+	// arctic
+
+	if( max_layer > 0 ) {
+		dd_families["1"] = [];
+
+		for( const face of pole ) {
+			const [ nextdd, ncolours ] = follow_and_colour(
+				nodes, links, faces, colours, pole, face
+			);
+				add_colours(colours, ncolours);
+			dds.push(nextdd);
+			dd_families["1"].push(nextdd);
+			seen[dd_fingerprint(nextdd)] = true;
+		}
+	}
+
+	// subarctic - interstitial
+
+	if( max_layer > 1 ) {
+		dd_families["2"] = [];
+
+		for( const a of dd_families["1"] ) {
+			for( const i of [ 6, 7, 8, 9, 10 ] ) {
+				const [ nextdd, ncolours ] = follow_and_colour(
+					nodes, links, faces, colours, a, a[i]
+				);
+				const fp = dd_fingerprint(nextdd);
+				if( !(fp in seen) ) {
+					add_colours(colours, ncolours);
+					dds.push(nextdd);
+					dd_families["2"].push(nextdd);
+					seen[fp] = true;
+				}
+			}
+		}
+	}
+	// tropic of cancer
+
+	if( max_layer > 2 ) {
+		dd_families["3"] = [];
+
+		for( const a of dd_families["1"] ) {
+			const [ nextdd, ncolours ] = follow_and_colour(
+				nodes, links, faces, colours, a, a[11]
+			);
+			const fp = dd_fingerprint(nextdd);
+			if( !(fp in seen) ) {
+				add_colours(colours, ncolours);
+				dds.push(nextdd);
+				dd_families["3"].push(nextdd);
+				seen[fp] = true;
+			}
+		}
+	}
+
+	if( max_layer > 3 ) {
+		// equator
+
+		dd_families["4"] = [];
+
+		for( const a of dds.slice(13, 46) ) {
+			for( const i of [ 6, 7, 8, 9, 10 ] ) {
+				const [ nextdd, ncolours ] = follow_and_colour(
+					nodes, links, faces, colours, a, a[i]
+				);
+				const fp = dd_fingerprint(nextdd);
+				if( !(fp in seen) ) {
+					add_colours(colours, ncolours);
+					dd_families["4"].push(nextdd);
+					dds.push(nextdd);
+					seen[fp] = true;
+				}
+			}
+		}
+	}
+
+	if( max_layer > 4 ) {
+		dd_families["5"] = [];
+
+		for( const a of dd_families["4"] ) {
+			for( const i of [ 6, 7, 8, 9, 10 ] ) {
+				const [ nextdd, ncolours ] = follow_and_colour(
+					nodes, links, faces, colours, a, a[i]
+				);
+				const fp = dd_fingerprint(nextdd);
+				if( !(fp in seen) ) {
+					add_colours(colours, ncolours);
+					dds.push(nextdd);
+					dd_families["5"].push(nextdd);
+					seen[fp] = true;
+				}
+			}
+		}
+	}
+
+	const labels = { 1: [], 2:[], 3:[], 4:[], 5:[] };
+	for( const vstr in colours ) {
+		labels[colours[vstr]].push(Number(vstr));
+	}
+
+
+	return { dodecahedra: dds, labels: labels, families: dd_families };
+}
+
+
+
+
 // 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 
@@ -815,7 +963,6 @@ function make_120cell_cells(faces) {
 		for( const dd of dds ) {
 			const fp = dd_fingerprint(dd);
 			if( ! (fp in seen) ) {
-				//console.log(`added dodeca ${fp}`);
 				const d = {
 					id: i,
 					faces: dd,
@@ -895,7 +1042,7 @@ function meridian_label_120cell(nodes) {
 		//label_nodes(nodes, [313], 6);
 }
 
-
+1
 function check_120cell_nodes(nodes) {
 	nodes.map((n) => {
 		const vs = find_adjacent_labels(nodes, links, n.id);
@@ -927,9 +1074,120 @@ function make_dodecahedron_vertices() {
 }
  
 
-// const nodes = make_120cell_vertices();
+// this one does the coherent indexing / partition into 600-cells
-// const links = auto_detect_edges(nodes, 4);
+
-// const faces = auto_120cell_faces(links);
+export function make_labelled_120cell() {
+	const nodes = make_120cell_vertices();
+	const links = auto_detect_edges(nodes, 4);
+	const faces = auto_120cell_faces(links);
+
+	const labelled = label_120cell(nodes, links, faces, faces[0], 341);
+	return labelled;
+}
+
+// calculate the w-distance of a dodecahedron's centroid
+
+export function dd_w_distance(nodes, dd) {
+	const vertices = new Set();
+	dd.map((f) => f.nodes.map((n) => vertices.add(n)));
+
+	let w = 0;
+	for( const nid of vertices ) {
+		const node = node_by_id(nodes, nid);
+		w += node.w;
+	}
+	return w / 20;
+}
+
+
+export function sort_dds_w(nodes, dds) {
+	dds.sort((a, b) => {
+		return dd_w_distance(nodes, a) - dd_w_distance(nodes, b)
+	})
+}
+
+
+
+export function find_antipode_dd(nodes, links, dd) {
+
+}
+
+// notes because I'm too sick to continue working on this today
+// the vertices which aren't counted by the layers are showing
+// up in the visualisation because they are labelled "0" by default -
+// for this to work better there needs to be a value which is never
+// displayed.
+
+// in the current layer algorithm, layer '5' (the one after the equator)
+// is too greedy 
+
+export function make_layered_120cell(max_layer) {
+	const nodes = make_120cell_vertices();
+	const links = auto_detect_edges(nodes, 4);
+	const faces = auto_120cell_faces(links);
+
+	const labelled = label_120cell(nodes, links, faces, faces[628], 250, max_layer);
+
+	// get layers from sorted w-distance order
+
+	const dds = labelled.dodecahedra;
+	dds.sort((a, b) => dd_w_distance(nodes, b) - dd_w_distance(nodes, a));
+
+	const LAYERS = [
+		[ "0", 1 ],
+		[ "1", 12 ],
+		[ "2", 20 ],
+		[ "3", 12 ],
+		[ "4", 30 ],
+		[ "5", 12 ],
+		[ "6", 20 ],
+		[ "7", 12 ],
+		[ "8", 1]
+	];
+
+	const layer_dds = labelled["families"];
+	const vertices_layers = {};
+	const seen = {};
+	let i = 0;
+
+	for( const layer of LAYERS ) {
+		const label = layer[0];
+		const n = layer[1];
+		vertices_layers[label] = [];
+		console.log(`Layer ${label} starting at ${i}`);
+		for( const dd of dds.slice(i, i + n) ) {
+			console.log(dd_w_distance(nodes, dd));
+			for( const face of dd ) {
+				for( const n of face.nodes ) {
+					if( !seen[n] ) {
+						vertices_layers[label].push(n);
+						seen[n] = true;
+					}
+				}
+			}
+		}
+		i += n;
+	}
+	return JSON.stringify(vertices_layers);
+}
+
+export function make_meridians(bumpdir) {
+	const nodes = make_120cell_vertices();
+	const links = auto_detect_edges(nodes, 4);
+	const faces = auto_120cell_faces(links);
+
+	const mbs ={}
+	for( const bumpdir of [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 ] ) {
+		mbs[bumpdir] = meridian_bump(nodes, links, faces, faces[0], 341, bumpdir)
+	}
+
+	return mbs;
+    
+    // 
+
+}
+
+
 
 
 // console.log("Calculating 120-cell colours")

main.js

@@ -23,7 +23,10 @@ scene.add(light);
 const amblight = new THREE.AmbientLight(0xffffff, 0.5);
 scene.add(amblight);
 
-camera.position.z = 4;
+camera.position.set(0, 0, 4);
+
+camera.lookAt(0, 0, 0);
+//camera.position.z = 4;
 
 const renderer = new THREE.WebGLRenderer({antialias: true});
 renderer.setSize( window.innerWidth, window.innerHeight );
@@ -59,51 +62,26 @@ for( const face_m of face_ms ) {
 }
 
 
-const STRUCTURES = {
+const STRUCTURES = POLYTOPES.build_all();
-	'5-cell': POLYTOPES.cell5(),
-	'16-cell': POLYTOPES.cell16(),
-	'tesseract': POLYTOPES.tesseract(),
-	'24-cell': POLYTOPES.cell24(),
-	'dodecahedron': POLYTOPES.dodecahedron(),
-	'120-cell': POLYTOPES.cell120(),
-	'600-cell': POLYTOPES.cell600(),
-};
 
-const INSCRIBED = {
+const STRUCTURES_BY_NAME = {};
-	'tesseract': POLYTOPES.tesseract_inscribed(),
-	'24-cell': POLYTOPES.cell24_inscribed(),
-	'120-cell': POLYTOPES.cell120_inscribed(),
-	'600-cell': POLYTOPES.cell600_inscribed(),
-	'dodecahedron': POLYTOPES.dodecahedron_inscribed(),
-};
 
-const ALL_INSCRIBED = {
+STRUCTURES.map((s) => STRUCTURES_BY_NAME[s.name] = s);
-	'tesseract': POLYTOPES.tesseract_all_inscribed(),
-	'24-cell': POLYTOPES.cell24_all_inscribed(),
-	'120-cell': POLYTOPES.cell120_all_inscribed(),
-	'600-cell': POLYTOPES.cell600_all_inscribed(),
-	'dodecahedron': POLYTOPES.dodecahedron_all_inscribed(),
-}
 
 let shape = false;
+let structure = false;
+let node_show = [];
+let link_show = []; 
 
-function createShape(name, inscribed, all) {
+
+function createShape(name, option) {
 	if( shape ) {
 		scene.remove(shape);
 	}
-	let structure = STRUCTURES[name];
+	structure = STRUCTURES_BY_NAME[name];
-	if( inscribed ) {
-		if( name in INSCRIBED ) {
-			if( all ) {
-				structure = ALL_INSCRIBED[name];
-			} else {
-				structure = INSCRIBED[name];
-			}
-		} 
-	}
-
 	shape = new FourDShape(node_ms, link_ms, face_ms, structure);
 	scene.add(shape);
+	setVisibility(option ? option : structure.options[0].name);
 }
 
 // initialise gui and read params from URL
@@ -136,12 +114,31 @@ function setLinkOpacity(o, primary) {
 
 let gui; // 
 
+
 function changeShape() {
-	console.log("change shape!")
+	createShape(gui.params.shape);	
-	createShape(gui.params.shape, gui.params.inscribed, gui.params.inscribe_all);
 }
 
-gui = new FourDGUI(changeShape, setColors, setBackground, setLinkOpacity);
+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`);
+	}
+}
+
+
+
+gui = new FourDGUI(
+	STRUCTURES,
+	changeShape,
+	setColors,
+	setBackground,
+	setLinkOpacity,
+	setVisibility
+);
 
 // these are here to pick up colour settings from the URL params
 setColors(gui.params.color);
@@ -184,7 +181,7 @@ renderer.domElement.addEventListener("pointerup", (event) => {
 	dragging = false;
 })
 
-createShape(gui.params.shape, gui.params.inscribed, gui.params.inscribe_all);
+createShape(gui.params.shape, gui.params.option);
 
 function animate() {
 	requestAnimationFrame( animate );
@@ -203,7 +200,7 @@ function animate() {
 	shape.hyperplane = gui.params.hyperplane;
 	shape.link_scale = gui.params.thickness;
 	shape.node_scale = gui.params.nodesize;
-	shape.render3(rotations);
+	shape.render3(rotations, node_show, link_show);
 
 	renderer.render( scene, camera );
 }

polytopes.js

@@ -61,6 +61,7 @@ export const cell5 = () => {
 	const r5 = Math.sqrt(5);
 	const r2 = Math.sqrt(2) / 2;
 	return {
+		name: '5-cell',
 		nodes: [
 	      {id:1, label: 1, x: r2, y: r2, z: r2, w: -r2 / r5 },
 	      {id:2, label: 2, x: r2, y: -r2, z: -r2, w: -r2 / r5 },
@@ -83,7 +84,8 @@ export const cell5 = () => {
 		geometry: {
 			node_size: 0.02,
 			link_size: 0.02
-		}
+		},
+		options: [ { name: '--' }]
 	};
 };
 
@@ -106,12 +108,14 @@ export const cell16 = () => {
 	const links = auto_detect_edges(nodes, 6);
 
 	return {
+		name: '16-cell',
 		nodes: nodes,
 		links: links,
 		geometry: {
 			node_size: 0.02,
 			link_size: 0.02
-		}
+		},
+		options: [ { name: '--' }]
 	};
 };
 
@@ -131,39 +135,33 @@ export const tesseract = () => {
 
 	scale_nodes(nodes, Math.sqrt(2) / 2);
 	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,
 		geometry: {
 			node_size: 0.02,
 			link_size: 0.02
-		}
+		},
+		options: [
+			{ name: 'none', links: [ 0 ] },
+			{ name: 'one 16-cell', links: [ 0, 1 ] },
+			{ name: 'both 16-cells', links: [ 0, 1, 2 ] },
+		],
 	};
 }
 
 
-const tesseract_some_inscribed = (ps) => {
-	const t = tesseract();
-
-	const i_links = []; 
-
-	for( const p of ps ) {
-		const nodes16 = t.nodes.filter((n) => n.label === p);
-		const links16 = auto_detect_edges(nodes16, 6);
-		links16.map((l) => l.label = p);
-		i_links.push(...links16);
-	}
-
-	t.links.push(...i_links);
-	return t;
-}
-
-
-export const tesseract_inscribed = () => tesseract_some_inscribed([1]);
-export const tesseract_all_inscribed = () => tesseract_some_inscribed([1,2]);
-
-
 const CELL24_INDEXING = {
 	x: { y: 1, z: 3, w: 2 },
 	y: { z: 2, w: 3 },
@@ -187,7 +185,14 @@ export const cell24 = () => {
 
 	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] ) {
@@ -198,35 +203,23 @@ export const cell24 = () => {
 	// });
 
 	return {
+		name: '24-cell',
 		nodes: nodes,
 		links: links,
 		geometry: {
 			node_size: 0.02,
 			link_size: 0.02
-		}
+		},
+		base: {},
+		options: [
+			{ name: 'none', links: [ 0 ] },
+			{ name: 'one 16-cell', links: [ 0, 1 ] },
+			{ name: 'three 16-cells', links: [ 0, 1, 2, 3 ] }
+		]
 	};
 }
 
 
-const cell24_some_inscribed = (ps) => {
-	const t = cell24();
-
-	const i_links = []; 
-
-	for( const p of ps ) {
-		const nodes16 = t.nodes.filter((n) => n.label === p);
-		const links16 = auto_detect_edges(nodes16, 6);
-		links16.map((l) => l.label = p);
-		i_links.push(...links16);
-	}
-
-	t.links.push(...i_links);
-	return t;
-}
-
-
-export const cell24_inscribed = () => cell24_some_inscribed([1]);
-export const cell24_all_inscribed = () => cell24_some_inscribed([1,2,3]);
 
 
 
@@ -332,6 +325,8 @@ function make_120cell_vertices() {
 
 
 
+
+
 function label_nodes(nodes, ids, label) {
 	nodes.filter((n) => ids.includes(n.id)).map((n) => n.label = label);
 }
@@ -339,16 +334,8 @@ function label_nodes(nodes, ids, label) {
 
 
 
-
-
-
-
-
-
-
 function label_faces_120cell(nodes, faces, cfaces, label) {
 	const ns = new Set();
-	console.log(`label faces from ${cfaces}`);
 	for( const fid of cfaces ) {
 		const face = faces.filter((f)=> f.id === fid );
 		if( face.length > 0 ) {
@@ -361,33 +348,6 @@ function label_faces_120cell(nodes, faces, cfaces, label) {
 }
 
 
-function basic_auto_label_120cell(nodes, links) {
-
-	const faces = auto_120cell_faces(links);
-	const dodecas = DODECAHEDRA.DODECAHEDRA;
-	//const cfaces = [ 1, 2, 4, 145, 169 ];
-
-	let colour = 1;
-	for( const dd of dodecas ) {
-		label_faces_120cell(nodes, faces, dd, colour);
-		colour++;
-		if( colour > 8 ) {
-			colour = 1;
-		}
-	}
-
-}
-
-function label_120cell(nodes) {
-
-  	for( const cstr in CELL120.INDEX ) {
-			label_nodes(nodes, CELL120.INDEX[cstr], Number(cstr));
-		}
-
-}
-
-
-
 function link_labels(nodes, link) {
 	const n1 = nodes.filter((n) => n.id === link.source);
 	const n2 = nodes.filter((n) => n.id === link.target);
@@ -395,52 +355,88 @@ function link_labels(nodes, link) {
 }
 
 
+// version of the 120-cell where nodes are partitioned by 
+// layer and the links follow that
 
-export const cell120 = () => {
+export const cell120_layered = (max) => {
 	const nodes  = make_120cell_vertices();
 	const links = auto_detect_edges(nodes, 4);
 
-	label_120cell(nodes);
+	nodes.map((n) => n.label = 9); // make all invisible by default
+
+	for (const cstr in CELL120.LAYERS ) {
+		label_nodes(nodes, CELL120.LAYERS[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.unshift({
+			name: "Layer " + String(i),
+			links: [...layers],
+			nodes: [...layers]
+		})
+	}
 
 	return {
+		name: '120-cell layered',
 		nodes: nodes,
 		links: links,
 		geometry: {
 			node_size: 0.02,
 			link_size: 0.02
 		},
+		options: options
 	}
 }
 
 
-const cell120_some_inscribed = (ps) => {
+
+
+export const cell120_inscribed = () => {
 	const nodes  = make_120cell_vertices();
 	const links = auto_detect_edges(nodes, 4);
 
-	label_120cell(nodes);
+  	for( const cstr in CELL120.INDEX ) {
+		label_nodes(nodes, CELL120.INDEX[cstr], Number(cstr));
+	}
 
-	const all_links = links;
+	links.map((l) => l.label = 0);
-	all_links.map((l) => l.label = 0);
 
-	for( const p of ps) {
+	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);
-		all_links.push(...links600);
+		links.push(...links600);
 	}
 
 	return {
+		name: '120-cell',
 		nodes: nodes,
-		links: all_links,
+		links: links,
 		geometry: {
 			node_size: 0.02,
 			link_size: 0.02
 		},
+		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 ] }
+		]
 	}
 }
 
-export const cell120_inscribed = () => cell120_some_inscribed([1]);
-export const cell120_all_inscribed = () => cell120_some_inscribed([1,2,3,4,5]);
 
 
 // Schoute's partition via https://arxiv.org/abs/1010.4353
@@ -618,48 +614,31 @@ 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,
-		geometry: {
-			node_size: 0.02,
-			link_size: 0.02
-		}
-	}
-}
-
-
-
-const cell600_some_inscribed = (ps) => {
-	const nodes  = make_600cell_vertices();
-	const links = auto_detect_edges(nodes, 12);
-
-	const all_links = links;
-	all_links.map((l) => l.label = 0);
-
-	for( const p of ps) {
-		const nodes24 = nodes.filter((n) => n.label === p);
-		const links24 = auto_detect_edges(nodes24, 8);
-		links24.map((l) => l.label = p);
-		all_links.push(...links24);
-	}
-
-	return {
-		nodes: nodes,
-		links: all_links,
 		geometry: {
 			node_size: 0.02,
 			link_size: 0.02
 		},
+		options: [
+			{ name: "none", links: [ 0 ]},
+			{ name: "one 24-cell", links: [ 0, 1 ] },
+			{ name: "five 24-cells", links: [ 0, 1, 2, 3, 4, 5 ] }
+		]
 	}
 }
 
-
-export const cell600_inscribed = () => cell600_some_inscribed([1]);
-export const cell600_all_inscribed = () => cell600_some_inscribed([1,2,3,4,5]);
-
-
-
 function make_dodecahedron_vertices() {
 	const phi = 0.5 * (1 + Math.sqrt(5));  
 	const phiinv = 1 / phi;    
@@ -697,41 +676,42 @@ function make_dodecahedron_vertices() {
 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,
-		geometry: {
-			node_size: 0.02,
-			link_size: 0.02
-		}
-	}
-}
-
-const dodecahedron_some_inscribed = (ps) => {
-	const nodes  = make_dodecahedron_vertices();
-	const links = auto_detect_edges(nodes, 3);
-	const all_links = links;
-	all_links.map((l) => l.label = 0);
-
-	for( const p of ps) {
-		const tetran = nodes.filter((n) => n.label === p);
-		const tetral = auto_detect_edges(tetran, 3);
-		tetral.map((l) => l.label = p);
-		all_links.push(...tetral);
-	}
-
-	return {
-		nodes: nodes,
-		links: all_links,
 		geometry: {
 			node_size: 0.02,
 			link_size: 0.02
 		},
+		options: [
+			{ name: "none", links: [ 0 ]},
+			{ name: "one tetrahedron", links: [ 0, 1 ] },
+			{ name: "five tetrahedra", links: [ 0, 1, 2, 3, 4, 5 ] }
+		]
+
 	}
 }
 
 
-export const dodecahedron_inscribed = () => dodecahedron_some_inscribed([1]);
+export const build_all = () => {
-export const dodecahedron_all_inscribed = () => dodecahedron_some_inscribed([1,2,3,4,5]);
+	return [
-
+	 	dodecahedron(),
+	 	cell5(),
+		cell16(),
+		tesseract(),
+		cell24(),
+		cell600(),
+	 	cell120_inscribed(),
+	 	cell120_layered()
+	 	];
+}