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

is making large objects like the 120-cell noticeably stuttery

cellindex.js

@@ -1 +1,188 @@
-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 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

@@ -1,12 +1,29 @@
 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;
-	const hexbasis = basis.toString(16).padStart(6, "0");
+	scheme.from_hue(hue).scheme("tetrade").distance(0.75);
-	scheme.from_hex(hexbasis).scheme("tetrade").variation("hard").distance(0.5);
+	const colours = scheme.colors().slice(1, 9);
-	return scheme.colors().map((cs) => parseInt('0x' + cs));
+	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,

fourDShape.js

@@ -2,7 +2,7 @@ import * as THREE from 'three';
 
 
 const HYPERPLANE = 2.0;
-
+const W_FORESHORTENING = 0.04;
 
 class FourDShape extends THREE.Group {
 
@@ -15,11 +15,10 @@ class FourDShape extends THREE.Group {
 		this.nodes3 = {};
 		this.links = structure.links;
 		this.faces = ( "faces" in structure ) ? structure.faces : [];
-		this.node_size = structure.geometry.node_size;
-		this.link_size = structure.geometry.link_size;
 		this.node_scale = 1;
 		this.link_scale = 1;
 		this.hyperplane = HYPERPLANE;
+		this.foreshortening = W_FORESHORTENING;
 		this.initShapes();
 	}
 
@@ -35,7 +34,7 @@ class FourDShape extends THREE.Group {
 		}
 	}
 
-	makeNode(material, v3) {
+	makeNode(material, v3, scale) {
 		const geometry = new THREE.SphereGeometry(this.node_size);
 		const sphere = new THREE.Mesh(geometry, material);
 		sphere.position.copy(v3);
@@ -44,33 +43,45 @@ 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(this.link_size, this.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(this.link_scale, this.link_scale, 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); 
 	}
 
 
@@ -99,23 +110,42 @@ class FourDShape extends THREE.Group {
 	}
 
 
-	fourDtoV3(x, y, z, w, rotations) {
+	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 ) {
@@ -129,17 +159,22 @@ 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);
+			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);
-			this.nodes3[n.id].object.scale.copy(this.scalev3);
+			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);
+			this.updateLink(l, links_show);
 		}
 
 		for( const f of this.faces ) {
@@ -147,7 +182,6 @@ class FourDShape extends THREE.Group {
 		}
 	}
 
-
 }
 
 export { FourDShape };

gui.js

@@ -1,18 +1,26 @@
 import { GUI } from 'lil-gui';
 
 
-
 const DEFAULTS = {
-	thickness: 0.25,
+	nodesize: 0.25,
-	nodesize: 1.25,
+	nodeopacity: 1,
-	linkopacity: 0.5,
+	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: 2,
+	hyperplane: 0.93,
+	zoom: 1,
 	xRotate: 'YW',
-	yRotate: 'XZ',
+	yRotate: 'XW',
 	dtheta: 0,
+	damping: false,
+	captions: true,
 	dpsi: 0,
 }
 
@@ -20,43 +28,78 @@ const DEFAULTS = {
 
 class FourDGUI {
 
-	constructor(createShape, setColor, setBackground, setLinkOpacity) {
+	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'],
-			thickness: this.link['thickness'],
+			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',
+		this.gui.add(this.params, 'shape', SHAPE_NAMES).onChange((shape) => {
-			[ '5-cell', '16-cell', 'tesseract', '24-cell', '600-cell', '120-cell', '120-cell-inscribed' ]
+			const options = this.getShapeOptions(shapes, shape);
-		).onChange(createShape)
+			options_ctrl = options_ctrl.options(options).onChange((option) => {
-
+				setVisibility(option)
-		this.gui.add(this.params, 'hyperplane', 1.5, 2.25);
+			});
-		this.gui.add(this.params, 'thickness', 0.1, 2);
+			options_ctrl.setValue(options[0])
-		this.gui.add(this.params, 'linkopacity', 0, 1).onChange(setLinkOpacity);
+			changeShape(shape)
-		this.gui.add(this.params, 'nodesize', 0.1, 4);
+		});
+		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);
@@ -82,9 +125,10 @@ class FourDGUI {
 	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" ]) {
+		for( const param of [ "shape", "xRotate", "yRotate", "option" ]) {
 			const value = this.urlParams.get(param);
 			if( value ) {
 				this.link[param] = value;
@@ -92,11 +136,16 @@ class FourDGUI {
 				this.link[param] = DEFAULTS[param];
 			}
 		}
-		const guiObj = this;
+		for( const param of [ "inscribed", "inscribe_all"] ) {
+			this.link[param] = ( this.urlParams.get(param) === 'y' );
+		}
 		this.link['hyperplane'] = this.numParam('hyperplane', parseFloat);
-		this.link['thickness'] = this.numParam('thickness', 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);
@@ -107,11 +156,18 @@ class FourDGUI {
 	copyUrl() {
 		const url = new URL(this.linkUrl.origin + this.linkUrl.pathname);
 		url.searchParams.append("shape", this.params.shape);
-		url.searchParams.append("thickness", this.params.thickness.toString());
+		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());

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>

label120cell.js

@@ -1,5 +1,6 @@
 
-//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');
 
@@ -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);
@@ -908,24 +1055,153 @@ function check_120cell_nodes(nodes) {
 	});
 }
 
+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 },
+			{ x: 1, y: 1, z: -1, w: 0 },
+			{ x: 1, y: -1, z: 1, w: 0 },
+			{ x: 1, y: -1, z: -1, w: 0 },
+			{ x: -1, y: 1, z: 1, w: 0 },
+			{ x: -1, y: 1, z: -1, w: 0 },
+			{ x: -1, y: -1, z: 1, w: 0 },
+			{ x: -1, y: -1, z: -1, w: 0 }
+		].flat();
+	scale_nodes(nodes, 0.5);
+	return nodes;
+}
+ 
+
+// this one does the coherent indexing / partition into 600-cells
+
+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;
+}
 
-console.log("Calculating 120-cell colours")
+// calculate the w-distance of a dodecahedron's centroid
 
-const a2 = arctic_two(nodes, links, faces, faces[0], 341)
+export function dd_w_distance(nodes, dd) {
+	const vertices = new Set();
+	dd.map((f) => f.nodes.map((n) => vertices.add(n)));
 
-console.log(`got ${a2.dodecahedra.length}`);
+	let w = 0;
+	for( const nid of vertices ) {
+		const node = node_by_id(nodes, nid);
+		w += node.w;
+	}
+	return w / 20;
+}
 
-const labels = a2.labels;
 
-console.log("labelling nodes");
+export function sort_dds_w(nodes, dds) {
-for( const cstr in labels ) {
+	dds.sort((a, b) => {
-	label_nodes(nodes, labels[cstr], Number(cstr));
+		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")
+
+// const a2 = arctic_two(nodes, links, faces, faces[0], 341)
+
+// console.log(`got ${a2.dodecahedra.length}`);
+
+// const labels = a2.labels;
+
+// console.log("labelling nodes");
+// for( const cstr in labels ) {
+// 	label_nodes(nodes, labels[cstr], Number(cstr));
+// }
+
+
+

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

@@ -9,6 +9,7 @@ import { FourDShape } from './fourDShape.js';
 import { get_colours } from './colours.js';
 
 const FACE_OPACITY = 0.3;
+const CAMERA_K = 5;
 
 // scene, lights and camera
 
@@ -23,7 +24,10 @@ scene.add(light);
 const amblight = new THREE.AmbientLight(0xffffff, 0.5);
 scene.add(amblight);
 
-camera.position.z = 4;
+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 );
@@ -43,11 +47,19 @@ material.opacity = 0.5;
 const node_ms = node_colours.map((c) => new THREE.MeshStandardMaterial({color: c}));
 const link_ms = node_colours.map((c) => new THREE.MeshStandardMaterial({color: c}));
 
+node_ms.map((m) => {
+	m.transparent =  true;
+	m.opacity = 1.0;
+	}
+);
+
 link_ms.map((m) => {
 	m.transparent =  true;
 	m.opacity = 0.5;
 	}
-)
+);
+
+
 
 const face_ms = [
 	new THREE.MeshLambertMaterial( { color: 0x44ff44 } )
@@ -59,24 +71,46 @@ for( const face_m of face_ms ) {
 }
 
 
-const STRUCTURES = {
+const STRUCTURES = POLYTOPES.build_all();
-	'5-cell': POLYTOPES.cell5(),
+
-	'16-cell': POLYTOPES.cell16(),
+const STRUCTURES_BY_NAME = {};
-	'tesseract': POLYTOPES.tesseract(),
+
-	'24-cell': POLYTOPES.cell24(),
+STRUCTURES.map((s) => STRUCTURES_BY_NAME[s.name] = s);
-	'120-cell': POLYTOPES.cell120(),
-	'120-cell-inscribed': POLYTOPES.cell120_inscribed(),
-	'600-cell': POLYTOPES.cell600()
-};
 
 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, face_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
@@ -97,13 +131,52 @@ function setBackground(c) {
 	scene.background = new THREE.Color(c)
 }
 
-function setLinkOpacity(o) {
+function setLinkOpacity(o, primary) {
-	for( const lm of link_ms ) {
+	if( structure.nolink2opacity ) {
-		lm.opacity = o;
+		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);
+		}
 	}
 }
 
-const gui = new FourDGUI(createShape, setColors, setBackground, setLinkOpacity);
+function setNodeOpacity(o) {
+	node_ms.map((nm) => nm.opacity = o);
+}
+
+
+let gui; 
+
+
+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`);
+	}
+}
+
+
+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);
@@ -146,7 +219,8 @@ renderer.domElement.addEventListener("pointerup", (event) => {
 	dragging = false;
 })
 
-createShape(gui.params.shape);
+createShape(gui.params.shape, gui.params.option);
+displayDocs(gui.params.shape);
 
 function animate() {
 	requestAnimationFrame( animate );
@@ -164,10 +238,14 @@ function animate() {
 		rotfn[gui.params.xRotate](theta), 
 		rotfn[gui.params.yRotate](psi)
 	];
-	shape.hyperplane = gui.params.hyperplane;
+	shape.hyperplane = 1 / gui.params.hyperplane;
-	shape.link_scale = gui.params.thickness;
+	camera.position.set(0, 0, gui.params.zoom * CAMERA_K * gui.params.hyperplane);
+
 	shape.node_scale = gui.params.nodesize;
-	shape.render3(rotations);
+	shape.link_scale = gui.params.linksize * gui.params.nodesize * 0.5;
+	shape.render3(rotations, node_show, link_show);
+
+
 
 	renderer.render( scene, camera );
 }

package-lock.json

@@ -4,9 +4,11 @@
   "requires": true,
   "packages": {
     "": {
+      "name": "fourdjs",
       "dependencies": {
+        "color": "^4.2.3",
         "color-scheme": "^1.0.1",
-        "lil-gui": "^0.18.2",
+        "lil-gui": "^0.19.0",
         "three": "^0.154.0"
       },
       "devDependencies": {
@@ -14,9 +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"
       ],
@@ -30,9 +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"
       ],
@@ -46,9 +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"
       ],
@@ -62,9 +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"
       ],
@@ -78,9 +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"
       ],
@@ -94,9 +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"
       ],
@@ -110,9 +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"
       ],
@@ -126,9 +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"
       ],
@@ -142,9 +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"
       ],
@@ -158,9 +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"
       ],
@@ -174,9 +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"
       ],
@@ -190,9 +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"
       ],
@@ -206,9 +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"
       ],
@@ -222,9 +224,9 @@
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     "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==",
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       "cpu": [
         "riscv64"
       ],
@@ -238,9 +240,9 @@
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     },
     "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"
       ],
@@ -254,9 +256,9 @@
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     },
     "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"
       ],
@@ -270,9 +272,9 @@
       }
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     "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"
       ],
@@ -286,9 +288,9 @@
       }
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     "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"
       ],
@@ -302,9 +304,9 @@
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     "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"
       ],
@@ -318,9 +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"
       ],
@@ -334,9 +336,9 @@
       }
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     "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"
       ],
@@ -350,9 +352,9 @@
       }
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     "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"
       ],
@@ -365,15 +367,52 @@
         "node": ">=12"
       }
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+    "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": {
@@ -383,34 +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,
@@ -421,10 +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",
@@ -451,9 +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": [
         {
@@ -479,9 +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"
@@ -494,6 +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",
@@ -509,14 +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

@@ -1,7 +1,8 @@
 {
   "dependencies": {
+    "color": "^4.2.3",
     "color-scheme": "^1.0.1",
-    "lil-gui": "^0.18.2",
+    "lil-gui": "^0.19.0",
     "three": "^0.154.0"
   },
   "devDependencies": {

polytopes.js

@@ -1,6 +1,6 @@
 import * as PERMUTE from './permute.js';
 
-import * as CELL120 from './cellindex.js';
+import * as CELLINDEX from './cellindex.js';
 
 function index_nodes(nodes, scale) {
 	let i = 1;
@@ -22,7 +22,7 @@ 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 = [];
@@ -58,15 +58,15 @@ function auto_detect_edges(nodes, neighbours, debug=false) {
 // 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, label: 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, label: 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, label: 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, label: 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, label: 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},
@@ -80,10 +80,12 @@ export const cell5 = () => {
 			{ id:9, source:3, target: 5},
 			{ id:10, source:4, target: 5},
 		],
-		geometry: {
+		options: [ { name: '--' }],
-			node_size: 0.02,
+		description: `Five tetrahedra joined at ten faces with three
-			link_size: 0.02
+		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.`,
 	};
 };
 
@@ -102,16 +104,18 @@ export const cell16 = () => {
 	nodes[1].label = 4;
 
 	index_nodes(nodes);
-	scale_nodes(nodes, 0.75);
+	scale_nodes(nodes, 0.5);
 	const links = auto_detect_edges(nodes, 6);
 
 	return {
+		name: '16-cell',
 		nodes: nodes,
 		links: links,
-		geometry: {
+		options: [ { name: '--' }],
-			node_size: 0.02,
+		description: `Sixteen tetrahedra joined at 32 faces with four
-			link_size: 0.02
+		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.`,
 	};
 };
 
@@ -129,21 +133,37 @@ export const tesseract = () => {
 		}
 	}
 
-	scale_nodes(nodes, Math.sqrt(2) / 2);
+	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,
-		geometry: {
+		options: [
-			node_size: 0.02,
+			{ name: 'none', links: [ 0 ] },
-			link_size: 0.02
+			{ 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 },
@@ -151,6 +171,11 @@ const CELL24_INDEXING = {
 };
 
 
+function node_by_id(nodes, nid) {
+	const ns = nodes.filter((n) => n.id === nid);
+	return ns[0];
+}
+
 
 export const cell24 = () => {
 	const nodes = PERMUTE.coordinates([0, 0, 1, 1], 0);
@@ -160,20 +185,47 @@ export const cell24 = () => {
 		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,
-		geometry: {
+		base: {},
-			node_size: 0.02,
+		options: [
-			link_size: 0.02
+			{ 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.`,
 	};
 }
 
 
+
+
+
 // face detection for the 120-cell
 
 // NOTE: all of these return node ids, not nodes
@@ -252,7 +304,7 @@ function auto_120cell_faces(links) {
 
 
 
-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;    
@@ -270,12 +322,14 @@ function make_120cell_vertices() {
 		PERMUTE.coordinates([2, 1, phi, phiinv], 0, true),
 		].flat();
 	index_nodes(nodes);
-	scale_nodes(nodes, 0.5);
+	scale_nodes(nodes, 0.25 * Math.sqrt(2));
 	return nodes;
 }
 
 
 
+
+
 function label_nodes(nodes, ids, label) {
 	nodes.filter((n) => ids.includes(n.id)).map((n) => n.label = label);
 }
@@ -283,16 +337,8 @@ 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 ) {
@@ -305,33 +351,6 @@ 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);
@@ -339,120 +358,88 @@ 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 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,
-		geometry: {
+		nolink2opacity: true,
-			node_size: 0.02,
+		options: options,
-			link_size: 0.02
+		description: `This version of the 120-cell lets you explore its
-		},
+		structure by building each layer from the 'north pole' onwards.`,
 	}
 }
 
 
+
+
 export const cell120_inscribed = () => {
 	const nodes  = make_120cell_vertices();
 	const links = auto_detect_edges(nodes, 4);
 
-	label_120cell(nodes);
+  	for( const cstr in CELLINDEX.INDEX120 ) {
+		label_nodes(nodes, CELLINDEX.INDEX120[cstr], Number(cstr));
+	}
 
-	const all_links = links;
+	links.map((l) => l.label = 0);
-	all_links.map((l) => l.label = 0);
 
-	for( const p of [ 5 ]) {
+	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: {
+		options: [
-			node_size: 0.02,
+			{ name: "none", links: [ 0 ]},
-			link_size: 0.02
+			{ 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.`,
 	}
 }
 
 
-// Schoute's partition via https://arxiv.org/abs/1010.4353
-
-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
-};
 
 
 
@@ -494,7 +481,7 @@ function map_coord(i, coords, values) {
 }
 
 
-function make_600cell_vertices() {
+export function make_600cell_vertices() {
 	const coords = {
 		0: '0',
 		1: '1',
@@ -518,7 +505,7 @@ function make_600cell_vertices() {
 	].flat();
 
 	for( const n of nodes ) {
-		n.label = label_vertex(n, coords, partition600) - 1;
+		n.label = label_vertex(n, coords, CELLINDEX.PARTITION600);
 	}
 
 	for( const n of nodes ) {
@@ -529,7 +516,7 @@ function make_600cell_vertices() {
 
 
 	index_nodes(nodes);
-	scale_nodes(nodes, 0.75);
+	scale_nodes(nodes, 0.5);
 	return nodes;
 }
 
@@ -543,7 +530,6 @@ function get_node(nodes, id) {
 }
 
 function audit_link_labels(nodes, links) {
-	console.log("Link audit");
 	for( const l of links ) {
 		const n1 = get_node(nodes, l.source);
 		const n2 = get_node(nodes, l.target);
@@ -559,14 +545,322 @@ 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: {
+		options: [
-			node_size: 0.02,
+			{ name: "none", links: [ 0 ]},
-			link_size: 0.02
+			{ 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))
+}

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' ]
+				}
+			}		
+		}
+	}	
 })