Added dodecahedron with compound of five cubes, refactored the

inscribed polytopes into one function

cellindex.js

@@ -1,188 +1 @@
-
+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

@@ -1,20 +1,14 @@
 import ColorScheme from 'color-scheme';
-import Color from 'color';
 
 export const get_colours = (basis) => {
-	const basis_c = Color(basis);
-	const hslb = basis_c.hsl();
-	const hue = hslb['color'][0];
-	const saturation = hslb['color'][1];
-	const luminance = hslb['color'][2];
 	const scheme = new ColorScheme;
-	scheme.from_hue(hue).scheme("tetrade").distance(0.75);
+	const hexbasis = basis.toString(16).padStart(6, "0");
-	const colours = scheme.colors().slice(1, 9);
+	scheme.from_hex(hexbasis).scheme("tetrade").variation("hard").distance(0.5);
-	colours.reverse();
+	const colours = scheme.colors().map((cs) => parseInt('0x' + cs));
-	const hsl = colours.map((c) => Color("#" + c).hsl());
+	const set = colours.slice(1, 6);
-	const resaturated = hsl.map((hslc) => hslc.saturationl(saturation).rgbNumber()); 
+	set.reverse();
-	resaturated.unshift(basis);
+	set.unshift(colours[0]);
-	return resaturated;
+	return set;
 }
 
 // basic colours where 0 = blue

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 {
 
@@ -15,10 +15,11 @@ 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();
 	}
 
@@ -34,7 +35,7 @@ class FourDShape extends THREE.Group {
 		}
 	}
 
-	makeNode(material, v3, scale) {
+	makeNode(material, v3) {
 		const geometry = new THREE.SphereGeometry(this.node_size);
 		const sphere = new THREE.Mesh(geometry, material);
 		sphere.position.copy(v3);
@@ -43,45 +44,33 @@ class FourDShape extends THREE.Group {
 	}
 
 	makeLink(material, link) {
-		const n1 = this.nodes3[link.source];
+		const n1 = this.nodes3[link.source].v3;
-		const n2 = this.nodes3[link.target];
+		const n2 = this.nodes3[link.target].v3;
-		const s1 = n1.scale;
+		const length = n1.distanceTo(n2);
-		const s2 = n2.scale;
-		const length = n1.v3.distanceTo(n2.v3);
 		const centre = new THREE.Vector3();
-		centre.lerpVectors(n1.v3, n2.v3, 0.5);
+		centre.lerpVectors(n1, n2, 0.5);
-		const geometry = new THREE.CylinderGeometry(
+		const geometry = new THREE.CylinderGeometry(this.link_size, this.link_size, 1);
-			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.v3);
+		edge.lookAt(n2);
 		cyl.rotation.x = Math.PI / 2.0;
 		this.add(edge);
 		return edge;
 	}
 
-	updateLink(link, links_show) {
+	updateLink(link) {
-		const n1 = this.nodes3[link.source];
+		const n1 = this.nodes3[link.source].v3;
-		const n2 = this.nodes3[link.target];
+		const n2 = this.nodes3[link.target].v3;
-		const s1 = n1.scale;
+		const length = n1.distanceTo(n2);
-		const s2 = n2.scale;
-		const length = n1.v3.distanceTo(n2.v3);
 		const centre = new THREE.Vector3();
-		centre.lerpVectors(n1.v3, n2.v3, 0.5);
+		centre.lerpVectors(n1, n2, 0.5);
-		// take the average of the ends as the thickness - as a workaround,
+		link.object.scale.copy(new THREE.Vector3(this.link_scale, this.link_scale, length));
-		// 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.v3);
+		link.object.lookAt(n2);
 		link.object.children[0].rotation.x = Math.PI / 2.0;
-		link.object.visible = (!links_show || link.label in links_show); 
 	}
 
 
@@ -110,42 +99,23 @@ class FourDShape extends THREE.Group {
 	}
 
 
-	fourDtoV3_old(x, y, z, w, rotations) {
+	fourDtoV3(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.fourDscale(v4.w);
+		const k = this.hyperplane / (this.hyperplane + 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 k = this.fourDscale(n.w);
+			const v3 = this.fourDtoV3(n.x, n.y, n.z, 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,
-				scale: k,
+				object: this.makeNode(material, v3)
-				label: n.label,
-				object: this.makeNode(material, v3, k)
 			};
 		}
 		for( const l of this.links ) {
@@ -159,22 +129,17 @@ class FourDShape extends THREE.Group {
 	}
 
 
-	render3(rotations, nodes_show, links_show) {
+	render3(rotations) {
 		this.scalev3 = new THREE.Vector3(this.node_scale, this.node_scale, this.node_scale);
 		for( const n of this.nodes4 ) {
-			const v4 = this.fourDrotate(n.x, n.y, n.z, n.w,  rotations);
+			const v3 = this.fourDtoV3(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(s3);
+			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, links_show);
+			this.updateLink(l);
 		}
 
 		for( const f of this.faces ) {
@@ -182,6 +147,7 @@ class FourDShape extends THREE.Group {
 		}
 	}
 
+
 }
 
 export { FourDShape };

gui.js

@@ -1,26 +1,20 @@
 import { GUI } from 'lil-gui';
 
 
+
 const DEFAULTS = {
-	nodesize: 0.25,
+	thickness: 0.25,
-	nodeopacity: 1,
+	nodesize: 1.25,
-	linksize: 0.2,
+	linkopacity: 0.5,
-	linkopacity: 0.75,
+	link2opacity: 0.5,
-	link2opacity: 0.75,
+	shape: 'five-cubes',
-	shape: '120-cell',
-	option: 'none',
-	visibility: 5,
 	inscribed: false,
 	inscribe_all: false,
 	color: 0x3293a9,
 	background: 0xd4d4d4,
-	hyperplane: 0.93,
+	hyperplane: 2,
-	zoom: 1,
+	rotation: 'rigid',
-	xRotate: 'YW',
-	yRotate: 'XW',
 	dtheta: 0,
-	damping: false,
-	captions: true,
 	dpsi: 0,
 }
 
@@ -28,78 +22,51 @@ const DEFAULTS = {
 
 class FourDGUI {
 
-	constructor(shapes, changeShape, setColor, setBackground, setNodeOpacity,setLinkOpacity, setVisibility, showDocs) {
+	constructor(changeShape, setColor, setBackground, setLinkOpacity) {
 		this.gui = new GUI();
-		const SHAPE_NAMES = shapes.map((s) => s.name);
-
 		this.parseLinkParams();
 		const guiObj = this;
 		this.params = {
 			shape: this.link['shape'],
-			option: this.link['option'],
 			inscribed: this.link['inscribed'],
 			inscribe_all: this.link['inscribe_all'],
-			linksize: this.link['linksize'],
+			thickness: this.link['thickness'],
 			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'],
+			rotation: this.link['rotation'],
-			xRotate: this.link['xRotate'],
-			yRotate: this.link['yRotate'],
 			damping: false,
-			captions: true,
 			dtheta: this.link['dtheta'],
 			dpsi: this.link['dpsi'],
 			"copy link": function () { guiObj.copyUrl() }
 		};
-		let options_ctrl;
+
-		this.gui.add(this.params, 'shape', SHAPE_NAMES).onChange((shape) => {
+		this.gui.add(this.params, 'shape',
-			const options = this.getShapeOptions(shapes, shape);
+			[ 'dodecahedron', 'five-cubes', '5-cell', '16-cell', 'tesseract',
-			options_ctrl = options_ctrl.options(options).onChange((option) => {
+				'24-cell', '600-cell', '120-cell' ]
-				setVisibility(option)
+		).onChange(changeShape)
-			});
+		this.gui.add(this.params, 'inscribed').onChange(changeShape);
-			options_ctrl.setValue(options[0])
+		this.gui.add(this.params, 'inscribe_all').onChange(changeShape);
-			changeShape(shape)
+		this.gui.add(this.params, 'hyperplane', 1.5, 2.25);
-		});
+		this.gui.add(this.params, 'thickness', 0.1, 2);
-		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.add(this.params, 'nodesize', 0.1, 4);
 		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, 'rotation', [ 'rigid', 'tumbling', 'inside-out', 'axisymmetrical' ]);
-		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);
@@ -128,7 +95,7 @@ class FourDGUI {
 		const guiObj = this;
 
 		this.urlParams = this.linkUrl.searchParams;
-		for( const param of [ "shape", "xRotate", "yRotate", "option" ]) {
+		for( const param of [ "shape", "rotation" ]) {
 			const value = this.urlParams.get(param);
 			if( value ) {
 				this.link[param] = value;
@@ -140,12 +107,10 @@ class FourDGUI {
 			this.link[param] = ( this.urlParams.get(param) === 'y' );
 		}
 		this.link['hyperplane'] = this.numParam('hyperplane', parseFloat);
-		this.link['zoom'] = this.numParam('zoom', parseFloat);
+		this.link['thickness'] = this.numParam('thickness', 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);
@@ -156,20 +121,16 @@ 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("linksize", this.params.linksize.toString());
+		url.searchParams.append("thickness", this.params.thickness.toString());
 		url.searchParams.append("nodesize", this.params.nodesize.toString());
-		url.searchParams.append("nodeopacity", this.params.nodesize.toString());
+		url.searchParams.append("linkopacity", this.params.thickness.toString());
-		url.searchParams.append("linkopacity", this.params.nodeopacity.toString());
+		url.searchParams.append("link2opacity", this.params.nodesize.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("rotation", this.params.rotation);
-		url.searchParams.append("xRotate", this.params.xRotate);
-		url.searchParams.append("yRotate", this.params.yRotate);
 		url.searchParams.append("dtheta", this.params.dtheta.toString());
 		url.searchParams.append("dpsi", this.params.dpsi.toString());
 		this.copyTextToClipboard(url);

index.html

@@ -5,15 +5,6 @@
 		<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;
@@ -25,8 +16,7 @@
 	</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>
+			<a target="_blank" href="https://github.com/spikelynch/fourdjs">source</a></div>
 	</body>
 </html>

layer600cell.js

@@ -1,173 +0,0 @@
-
-
-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

@@ -3,13 +3,12 @@ import * as THREE from 'three';
 
 
 import * as POLYTOPES from './polytopes.js';
-import { rotfn } from './rotation.js';
+import { get_rotation } from './rotation.js';
 import { FourDGUI, DEFAULTS } from './gui.js';
 import { FourDShape } from './fourDShape.js';
 import { get_colours } from './colours.js';
 
 const FACE_OPACITY = 0.3;
-const CAMERA_K = 5;
 
 // scene, lights and camera
 
@@ -24,10 +23,7 @@ scene.add(light);
 const amblight = new THREE.AmbientLight(0xffffff, 0.5);
 scene.add(amblight);
 
-camera.position.set(0, 0, CAMERA_K / 2);
+camera.position.z = 4;
-
-camera.lookAt(0, 0, 0);
-//camera.position.z = 4;
 
 const renderer = new THREE.WebGLRenderer({antialias: true});
 renderer.setSize( window.innerWidth, window.innerHeight );
@@ -47,19 +43,11 @@ 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 } )
@@ -71,46 +59,54 @@ for( const face_m of face_ms ) {
 }
 
 
-const STRUCTURES = POLYTOPES.build_all();
+const STRUCTURES = {
+	'5-cell': POLYTOPES.cell5(),
+	'16-cell': POLYTOPES.cell16(),
+	'tesseract': POLYTOPES.tesseract(),
+	'24-cell': POLYTOPES.cell24(),
+	'dodecahedron': POLYTOPES.dodecahedron(),
+	'five-cubes': POLYTOPES.five_cubes(),
+	'120-cell': POLYTOPES.cell120(),
+	'600-cell': POLYTOPES.cell600(),
+};
 
-const STRUCTURES_BY_NAME = {};
+const INSCRIBED = {
+	'tesseract': POLYTOPES.tesseract_inscribed(),
+	'24-cell': POLYTOPES.cell24_inscribed(),
+	'120-cell': POLYTOPES.cell120_inscribed(),
+	'600-cell': POLYTOPES.cell600_inscribed(),
+	'dodecahedron': POLYTOPES.dodecahedron_inscribed(),
+	'five-cubes': POLYTOPES.five_cubes_inscribed(),
+};
 
-STRUCTURES.map((s) => STRUCTURES_BY_NAME[s.name] = s);
+const ALL_INSCRIBED = {
+	'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(),
+	'five-cubes': POLYTOPES.five_cubes_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);
 	}
-	structure = STRUCTURES_BY_NAME[name];
+	let structure = STRUCTURES[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);
-}
-
-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
@@ -132,51 +128,23 @@ function setBackground(c) {
 }
 
 function setLinkOpacity(o, primary) {
-	if( structure.nolink2opacity ) {
-		link_ms.map((lm) => lm.opacity = o);
-	} else {
 	if( primary ) {
 		link_ms[0].opacity = o;
 	} else {
-			link_ms.slice(1).map((lm) => lm.opacity = o);
+		for( const lm of link_ms.slice(1) ) {
+			lm.opacity = o;
 		}
 	}
 }
 
-function setNodeOpacity(o) {
+let gui; // 
-	node_ms.map((nm) => nm.opacity = o);
-}
-
-
-let gui; 
-
 
 function changeShape() {
-	createShape(gui.params.shape);
+	console.log("change shape!")
-	displayDocs(gui.params.shape);
+	createShape(gui.params.shape, gui.params.inscribed, gui.params.inscribe_all);
 }
 
-function setVisibility(option_name) {
+gui = new FourDGUI(changeShape, setColors, setBackground, setLinkOpacity);
-	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);
@@ -219,8 +187,7 @@ renderer.domElement.addEventListener("pointerup", (event) => {
 	dragging = false;
 })
 
-createShape(gui.params.shape, gui.params.option);
+createShape(gui.params.shape, gui.params.inscribed, gui.params.inscribe_all);
-displayDocs(gui.params.shape);
 
 function animate() {
 	requestAnimationFrame( animate );
@@ -234,18 +201,12 @@ function animate() {
 		}
 	}
 
-	const rotations = [
+	const rotations = get_rotation(gui.params.rotation, theta, psi);
-		rotfn[gui.params.xRotate](theta), 
-		rotfn[gui.params.yRotate](psi)
-	];
-	shape.hyperplane = 1 / gui.params.hyperplane;
-	camera.position.set(0, 0, gui.params.zoom * CAMERA_K * gui.params.hyperplane);
 
+	shape.hyperplane = gui.params.hyperplane;
+	shape.link_scale = gui.params.thickness;
 	shape.node_scale = gui.params.nodesize;
-	shape.link_scale = gui.params.linksize * gui.params.nodesize * 0.5;
+	shape.render3(rotations);
-	shape.render3(rotations, node_show, link_show);
-
-
 
 	renderer.render( scene, camera );
 }

package-lock.json

@@ -4,11 +4,9 @@
   "requires": true,
   "packages": {
     "": {
-      "name": "fourdjs",
       "dependencies": {
-        "color": "^4.2.3",
         "color-scheme": "^1.0.1",
-        "lil-gui": "^0.19.0",
+        "lil-gui": "^0.18.2",
         "three": "^0.154.0"
       },
       "devDependencies": {
@@ -16,9 +14,9 @@
       }
     },
     "node_modules/@esbuild/android-arm": {
-      "version": "0.18.20",
+      "version": "0.18.15",
-      "resolved": "https://registry.npmjs.org/@esbuild/android-arm/-/android-arm-0.18.20.tgz",
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       "optionalDependencies": {
-        "@esbuild/android-arm": "0.18.20",
+        "@esbuild/android-arm": "0.18.15",
-        "@esbuild/android-arm64": "0.18.20",
+        "@esbuild/android-arm64": "0.18.15",
-        "@esbuild/android-x64": "0.18.20",
+        "@esbuild/android-x64": "0.18.15",
-        "@esbuild/darwin-arm64": "0.18.20",
+        "@esbuild/darwin-arm64": "0.18.15",
-        "@esbuild/darwin-x64": "0.18.20",
+        "@esbuild/darwin-x64": "0.18.15",
-        "@esbuild/freebsd-arm64": "0.18.20",
+        "@esbuild/freebsd-arm64": "0.18.15",
-        "@esbuild/freebsd-x64": "0.18.20",
+        "@esbuild/freebsd-x64": "0.18.15",
-        "@esbuild/linux-arm": "0.18.20",
+        "@esbuild/linux-arm": "0.18.15",
-        "@esbuild/linux-arm64": "0.18.20",
+        "@esbuild/linux-arm64": "0.18.15",
-        "@esbuild/linux-ia32": "0.18.20",
+        "@esbuild/linux-ia32": "0.18.15",
-        "@esbuild/linux-loong64": "0.18.20",
+        "@esbuild/linux-loong64": "0.18.15",
-        "@esbuild/linux-mips64el": "0.18.20",
+        "@esbuild/linux-mips64el": "0.18.15",
-        "@esbuild/linux-ppc64": "0.18.20",
+        "@esbuild/linux-ppc64": "0.18.15",
-        "@esbuild/linux-riscv64": "0.18.20",
+        "@esbuild/linux-riscv64": "0.18.15",
-        "@esbuild/linux-s390x": "0.18.20",
+        "@esbuild/linux-s390x": "0.18.15",
-        "@esbuild/linux-x64": "0.18.20",
+        "@esbuild/linux-x64": "0.18.15",
-        "@esbuild/netbsd-x64": "0.18.20",
+        "@esbuild/netbsd-x64": "0.18.15",
-        "@esbuild/openbsd-x64": "0.18.20",
+        "@esbuild/openbsd-x64": "0.18.15",
-        "@esbuild/sunos-x64": "0.18.20",
+        "@esbuild/sunos-x64": "0.18.15",
-        "@esbuild/win32-arm64": "0.18.20",
+        "@esbuild/win32-arm64": "0.18.15",
-        "@esbuild/win32-ia32": "0.18.20",
+        "@esbuild/win32-ia32": "0.18.15",
-        "@esbuild/win32-x64": "0.18.20"
+        "@esbuild/win32-x64": "0.18.15"
       }
     },
     "node_modules/fsevents": {
-      "version": "2.3.3",
+      "version": "2.3.2",
-      "resolved": "https://registry.npmjs.org/fsevents/-/fsevents-2.3.3.tgz",
+      "resolved": "https://registry.npmjs.org/fsevents/-/fsevents-2.3.2.tgz",
-      "integrity": "sha512-5xoDfX+fL7faATnagmWPpbFtwh/R77WmMMqqHGS65C3vvB0YHrgF+B1YmZ3441tMj5n63k0212XNoJwzlhffQw==",
+      "integrity": "sha512-xiqMQR4xAeHTuB9uWm+fFRcIOgKBMiOBP+eXiyT7jsgVCq1bkVygt00oASowB7EdtpOHaaPgKt812P9ab+DDKA==",
       "dev": true,
       "hasInstallScript": true,
       "optional": true,
@@ -460,15 +421,10 @@
         "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": "0.19.0",
+      "version": "0.18.2",
-      "resolved": "https://registry.npmjs.org/lil-gui/-/lil-gui-0.19.0.tgz",
+      "resolved": "https://registry.npmjs.org/lil-gui/-/lil-gui-0.18.2.tgz",
-      "integrity": "sha512-02/Z7rPng3GXWFwkQVj1hQaJYo2fIEYctqe0ima5uI/N2HEagB9ZGCQKkVWr3UuKfTr0arto3Q9prTB8sxtJJw=="
+      "integrity": "sha512-DgdrLy3/KGC0PiQLKgOcJMPItP4xY4iWgJ9+91Zaxfr8GCTmMps05QS9w9jW7yspILlbscbquwjOwxmWnSx5Uw=="
     },
     "node_modules/nanoid": {
       "version": "3.3.6",
@@ -495,9 +451,9 @@
       "dev": true
     },
     "node_modules/postcss": {
-      "version": "8.4.31",
+      "version": "8.4.27",
-      "resolved": "https://registry.npmjs.org/postcss/-/postcss-8.4.31.tgz",
+      "resolved": "https://registry.npmjs.org/postcss/-/postcss-8.4.27.tgz",
-      "integrity": "sha512-PS08Iboia9mts/2ygV3eLpY5ghnUcfLV/EXTOW1E2qYxJKGGBUtNjN76FYHnMs36RmARn41bC0AZmn+rR0OVpQ==",
+      "integrity": "sha512-gY/ACJtJPSmUFPDCHtX78+01fHa64FaU4zaaWfuh1MhGJISufJAH4cun6k/8fwsHYeK4UQmENQK+tRLCFJE8JQ==",
       "dev": true,
       "funding": [
         {
@@ -523,9 +479,9 @@
       }
     },
     "node_modules/rollup": {
-      "version": "3.29.4",
+      "version": "3.26.3",
-      "resolved": "https://registry.npmjs.org/rollup/-/rollup-3.29.4.tgz",
+      "resolved": "https://registry.npmjs.org/rollup/-/rollup-3.26.3.tgz",
-      "integrity": "sha512-oWzmBZwvYrU0iJHtDmhsm662rC15FRXmcjCk1xD771dFDx5jJ02ufAQQTn0etB2emNk4J9EZg/yWKpsn9BWGRw==",
+      "integrity": "sha512-7Tin0C8l86TkpcMtXvQu6saWH93nhG3dGQ1/+l5V2TDMceTxO7kDiK6GzbfLWNNxqJXm591PcEZUozZm51ogwQ==",
       "dev": true,
       "bin": {
         "rollup": "dist/bin/rollup"
@@ -538,14 +494,6 @@
         "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",
@@ -561,14 +509,14 @@
       "integrity": "sha512-Uzz8C/5GesJzv8i+Y2prEMYUwodwZySPcNhuJUdsVMH2Yn4Nm8qlbQe6qRN5fOhg55XB0WiLfTPBxVHxpE60ug=="
     },
     "node_modules/vite": {
-      "version": "4.5.3",
+      "version": "4.4.6",
-      "resolved": "https://registry.npmjs.org/vite/-/vite-4.5.3.tgz",
+      "resolved": "https://registry.npmjs.org/vite/-/vite-4.4.6.tgz",
-      "integrity": "sha512-kQL23kMeX92v3ph7IauVkXkikdDRsYMGTVl5KY2E9OY4ONLvkHf04MDTbnfo6NKxZiDLWzVpP5oTa8hQD8U3dg==",
+      "integrity": "sha512-EY6Mm8vJ++S3D4tNAckaZfw3JwG3wa794Vt70M6cNJ6NxT87yhq7EC8Rcap3ahyHdo8AhCmV9PTk+vG1HiYn1A==",
       "dev": true,
       "dependencies": {
         "esbuild": "^0.18.10",
-        "postcss": "^8.4.27",
+        "postcss": "^8.4.26",
-        "rollup": "^3.27.1"
+        "rollup": "^3.25.2"
       },
       "bin": {
         "vite": "bin/vite.js"

package.json

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

polytopes.js

@@ -1,6 +1,6 @@
 import * as PERMUTE from './permute.js';
 
-import * as CELLINDEX from './cellindex.js';
+import * as CELL120 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;
 }
 
-export function auto_detect_edges(nodes, neighbours, debug=false) {
+function auto_detect_edges(nodes, neighbours, debug=false) {
 	const seen = {};
 	const nnodes = nodes.length;
 	const links = [];
@@ -58,15 +58,15 @@ export function auto_detect_edges(nodes, neighbours, debug=false) {
 // too small and simple to calculate
 
 export const cell5 = () => {
-	const c1 = Math.sqrt(5) / 4;
+	const r5 = Math.sqrt(5);
+	const r2 = Math.sqrt(2) / 2;
 	return {
-		name: '5-cell',
 		nodes: [
-	      {id:1, label: 1, x: c1, y: c1, z: c1, w: -0.25 },
+	      {id:1, label: 1, x: r2, y: r2, z: r2, w: -r2 / r5 },
-	      {id:2, label: 2, x: c1, y: -c1, z: -c1, w: -0.25 },
+	      {id:2, label: 2, x: r2, y: -r2, z: -r2, w: -r2 / r5 },
-	      {id:3, label: 3, x: -c1, y: c1, z: -c1, w: -0.25 },
+	      {id:3, label: 3, x: -r2, y: r2, z: -r2, w: -r2 / r5 },
-	      {id:4, label: 4, x: -c1, y: -c1, z: c1, w: -0.25 },
+	      {id:4, label: 4, x: -r2, y: -r2, z: r2, w: -r2 / r5 },
-	      {id:5, label: 5, x: 0, y: 0, z: 0, w: 1 },
+	      {id:5, label: 5, x: 0, y: 0, z: 0, w: 4 * r2 / r5 },
 		],
 		links: [
 			{ id:1, source:1, target: 2},
@@ -80,12 +80,10 @@ export const cell5 = () => {
 			{ id:9, source:3, target: 5},
 			{ id:10, source:4, target: 5},
 		],
-		options: [ { name: '--' }],
+		geometry: {
-		description: `Five tetrahedra joined at ten faces with three
+			node_size: 0.02,
-		tetrahedra around each edge. The 5-cell is the simplest regular
+			link_size: 0.02
-		four-D polytope and the four-dimensional analogue of the tetrahedron.
+		}
-		A corresponding polytope, or simplex, exists for every n-dimensional
-		space.`,
 	};
 };
 
@@ -104,18 +102,16 @@ export const cell16 = () => {
 	nodes[1].label = 4;
 
 	index_nodes(nodes);
-	scale_nodes(nodes, 0.5);
+	scale_nodes(nodes, 0.75);
 	const links = auto_detect_edges(nodes, 6);
 
 	return {
-		name: '16-cell',
 		nodes: nodes,
 		links: links,
-		options: [ { name: '--' }],
+		geometry: {
-		description: `Sixteen tetrahedra joined at 32 faces with four
+			node_size: 0.02,
-		tetrahedra around each edge. The 16-cell is the four-dimensional
+			link_size: 0.02
-		analogue of the octahedron and is dual to the tesseract. Every
+		}
-		n-dimensional space has a corresponding polytope in this family.`,
 	};
 };
 
@@ -133,37 +129,41 @@ export const tesseract = () => {
 		}
 	}
 
-	scale_nodes(nodes, 0.5);
+	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,
-		options: [
+		geometry: {
-			{ name: 'none', links: [ 0 ] },
+			node_size: 0.02,
-			{ name: 'one 16-cell', links: [ 0, 1 ] },
+			link_size: 0.02
-			{ 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 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 },
@@ -185,17 +185,9 @@ 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] ) {
@@ -206,23 +198,35 @@ export const cell24 = () => {
 	// });
 
 	return {
-		name: '24-cell',
 		nodes: nodes,
 		links: links,
-		base: {},
+		geometry: {
-		options: [
+			node_size: 0.02,
-			{ name: 'none', links: [ 0 ] },
+			link_size: 0.02
-			{ 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.`,
 	};
 }
 
 
+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]);
 
 
 
@@ -304,7 +308,7 @@ function auto_120cell_faces(links) {
 
 
 
-export function make_120cell_vertices() {
+function make_120cell_vertices() {
 	const phi = 0.5 * (1 + Math.sqrt(5));  
 	const r5 = Math.sqrt(5);   
 	const phi2 = phi * phi;    
@@ -322,14 +326,14 @@ export function make_120cell_vertices() {
 		PERMUTE.coordinates([2, 1, phi, phiinv], 0, true),
 		].flat();
 	index_nodes(nodes);
-	scale_nodes(nodes, 0.25 * Math.sqrt(2));
+	scale_nodes(nodes, 0.5);
+	label_120cell(nodes);
+
 	return nodes;
 }
 
 
 
-
-
 function label_nodes(nodes, ids, label) {
 	nodes.filter((n) => ids.includes(n.id)).map((n) => n.label = label);
 }
@@ -337,8 +341,16 @@ 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 ) {
@@ -351,6 +363,33 @@ 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);
@@ -358,88 +397,126 @@ function link_labels(nodes, link) {
 }
 
 
-// version of the 120-cell where nodes are partitioned by 
-// layer and the links follow that
 
-export const cell120_layered = (max) => {
+export const cell120 = () => {
 	const nodes  = make_120cell_vertices();
 	const links = auto_detect_edges(nodes, 4);
 
-	nodes.map((n) => n.label = 9); // make all invisible by default
+	label_120cell(nodes);
 
-	for (const cstr in CELLINDEX.LAYERS120 ) {
+	return {
-		label_nodes(nodes, CELLINDEX.LAYERS120[cstr], Number(cstr));
+		nodes: nodes,
+		links: links,
+		geometry: {
+			node_size: 0.02,
+			link_size: 0.02
+		},
+	}
 }
 
-	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 inscribed_polytope = (vertex_fn, edges, inscr_edges, parts) => {
-	const layers = [];
+	const nodes  = vertex_fn();
+	const links = auto_detect_edges(nodes, edges);
 
-	for( const i of [ 0, 1, 2, 3, 4, 5, 6, 7 ] ) {
+	const all_links = links;
-		layers.push(i);
+	all_links.map((l) => l.label = 0);
-		options.push({
+
-			name: CELLINDEX.LAYER_NAMES[i],
+	for( const p of parts ) {
-			links: [...layers],
+		const nodes_in = nodes.filter((n) => n.label === p);
-			nodes: [...layers]
+		const links_in = auto_detect_edges(nodes_in, inscr_edges);
-		})
+		links_in.map((l) => l.label = p);
+		all_links.push(...links_in);
 	}
 
 	return {
-		name: '120-cell layered',
 		nodes: nodes,
-		links: links,
+		links: all_links,
-		nolink2opacity: true,
+		geometry: {
-		options: options,
+			node_size: 0.02,
-		description: `This version of the 120-cell lets you explore its
+			link_size: 0.02
-		structure by building each layer from the 'north pole' onwards.`,
+		},
 	}
 }
 
 
+export const cell120_inscribed = () => inscribed_polytope(
+	make_120cell_vertices, 4, 12, [1]
+);
+export const cell120_all_inscribed = () => inscribed_polytope(
+	make_120cell_vertices, 4, 12, [1,2,3,4,5]
+);
 
 
-export const cell120_inscribed = () => {
+// Schoute's partition via https://arxiv.org/abs/1010.4353
-	const nodes  = make_120cell_vertices();
-	const links = auto_detect_edges(nodes, 4);
 
-  	for( const cstr in CELLINDEX.INDEX120 ) {
+const partition600 = {
-		label_nodes(nodes, CELLINDEX.INDEX120[cstr], Number(cstr));
-	}
 
-	links.map((l) => l.label = 0);
+	"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,
 
-	for( const p of [ 1, 2, 3, 4, 5 ]) {
+	"k,0,-t,-1": 2,
-		const nodes600 = nodes.filter((n) => n.label === p);
+	"0,k,1,-t": 2,
-		const links600 = auto_detect_edges(nodes600, 12);
+	"t,-1,k,0": 2,
-		links600.map((l) => l.label = p);
+	"1,t,0,k": 2,
-		links.push(...links600);
+	"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,
 
-	return {
+	"t,0,1,k": 3,
-		name: '120-cell',
+	"0,t,-k,1": 3,
-		nodes: nodes,
+	"1,-k,-t,0": 3,
-		links: links,
+	"k,1,0,-t": 3,
-		options: [
+	"0,k,1,t": 3,
-			{ name: "none", links: [ 0 ]},
+	"t,1,-k,0": 3,
-			{ name: "one inscribed 600-cell", links: [ 0, 1 ] },
+	"k,0,t,-1": 3,
-			{ name: "five inscribed 600-cells", links: [ 0, 1, 2, 3, 4, 5 ] }
+	"1,-t,0,k": 3,
-		],
+	"t,-k,0,-1": 3,
-		description: `The 120-cell is the four-dimensional analogue of the
+	"0,1,-t,-k": 3,
-		dodecahedron, and consists of 120 dodecahedra joined at 720 faces,
+	"1,0,-k,t": 3,
-		with three dodecahedra around each edge. It is dual to the 600-cell,
+	"k,t,1,0": 3,
-		and five 600-cells can be inscribed in its vertices.`,
-	}
-}
 
+	"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
+};
 
 
 
@@ -481,7 +558,7 @@ function map_coord(i, coords, values) {
 }
 
 
-export function make_600cell_vertices() {
+function make_600cell_vertices() {
 	const coords = {
 		0: '0',
 		1: '1',
@@ -505,7 +582,7 @@ export function make_600cell_vertices() {
 	].flat();
 
 	for( const n of nodes ) {
-		n.label = label_vertex(n, coords, CELLINDEX.PARTITION600);
+		n.label = label_vertex(n, coords, partition600);
 	}
 
 	for( const n of nodes ) {
@@ -516,7 +593,7 @@ export function make_600cell_vertices() {
 
 
 	index_nodes(nodes);
-	scale_nodes(nodes, 0.5);
+	scale_nodes(nodes, 0.75);
 	return nodes;
 }
 
@@ -530,6 +607,7 @@ 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);
@@ -545,108 +623,22 @@ export const cell600 = () => {
 	const nodes  = make_600cell_vertices();
 	const links = auto_detect_edges(nodes, 12);
 
-	links.map((l) => l.label = 0);
-
-	for( const p of [1, 2, 3, 4, 5]) {
-		const nodes24 = nodes.filter((n) => n.label === p);
-		const links24 = auto_detect_edges(nodes24, 8);
-		links24.map((l) => l.label = p);
-		links.push(...links24);
-	}
-
 	return {
-		name: '600-cell',
 		nodes: nodes,
 		links: links,
-		options: [
+		geometry: {
-			{ name: "none", links: [ 0 ]},
+			node_size: 0.02,
-			{ name: "one 24-cell", links: [ 0, 1 ] },
+			link_size: 0.02
-			{ 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_inscribed = () => inscribed_polytope(
-export const cell600_layered = () => {
+	make_600cell_vertices, 12, 8, [1]
-	const nodes  = make_600cell_vertices();
+);
-	const links = auto_detect_edges(nodes, 12);
+export const cell600_all_inscribed = () => inscribed_polytope(
-
+	make_600cell_vertices, 12, 8, [1,2,3,4,5]
-	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() {
@@ -679,7 +671,6 @@ function make_dodecahedron_vertices() {
 			{ 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;
 }
@@ -687,180 +678,65 @@ 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,
-		options: [
+		geometry: {
-			{ name: "none", links: [ 0 ]},
+			node_size: 0.02,
-			{ name: "one tetrahedron", links: [ 0, 1 ] },
+			link_size: 0.02
-			{ 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 dodecahedron_inscribed = () => inscribed_polytope(
+	make_dodecahedron_vertices, 3, 3, [1]
+);
+export const dodecahedron_all_inscribed = () => inscribed_polytope(
+	make_dodecahedron_vertices, 3, 3, [1,2,3,4,5]
+);
 
-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 = () => {
+// this can't be done with inscribed_polytope because each vertex
-	const nodes = [
+// belongs to two cubes
-		{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 dodecahedron_five_cubes = (parts) => {
-
+	const nodes  = make_dodecahedron_vertices();
-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 });
+	const all_links = links;
-	return {
+	all_links.map((l) => l.label = 0);
-		name: 'Cube',
+
-		nodes: nodes,
+	const CUBES = { 
-		links: links,
+		1: [ 1, 2, 3, 4, 5, 6, 7, 8 ],
-		options: [ { name: '--' }],
+		2: [ 4, 5, 10, 11, 13, 16, 17, 20],
-		description: `The three-dimensional measure polytope, the tesseract is its four-dimensional analogue.`,
+		3: [ 2, 7, 9, 12, 13, 16, 18, 19],
+		4: [ 1, 8, 10, 11, 14, 15, 18, 19],
+		5: [ 3, 6, 9, 12, 14, 15, 17, 20]
 	};
-
+	if( parts.length > 0 ) {
+	//	console.log(parts);
+		//console.log(parts.map(String));
+		//nodes.map((n) => n.label = 0);
+		for( const label of parts.map(String) ) {
+			console.log(`label = ${label}`);
+			const cube = nodes.filter((n) => CUBES[label].includes(n.id));
+			const cubel = auto_detect_edges(cube, 3);
+			cubel.map((l) => l.label = Number(label));
+			all_links.push(...cubel);
  		}
-
-
-
-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,
+		links: all_links,
-		options: [
+		geometry: {
-			{ name: "--"},
+			node_size: 0.02,
-		],
+			link_size: 0.02
-		description: `The icosahedron is a twenty-sided polyhedron and is dual to the dodecahedron. Its four-dimensional analogue is the 600-cell.`
+		}
-
 	}
 }
 
+export const five_cubes = () => dodecahedron_five_cubes([]);
+export const five_cubes_inscribed = () => dodecahedron_five_cubes([1]);
+export const five_cubes_all_inscribed = () => dodecahedron_five_cubes([1,2,3,4,5]);
 
-export const build_all = () => {
-	return [
-		tetrahedron(),
-		octahedron(),
-		cube(),
-		icosahedron(),
-	 	dodecahedron(),
-	 	cell5(),
-		cell16(),
-		tesseract(),
-		cell24(),
-		snub24cell(),
-		cell600(),
-		cell600_layered(),
-	 	cell120_inscribed(),
-	 	cell120_layered()
-	 	];
-}
-
-export const radii = (shape) => {
-	return shape.nodes.map(n => Math.sqrt(n.x * n.x + n.y * n.y + n.z * n.z + n.w * n.w))
-}

rotation.js

@@ -81,5 +81,24 @@ export const rotfn = {
 	ZW: rotZW,
 };
 
+const rotMode = {
+	'rigid': [ rotYW, rotXW ],
+	'tumbling': [ rotYW, rotXZ  ],
+	'inside-out': [ rotYW, rotXY ],
+	'axisymmetrical': [ rotZW, rotXY ]
+};
+
+
+export const get_rotation = (mode, theta, psi) => {
+	const fns = rotMode[mode];
+	return [ fns[0](theta), fns[1](psi) ];
+}
+
+
+
+	// [
+	// 	rotfn[gui.params.xRotate](theta), 
+	// 	rotfn[gui.params.yRotate](psi)
+	// ];
 
 

testbed.js

@@ -1,6 +1,5 @@
 
-// code for generating the 120-cell labels
+//testbed for playing with stuff in node repl
-// has some overlap with permute - FIXME
 
 const THREE =require('three');
 
@@ -134,7 +133,7 @@ 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;
 }
 
-export function auto_detect_edges(nodes, neighbours, debug=false) {
+function auto_detect_edges(nodes, neighbours, debug=false) {
 	const seen = {};
 	const nnodes = nodes.length;
 	const links = [];
@@ -169,7 +168,7 @@ export function auto_detect_edges(nodes, neighbours, debug=false) {
 
 
 
-export function make_120cell_vertices() {
+function make_120cell_vertices() {
 	const phi = 0.5 * (1 + Math.sqrt(5));  
 	const r5 = Math.sqrt(5);   
 	const phi2 = phi * phi;    
@@ -231,7 +230,7 @@ function fingerprint(ids) {
 
 
 
-export function auto_120cell_faces(links) {
+function auto_120cell_faces(links) {
 	const faces = [];
 	const seen = {};
 	let id = 1;
@@ -487,7 +486,7 @@ 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( let i = 0; i < 5; i ++ ) {
+	for( i = 0; i < 5; i ++ ) {
 		p[i] = colours[nextvs[i]];
 	}
 	const nlabels = colour_dodecahedron_from_face(nextdd, p);
@@ -530,33 +529,6 @@ 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);
 
@@ -696,9 +668,8 @@ function arctic(nodes, links, faces, startf, startn, max) {
 
 
 
-// this is the final one that works for the whole 120-cell
 
-export function label_120cell(nodes, links, faces, startf, startn) {
+function arctic_two(nodes, links, faces, startf, startn) {
 	const pole = face_plus_to_dodecahedron(faces, startf, startn);
 	const dds = [ pole ];
 
@@ -717,6 +688,10 @@ export function label_120cell(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 ] ) {
@@ -747,8 +722,6 @@ export function label_120cell(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(
@@ -777,10 +750,7 @@ export function label_120cell(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(
@@ -808,124 +778,6 @@ export function label_120cell(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 
@@ -963,6 +815,7 @@ 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,
@@ -1042,7 +895,7 @@ 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);
@@ -1060,134 +913,39 @@ function make_dodecahedron_vertices() {
 	const phiinv = 1 / phi;    
 
 	const nodes = [
-			{ x: 1, y: 1, z: 1, w: 0 },
+			{ x: 1, y: 1, z: 1, w: 0, 			label: 4 },
-			{ x: 1, y: 1, z: -1, w: 0 },
+			{ x: 1, y: 1, z: -1, w: 0, 			label: 3 },
-			{ x: 1, y: -1, z: 1, w: 0 },
+			{ x: 1, y: -1, z: 1, w: 0, 			label: 3 },
-			{ x: 1, y: -1, z: -1, w: 0 },
+			{ x: 1, y: -1, z: -1, w: 0, 		label: 2 },
-			{ x: -1, y: 1, z: 1, w: 0 },
+
-			{ x: -1, y: 1, z: -1, w: 0 },
+			{ x: -1, y: 1, z: 1, w: 0, 			label: 3 },
-			{ x: -1, y: -1, z: 1, w: 0 },
+			{ x: -1, y: 1, z: -1, w: 0, 		label: 1 },
-			{ x: -1, y: -1, z: -1, w: 0 }
+			{ x: -1, y: -1, z: 1, w: 0, 		label: 5 },
-		].flat();
+			{ x: -1, y: -1, z: -1, w: 0, 		label: 3 },
-	scale_nodes(nodes, 0.5);
+
+			{ 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},
+		];
+	index_nodes(nodes);
 	return nodes;
 }
  
 
-// this one does the coherent indexing / partition into 600-cells
+// const nodes = make_120cell_vertices();
-
+// const links = auto_detect_edges(nodes, 4);
-export function make_labelled_120cell() {
+// const faces = auto_120cell_faces(links);
-	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")

vite.config.js

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