Added inscriptions for 600-cell, improved the gui, you can now see

all five 600-cells in the 120-cell for full mindbending

gui.js

@@ -6,7 +6,10 @@ const DEFAULTS = {
 	thickness: 0.25,
 	nodesize: 1.25,
 	linkopacity: 0.5,
+	link2opacity: 0.5,
 	shape: '120-cell',
+	inscribed: false,
+	inscribe_all: false,
 	color: 0x3293a9,
 	background: 0xd4d4d4,
 	hyperplane: 2,
@@ -19,14 +22,17 @@ const DEFAULTS = {
 
 class FourDGUI {
 
-	constructor(createShape, setColor, setBackground, setLinkOpacity) {
+	constructor(changeShape, setColor, setBackground, setLinkOpacity) {
 		this.gui = new GUI();
 		this.parseLinkParams();
 		const guiObj = this;
 		this.params = {
 			shape: this.link['shape'],
+			inscribed: this.link['inscribed'],
+			inscribe_all: this.link['inscribe_all'],
 			thickness: this.link['thickness'],
 			linkopacity: this.link['linkopacity'],
+			link2opacity: this.link['linkopacity'],
 			nodesize: this.link['nodesize'],
 			color: this.link['color'],
 			background: this.link['background'],
@@ -39,12 +45,19 @@ class FourDGUI {
 		};
 
 		this.gui.add(this.params, 'shape',
-			[ '5-cell', '16-cell', 'tesseract', '24-cell', '600-cell', '120-cell', '120-cell-inscribed' ]
+			[ '5-cell', '16-cell', 'tesseract',
-		).onChange(createShape)
+				'24-cell', '600-cell', '120-cell' ]
-
+		).onChange(changeShape)
+		this.gui.add(this.params, 'inscribed').onChange(changeShape);
+		this.gui.add(this.params, 'inscribe_all').onChange(changeShape);
 		this.gui.add(this.params, 'hyperplane', 1.5, 2.25);
 		this.gui.add(this.params, 'thickness', 0.1, 2);
-		this.gui.add(this.params, 'linkopacity', 0, 1).onChange(setLinkOpacity);
+		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);
@@ -79,6 +92,7 @@ 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", "rotation" ]) {
@@ -89,10 +103,13 @@ 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['linkopacity'] = this.numParam('linkopacity', parseFloat);
+		this.link['link2opacity'] = this.numParam('link2opacity', parseFloat);
 		this.link['nodesize'] = this.numParam('nodesize', parseFloat);
 		this.link['color'] = this.numParam('color', (s) => guiObj.stringToHex(s));
 		this.link['background'] = this.numParam('background', (s) => guiObj.stringToHex(s));
@@ -104,8 +121,12 @@ class FourDGUI {
 	copyUrl() {
 		const url = new URL(this.linkUrl.origin + this.linkUrl.pathname);
 		url.searchParams.append("shape", this.params.shape);
+		url.searchParams.append("inscribed", this.params.inscribed ? 'y': 'n');
+		url.searchParams.append("inscribe_all", this.params.inscribe_all ? 'y': 'n');
 		url.searchParams.append("thickness", this.params.thickness.toString());
 		url.searchParams.append("nodesize", this.params.nodesize.toString());
+		url.searchParams.append("linkopacity", this.params.thickness.toString());
+		url.searchParams.append("link2opacity", this.params.nodesize.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());

main.js

@@ -65,17 +65,39 @@ const STRUCTURES = {
 	'tesseract': POLYTOPES.tesseract(),
 	'24-cell': POLYTOPES.cell24(),
 	'120-cell': POLYTOPES.cell120(),
-	'120-cell-inscribed': POLYTOPES.cell120_inscribed(),
+	'120-cell-all-inscribed': POLYTOPES.cell120_all_inscribed(),
-	'600-cell': POLYTOPES.cell600()
+	'600-cell': POLYTOPES.cell600(),
+	'600-cell-all-inscribed': POLYTOPES.cell600_all_inscribed(),
 };
 
+const INSCRIBED = {
+	'120-cell': POLYTOPES.cell120_inscribed(),
+	'600-cell': POLYTOPES.cell600_inscribed(),
+};
+
+const ALL_INSCRIBED = {
+	'120-cell': POLYTOPES.cell120_all_inscribed(),
+	'600-cell': POLYTOPES.cell600_all_inscribed(),
+}
+
 let shape = false;
 
-function createShape(name) {
+function createShape(name, inscribed, all) {
 	if( shape ) {
 		scene.remove(shape);
 	}
-	shape = new FourDShape(node_ms, link_ms, face_ms, STRUCTURES[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);
 }
 
@@ -97,13 +119,24 @@ function setBackground(c) {
 	scene.background = new THREE.Color(c)
 }
 
-function setLinkOpacity(o) {
+function setLinkOpacity(o, primary) {
-	for( const lm of link_ms ) {
+	if( primary ) {
+		link_ms[0].opacity = o;
+	} else {
+		for( const lm of link_ms.slice(1) ) {
 			lm.opacity = o;
 		}
 	}
+}
 
-const gui = new FourDGUI(createShape, setColors, setBackground, setLinkOpacity);
+let gui; // 
+
+function changeShape() {
+	console.log("change shape!")
+	createShape(gui.params.shape, gui.params.inscribed, gui.params.inscribe_all);
+}
+
+gui = new FourDGUI(changeShape, setColors, setBackground, setLinkOpacity);
 
 // these are here to pick up colour settings from the URL params
 setColors(gui.params.color);
@@ -146,7 +179,7 @@ renderer.domElement.addEventListener("pointerup", (event) => {
 	dragging = false;
 })
 
-createShape(gui.params.shape);
+createShape(gui.params.shape, gui.params.inscribed, gui.params.inscribe_all);
 
 function animate() {
 	requestAnimationFrame( animate );

polytopes.js

@@ -151,6 +151,11 @@ 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);
@@ -163,6 +168,15 @@ export const cell24 = () => {
 	index_nodes(nodes);
 	const links = auto_detect_edges(nodes, 8);
 
+	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 {
 		nodes: nodes,
 		links: links,
@@ -357,7 +371,7 @@ export const cell120 = () => {
 }
 
 
-export const cell120_inscribed = () => {
+const cell120_some_inscribed = (ps) => {
 	const nodes  = make_120cell_vertices();
 	const links = auto_detect_edges(nodes, 4);
 
@@ -366,7 +380,7 @@ export const cell120_inscribed = () => {
 	const all_links = links;
 	all_links.map((l) => l.label = 0);
 
-	for( const p of [ 5 ]) {
+	for( const p of ps) {
 		const nodes600 = nodes.filter((n) => n.label === p);
 		const links600 = auto_detect_edges(nodes600, 12);
 		links600.map((l) => l.label = p);
@@ -383,6 +397,9 @@ export const cell120_inscribed = () => {
 	}
 }
 
+export const cell120_inscribed = () => cell120_some_inscribed([5]);
+export const cell120_all_inscribed = () => cell120_some_inscribed([1,2,3,4,5]);
+
 
 // Schoute's partition via https://arxiv.org/abs/1010.4353
 
@@ -518,7 +535,7 @@ function make_600cell_vertices() {
 	].flat();
 
 	for( const n of nodes ) {
-		n.label = label_vertex(n, coords, partition600) - 1;
+		n.label = label_vertex(n, coords, partition600);
 	}
 
 	for( const n of nodes ) {
@@ -570,3 +587,42 @@ export const cell600 = () => {
 }
 
 
+
+const cell600_some_inscribed = (ps) => {
+	const nodes  = make_600cell_vertices();
+	const links = auto_detect_edges(nodes, 12);
+
+	const all_links = links;
+	all_links.map((l) => l.label = 0);
+
+	for( const p of ps) {
+		const nodes24 = nodes.filter((n) => n.label === p);
+		const links24 = auto_detect_edges(nodes24, 8);
+		links24.map((l) => l.label = p);
+		all_links.push(...links24);
+	}
+
+	return {
+		nodes: nodes,
+		links: all_links,
+		geometry: {
+			node_size: 0.02,
+			link_size: 0.02
+		},
+	}
+
+
+	return {
+		nodes: nodes,
+		links: links,
+		geometry: {
+			node_size: 0.02,
+			link_size: 0.02
+		}
+	}
+}
+
+
+export const cell600_inscribed = () => cell600_some_inscribed([5]);
+export const cell600_all_inscribed = () => cell600_some_inscribed([1,2,3,4,5]);
+