Added the rest of the regular 3-d polyhedra

better with unit radius normalisation

gui.js

@@ -2,8 +2,8 @@ import { GUI } from 'lil-gui';
 
 
 const DEFAULTS = {
-	thickness: 1.0,
+	thickness: 0.5,
-	nodesize: 2.0,
+	nodesize: 1.5,
 	linkopacity: 0.5,
 	link2opacity: 0.5,
 	shape: '120-cell',
@@ -13,10 +13,10 @@ const DEFAULTS = {
 	inscribe_all: false,
 	color: 0x3293a9,
 	background: 0xd4d4d4,
-	hyperplane: 1.5,
+	hyperplane: 0.93,
 	zoom: 1,
 	xRotate: 'YW',
-	yRotate: 'XZ',
+	yRotate: 'XW',
 	dtheta: 0,
 	dpsi: 0,
 }
@@ -65,9 +65,9 @@ class FourDGUI {
 		options_ctrl = this.gui.add(this.params, 'option').options(options).onChange((option) => {
 			setVisibility(option)
 		});
-		this.gui.add(this.params, 'hyperplane', 1.4, 2.0);
+		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, 'thickness', 0, 2);
+		this.gui.add(this.params, 'thickness', 0, 1);
 		this.gui.add(this.params, 'linkopacity', 0, 1).onChange(
 			(v) => setLinkOpacity(v, true)
 		);

main.js

@@ -9,7 +9,7 @@ import { FourDShape } from './fourDShape.js';
 import { get_colours } from './colours.js';
 
 const FACE_OPACITY = 0.3;
-const CAMERA_K = 10;
+const CAMERA_K = 5;
 
 // scene, lights and camera
 
@@ -213,8 +213,8 @@ function animate() {
 		rotfn[gui.params.xRotate](theta), 
 		rotfn[gui.params.yRotate](psi)
 	];
-	shape.hyperplane = gui.params.hyperplane;
+	shape.hyperplane = 1 / gui.params.hyperplane;
-	camera.position.set(0, 0, gui.params.zoom * CAMERA_K / gui.params.hyperplane);
+	camera.position.set(0, 0, gui.params.zoom * CAMERA_K * gui.params.hyperplane);
 
 	shape.link_scale = gui.params.thickness;
 	shape.node_scale = gui.params.nodesize;

polytopes.js

@@ -58,16 +58,15 @@ export 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},
@@ -109,7 +108,7 @@ 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 {
@@ -142,7 +141,7 @@ 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 });
 
@@ -198,6 +197,7 @@ 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);
@@ -338,7 +338,7 @@ export 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;
 }
 
@@ -540,7 +540,7 @@ export function make_600cell_vertices() {
 
 
 	index_nodes(nodes);
-	scale_nodes(nodes, 0.75);
+	scale_nodes(nodes, 0.5);
 	return nodes;
 }
 
@@ -715,6 +715,7 @@ 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;
 }
@@ -754,8 +755,155 @@ export const dodecahedron = () => {
 }
 
 
+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},
+		],
+		geometry: {
+			node_size: 0.02,
+			link_size: 0.02
+		},
+		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,
+		geometry: {
+			node_size: 0.02,
+			link_size: 0.02
+		},
+		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,
+		geometry: {
+			node_size: 0.02,
+			link_size: 0.02
+		},
+		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,
+		geometry: {
+			node_size: 0.02,
+			link_size: 0.02
+		},
+		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(),
@@ -768,3 +916,7 @@ export const build_all = () => {
 	 	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))
+}