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1ec7955861
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b22ac6546d
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@ -2,7 +2,7 @@ import * as THREE from 'three';
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const HYPERPLANE = 2.0;
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const NODE_FORESHORTENING = 0.4;
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class FourDShape extends THREE.Group {
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@ -35,7 +35,7 @@ class FourDShape extends THREE.Group {
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}
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}
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makeNode(material, v3, scale) {
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makeNode(material, v3) {
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const geometry = new THREE.SphereGeometry(this.node_size);
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const sphere = new THREE.Mesh(geometry, material);
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sphere.position.copy(v3);
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@ -100,41 +100,24 @@ class FourDShape extends THREE.Group {
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}
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fourDtoV3_old(x, y, z, w, rotations) {
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fourDtoV3(x, y, z, w, rotations) {
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const v4 = new THREE.Vector4(x, y, z, w);
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for ( const m4 of rotations ) {
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v4.applyMatrix4(m4);
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}
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const k = this.fourDscale(v4.w);
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const k = this.hyperplane / (this.hyperplane + v4.w);
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return new THREE.Vector3(v4.x * k, v4.y * k, v4.z * k);
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}
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fourDscale(w) {
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return this.hyperplane / ( this.hyperplane + w );
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}
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fourDrotate(x, y, z, w, rotations) {
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const v4 = new THREE.Vector4(x, y, z, w);
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for ( const m4 of rotations ) {
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v4.applyMatrix4(m4);
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}
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return v4;
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}
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fourDtoV3(v4) {
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const k = this.fourDscale(v4.w);
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return new THREE.Vector3(v4.x * k, v4.y * k, v4.z * k);
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}
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initShapes() {
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for( const n of this.nodes4 ) {
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const k = this.fourDscale(n.w);
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const v3 = new THREE.Vector3(n.x * k, n.y * k, n.z * k);
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const v3 = this.fourDtoV3(n.x, n.y, n.z, n.w, []);
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const material = this.getMaterial(n, this.node_ms);
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this.nodes3[n.id] = {
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v3: v3,
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label: n.label,
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object: this.makeNode(material, v3, k)
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object: this.makeNode(material, v3)
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};
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}
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for( const l of this.links ) {
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@ -151,14 +134,10 @@ class FourDShape extends THREE.Group {
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render3(rotations, nodes_show, links_show) {
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this.scalev3 = new THREE.Vector3(this.node_scale, this.node_scale, this.node_scale);
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for( const n of this.nodes4 ) {
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const v4 = this.fourDrotate(n.x, n.y, n.z, n.w, rotations);
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const k = this.fourDscale(v4.w);
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const v3 = new THREE.Vector3(v4.x * k, v4.y * k, v4.z * k);
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const s4 = k * this.node_scale * NODE_FORESHORTENING;
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const s3 = new THREE.Vector3(s4, s4, s4);
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const v3 = this.fourDtoV3(n.x, n.y, n.z, n.w, rotations);
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this.nodes3[n.id].v3 = v3;
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this.nodes3[n.id].object.position.copy(v3);
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this.nodes3[n.id].object.scale.copy(s3);
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this.nodes3[n.id].object.scale.copy(this.scalev3);
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this.nodes3[n.id].object.visible = ( !nodes_show || n.label in nodes_show );
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}
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for( const l of this.links ) {
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10
index.html
10
index.html
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@ -5,15 +5,6 @@
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<title>FourD</title>
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<style>
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body { margin: 0; }
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div#description {
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position: fixed;
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top: 0;
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left: 0;
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width: 20%;
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z-index: 2;
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font-family: sans-serif;
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padding: 1em;
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}
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div#info {
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position: fixed;
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bottom:0;
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@ -25,7 +16,6 @@
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</head>
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<body>
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<script type="module" src="/main.js"></script>
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<div id="description"></div>
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<div id="info">by <a target="_blank" href="https://mikelynch.org/">Mike Lynch</a> -
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<a target="_blank" href="https://git.tilde.town/bombinans/fourdjs">source</a></div>
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</body>
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12
main.js
12
main.js
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@ -85,16 +85,6 @@ function createShape(name, option) {
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setVisibility(option ? option : structure.options[0].name);
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}
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function displayDocs(name) {
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const docdiv = document.getElementById("description");
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const description = STRUCTURES_BY_NAME[name].description;
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if( description ) {
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docdiv.innerHTML =`<p>${name}</p><p>${description}</p>`;
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} else {
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docdiv.innerHTML =`<p>${name}</p>`;
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}
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}
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// initialise gui and read params from URL
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// callbacks to do things which are triggered by controls: reset the shape,
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@ -130,7 +120,6 @@ let gui;
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function changeShape() {
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createShape(gui.params.shape);
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displayDocs(gui.params.shape);
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}
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function setVisibility(option_name) {
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@ -195,7 +184,6 @@ renderer.domElement.addEventListener("pointerup", (event) => {
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})
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createShape(gui.params.shape, gui.params.option);
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displayDocs(gui.params.shape);
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function animate() {
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requestAnimationFrame( animate );
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64
polytopes.js
64
polytopes.js
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@ -85,12 +85,7 @@ export const cell5 = () => {
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node_size: 0.02,
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link_size: 0.02
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},
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options: [ { name: '--' }],
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description: `Five tetrahedra joined at ten faces with three
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tetrahedra around each edge. The 5-cell is the simplest regular
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four-D polytope and the four-dimensional analogue of the tetrahedron.
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A corresponding polytope, or simplex, exists for every n-dimensional
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space.`,
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options: [ { name: '--' }]
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};
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};
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@ -120,11 +115,7 @@ export const cell16 = () => {
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node_size: 0.02,
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link_size: 0.02
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},
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options: [ { name: '--' }],
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description: `Sixteen tetrahedra joined at 32 faces with four
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tetrahedra around each edge. The 16-cell is the four-dimensional
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analogue of the octahedron and is dual to the tesseract. Every
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n-dimensional space has a corresponding polytope in this family.`,
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options: [ { name: '--' }]
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};
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};
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@ -155,7 +146,7 @@ export const tesseract = () => {
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return {
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name: 'Tesseract',
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name: 'tesseract',
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nodes: nodes,
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links: links,
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geometry: {
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@ -167,12 +158,6 @@ export const tesseract = () => {
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{ name: 'one 16-cell', links: [ 0, 1 ] },
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{ name: 'both 16-cells', links: [ 0, 1, 2 ] },
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],
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description: `The most well-known four-dimensional shape, the
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tesseract is analogous to the cube, and is constructed by placing two
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cubes in parallel hyperplanes and joining their corresponding
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vertices. It consists of eight cubes joined at 32 face with three
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cubes around each edge, and is dual to the 16-cell. Every
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n-dimensional space has a cube analogue or measure polytope.`,
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};
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}
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@ -230,11 +215,7 @@ export const cell24 = () => {
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{ name: 'none', links: [ 0 ] },
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{ name: 'one 16-cell', links: [ 0, 1 ] },
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{ name: 'three 16-cells', links: [ 0, 1, 2, 3 ] }
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],
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description: `A unique object without an exact analogue in higher
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or lower dimensions, the 24-cell is made of twenty-four octahedra
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joined at 96 faces, with three around each edge. The 24-cell is
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self-dual.`,
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]
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};
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}
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@ -417,9 +398,7 @@ export const cell120_layered = (max) => {
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link_size: 0.02
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},
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nolink2opacity: true,
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options: options,
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description: `This version of the 120-cell lets you explore its
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structure by building each layer from the 'north pole' onwards.`,
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options: options
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}
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}
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@ -455,11 +434,7 @@ export const cell120_inscribed = () => {
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{ name: "none", links: [ 0 ]},
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{ name: "one inscribed 600-cell", links: [ 0, 1 ] },
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{ name: "five inscribed 600-cells", links: [ 0, 1, 2, 3, 4, 5 ] }
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],
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description: `The 120-cell is the four-dimensional analogue of the
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dodecahedron, and consists of 120 dodecahedra joined at 720 faces,
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with three dodecahedra around each edge. It is dual to the 600-cell,
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and five 600-cells can be inscribed in its vertices.`,
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]
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}
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}
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@ -590,12 +565,7 @@ export const cell600 = () => {
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{ name: "none", links: [ 0 ]},
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{ name: "one 24-cell", links: [ 0, 1 ] },
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{ name: "five 24-cells", links: [ 0, 1, 2, 3, 4, 5 ] }
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],
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description: `The 600-cell is the four-dimensional analogue of the
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icosahedron, and consists of 600 tetrahedra joined at 1200 faces
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with five tetrahedra around each edge. It is dual to the 120-cell.
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Its 120 vertices can be partitioned into five sets which form the
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vertices of five inscribed 24-cells.`,
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]
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}
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}
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@ -640,9 +610,7 @@ export const cell600_layered = () => {
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link_size: 0.02
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},
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nolink2opacity: true,
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options: options,
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description: `This version of the 600-cell lets you explore its
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structure by building each layer from the 'north pole' onwards.`,
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options: options
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}
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@ -663,7 +631,7 @@ export const snub24cell = () => {
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links.map((l) => l.label = 0);
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return {
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name: 'Snub 24-cell',
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name: 'snub 24-cell',
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nodes: nodes,
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links: links,
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geometry: {
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@ -671,11 +639,6 @@ export const snub24cell = () => {
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link_size: 0.02
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},
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options: [ { name: "--" } ],
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description: `The snub 24-cell is a semiregular polytope which
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connects the 24-cell with the 600-cell. It consists of 24 icosahedra
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and 120 tetrahedra, and is constructed by removing one of the
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five inscribed 24-cells from a 600-cell.`
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}
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@ -732,7 +695,7 @@ export const dodecahedron = () => {
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}
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return {
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name: 'Dodecahedron',
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name: 'dodecahedron',
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nodes: nodes,
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links: links,
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geometry: {
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@ -743,12 +706,7 @@ export const dodecahedron = () => {
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{ name: "none", links: [ 0 ]},
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{ name: "one tetrahedron", links: [ 0, 1 ] },
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{ name: "five tetrahedra", links: [ 0, 1, 2, 3, 4, 5 ] }
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],
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description: `The dodecahedron is a three-dimensional polyhedron
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which is included here so that you can see the partition of its
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vertices into five interlocked tetrahedra. This structure is the
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basis for the partition of the 120-cell's vertices into five
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600-cells.`
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]
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}
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}
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