Added the rest of the regular 3-d polyhedra
Mike Lynch
parent
78ebb381ee
commit
f79a90e0d9
147
polytopes.js
147
polytopes.js
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@ -755,8 +755,155 @@ export const dodecahedron = () => {
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}
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}
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export const tetrahedron = () => {
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const r2 = Math.sqrt(2);
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const r3 = Math.sqrt(3);
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return {
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name: 'Tetrahedron',
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nodes: [
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{id:1, label: 1, x: 2 * r2 / 3, y: 0, z: -1/3, w: 0 },
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{id:2, label: 2, x: -r2 / 3, y: r2 / r3, z: -1/3, w: 0 },
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{id:3, label: 3, x: -r2 / 3, y: -r2 / r3, z: -1/3, w: 0 },
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{id:4, label: 4, x: 0, y: 0, z: 1, w: 0 },
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],
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links: [
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{ id:1, source:1, target: 2},
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{ id:2, source:1, target: 3},
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{ id:3, source:1, target: 4},
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{ id:4, source:2, target: 3},
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{ id:5, source:2, target: 4},
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{ id:6, source:3, target: 4},
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],
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geometry: {
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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: `The simplest three-dimensional polytope, consisting of four triangles joined at six edges. The 5-cell is its four-dimensional analogue.`,
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};
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};
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export const octahedron = () => {
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const nodes = [
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{id: 1, label: 1, x: 1, y: 0, z: 0, w: 0},
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{id: 2, label: 1, x: -1, y: 0, z: 0, w: 0},
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{id: 3, label: 2, x: 0, y: 1, z: 0, w: 0},
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{id: 4, label: 2, x: 0, y: -1, z: 0, w: 0},
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{id: 5, label: 3, x: 0, y: 0, z: 1, w: 0},
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{id: 6, label: 3, x: 0, y: 0, z: -1, w: 0},
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];
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const links = [
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{id:1, source: 1, target: 3},
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{id:2, source: 1, target: 4},
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{id:3, source: 1, target: 5},
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{id:4, source: 1, target: 6},
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{id:5, source: 2, target: 3},
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{id:6, source: 2, target: 4},
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{id:7, source: 2, target: 5},
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{id:8, source: 2, target: 6},
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{id:9, source: 3, target: 5},
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{id:10, source: 3, target: 6},
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{id:11, source: 4, target: 5},
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{id:12, source: 4, target: 6},
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]
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links.map((l) => { l.label = 0 });
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return {
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name: 'Octahedron',
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nodes: nodes,
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links: links,
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geometry: {
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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: `The three-dimensional cross-polytope, the 16-cell is its four-dimensional analogue.`,
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};
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}
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export const cube = () => {
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const nodes = [
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{id: 1, label: 1, x: 1, y: 1, z: 1, w: 0},
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{id: 2, label: 2, x: -1, y: 1, z: 1, w: 0},
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{id: 3, label: 2, x: 1, y: -1, z: 1, w: 0},
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{id: 4, label: 1, x: -1, y: -1, z: 1, w: 0},
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{id: 5, label: 2, x: 1, y: 1, z: -1, w: 0},
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{id: 6, label: 1, x: -1, y: 1, z: -1, w: 0},
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{id: 7, label: 1, x: 1, y: -1, z: -1, w: 0},
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{id: 8, label: 2, x: -1, y: -1, z: -1, w: 0},
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];
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scale_nodes(nodes, 1/Math.sqrt(3));
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const links = auto_detect_edges(nodes, 3);
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links.map((l) => { l.label = 0 });
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return {
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name: 'Cube',
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nodes: nodes,
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links: links,
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geometry: {
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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: `The three-dimensional measure polytope, the tesseract is its four-dimensional analogue.`,
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};
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}
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function make_icosahedron_vertices() {
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const phi = 0.5 * (1 + Math.sqrt(5));
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const nodes = [
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{ x: 0, y: 1, z: phi, w: 0, label: 1 },
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{ x: 0, y: -1, z: phi, w: 0, label: 1 },
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{ x: 0, y: 1, z: -phi, w: 0, label: 1 },
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{ x: 0, y: -1, z: -phi, w: 0, label: 1 },
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{ x: 1, y: phi, z: 0, w: 0, label: 2 },
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{ x: -1, y: phi, z: 0, w: 0, label: 2 },
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{ x: 1, y: -phi, z: 0, w: 0, label: 2 },
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{ x: -1, y: -phi, z: 0, w: 0, label: 2 },
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{ x: phi, y: 0, z: 1, w: 0, label: 3},
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{ x: phi, y: 0, z: -1, w: 0, label: 3},
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{ x: -phi, y: 0, z: 1, w: 0, label: 3},
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{ x: -phi, y: 0, z: -1, w: 0, label: 3},
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];
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scale_nodes(nodes, 1/Math.sqrt((5 + Math.sqrt(5)) / 2));
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index_nodes(nodes);
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return nodes;
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}
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export const icosahedron = () => {
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const nodes = make_icosahedron_vertices();
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const links = auto_detect_edges(nodes, 5);
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links.map((l) => l.label = 0);
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return {
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name: 'Icosahedron',
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nodes: nodes,
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links: links,
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geometry: {
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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: [
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{ name: "--"},
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],
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description: `The icosahedron is a twenty-sided polyhedron and is dual to the dodecahedron. Its four-dimensional analogue is the 600-cell.`
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}
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}
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export const build_all = () => {
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export const build_all = () => {
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return [
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return [
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tetrahedron(),
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octahedron(),
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cube(),
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icosahedron(),
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dodecahedron(),
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dodecahedron(),
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cell5(),
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cell5(),
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cell16(),
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cell16(),
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