Finished layered view of 600-cell, refactored cellindex and moved all
of the reference data there.pull/12/head
Mike Lynch
parent
6c360fcafd
commit
777b36d048
100
cellindex.js
100
cellindex.js
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@ -1,4 +1,17 @@
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export const INDEX = {
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export const LAYER_NAMES = {
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0: "North pole",
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1: "Arctic circle",
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2: "North temperate",
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3: "Tropic of Cancer",
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4: "Equator",
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5: "Tropic of Capricorn",
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6: "South temperate",
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7: "Antarctic circle (all)"
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};
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export const INDEX120 = {
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"1": [
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27,38,48,49,61,68,74,87,95,98,105,120, 126,131,140,149,156,165,174,
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179,185,200,207,210,218,223,226,231,234,239,241,248,252,253,258,263,
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@ -46,7 +59,7 @@ export const INDEX = {
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};
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export const LAYERS = {
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export const LAYERS120 = {
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"0": [154,266,158,222,218,250,254,162,268,156,160,252,256,166,270,272,
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164,220,224,168],
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"1": [2,318,314,30,414,510,362,26,506,410,338,458,462,110,
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@ -90,3 +103,86 @@ export const LAYERS = {
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"7":[217,153,221,157,265,161,165,269,249,253,251,255,267,159,155,
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163,219,271,223,167]
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};
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// Schoute's partition via https://arxiv.org/abs/1010.4353
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export const PARTITION600 = {
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"2,0,0,0": 1,
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"0,2,0,0": 1,
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"0,0,2,0": 1,
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"0,0,0,2": 1,
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"1,1,1,1": 1,
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"1,1,-1,-1": 1,
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"1,-1,1,-1": 1,
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"1,-1,-1,1": 1,
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"1,-1,-1,-1": 1,
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"1,-1,1,1": 1,
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"1,1,-1,1": 1,
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"1,1,1,-1": 1,
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"k,0,-t,-1": 2,
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"0,k,1,-t": 2,
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"t,-1,k,0": 2,
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"1,t,0,k": 2,
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"t,k,0,-1": 2,
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"1,0,k,t": 2,
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"k,-t,-1,0": 2,
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"0,1,-t,k": 2,
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"1,k,t,0": 2,
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"t,0,-1,k": 2,
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"0,t,-k,-1": 2,
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"k,-1,0,-t": 2,
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"t,0,1,k": 3,
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"0,t,-k,1": 3,
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"1,-k,-t,0": 3,
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"k,1,0,-t": 3,
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"0,k,1,t": 3,
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"t,1,-k,0": 3,
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"k,0,t,-1": 3,
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"1,-t,0,k": 3,
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"t,-k,0,-1": 3,
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"0,1,-t,-k": 3,
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"1,0,-k,t": 3,
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"k,t,1,0": 3,
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"t,0,-1,-k": 4,
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"0,t,k,-1": 4,
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"1,-k,t,0": 4,
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"k,1,0,t": 4,
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"t,1,k,0": 4,
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"0,k,-1,-t": 4,
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"1,-t,0,-k": 4,
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"k,0,-t,1": 4,
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"0,1,t,k": 4,
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"t,-k,0,1": 4,
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"k,t,-1,0": 4,
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"1,0,k,-t": 4,
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"k,0,t,1": 5,
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"0,k,-1,t": 5,
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"t,-1,-k,0": 5,
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"1,t,0,-k": 5,
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"1,0,-k,-t": 5,
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"t,k,0,1": 5,
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"0,1,t,-k": 5,
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"k,-t,1,0": 5,
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"t,0,1,-k": 5,
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"1,k,-t,0": 5,
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"k,-1,0,t": 5,
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"0,t,k,1": 5
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};
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export const LAYERS600 = {
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"0":[2,42,46,50,54,106,110,44,48,52,56,108,112],
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"1":[10,12,14,16,18,20,22,24,34,36,38,40,98,102,100,104,90,92,94,96],
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"2":[26,58,74,28,76,30,60,32,62,78,80,64],
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"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],
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"4":[25,29,27,31,57,61,59,63,73,75,77,79],
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"5":[97,101,99,103,33,35,37,39,89,91,93,95,9,11,13,15,17,19,21,23],
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"6":[41,105,49,43,51,45,107,47,109,53,55,111],
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"7":[1]
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};
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@ -69,7 +69,7 @@ export function link_to_tetras(nodes, links, link) {
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const fp = fingerprint([n1, n2, p1, p2]);
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if( !seen[fp] ) {
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seen[fp] = true;
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tetras.push([n1, n2, p1, p2])
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tetras.push({fingerprint: fp, nodes: [n1, n2, p1, p2]})
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}
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}
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}
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@ -79,3 +79,95 @@ export function link_to_tetras(nodes, links, link) {
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}
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export function auto_600cell_cells(nodes, links) {
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const seen = {};
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const tetras = [];
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links.map((link) => {
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link_to_tetras(nodes, links, link).map((lt) => {
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if( !seen[lt.fingerprint] ) {
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seen[lt.fingerprint] = true;
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tetras.push(lt.nodes);
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}
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})
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});
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return tetras;
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}
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function node_by_id(nodes, nid) {
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const ns = nodes.filter((n) => n.id === nid);
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return ns[0];
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}
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export function tetra_w(nodes, tetra) {
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let w = 0;
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for( const nid of tetra ) {
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const node = node_by_id(nodes, nid);
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w += node.w;
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}
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return w / 4;
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}
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export function sorted_600cells() {
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const cell600 = make_600cell();
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const tetras = auto_600cell_cells(cell600.nodes, cell600.links);
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const layers = tetras.map((t) => { return { "nodes": t, w: tetra_w(cell600.nodes, t) } });
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layers.sort((a, b) => b.w - a.w);
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return layers;
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}
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// const cell600 = make_600cell();
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// const layers = sorted_600cells(cell600.nodes, cell600.links);
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// for( const cell of layers ) {
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// // const fp = fingerprint(cell.nodes);
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// console.log(`${cell.w} ${cell.nodes}`);
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// }
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export function make_layered_600cell() {
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const tetras = sorted_600cells()
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const LAYERS = [
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[ "00", 20 ],
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[ "01", 20 ],
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[ "02", 30 ],
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[ "03", 60 ],
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[ "04", 60 ],
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[ "05", 60 ],
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[ "06", 20 ],
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[ "07", 60 ],
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[ "08", 20 ],
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[ "09", 60 ],
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[ "10", 60 ],
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[ "11", 60 ],
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[ "12", 30 ],
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[ "13", 20 ],
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[ "14", 20 ]
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];
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const vertices = {};
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const seen = {};
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let i = 0;
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for( const layer of LAYERS ) {
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const label = layer[0];
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const n = layer[1];
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vertices[label] = [];
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console.log(`Layer ${label} starting at ${i}`);
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for( const t of tetras.slice(i, i + n) ) {
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console.log(t);
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for( const n of t.nodes ) {
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if( !seen[n] ) {
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vertices[label].push(n);
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seen[n] = true;
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}
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}
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}
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i += n;
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}
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return JSON.stringify(vertices);
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}
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149
polytopes.js
149
polytopes.js
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@ -1,6 +1,6 @@
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import * as PERMUTE from './permute.js';
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import * as CELL120 from './cellindex.js';
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import * as CELLINDEX from './cellindex.js';
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function index_nodes(nodes, scale) {
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let i = 1;
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@ -359,23 +359,13 @@ function link_labels(nodes, link) {
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// layer and the links follow that
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export const cell120_layered = (max) => {
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const LAYER_NAMES = {
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0: "North pole",
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1: "Arctic circle",
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2: "North temperate",
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3: "Tropic of Cancer",
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4: "Equator",
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5: "Tropic of Capricorn",
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6: "South temperate",
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7: "Antarctic circle (all)"
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};
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const nodes = make_120cell_vertices();
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const links = auto_detect_edges(nodes, 4);
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nodes.map((n) => n.label = 9); // make all invisible by default
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for (const cstr in CELL120.LAYERS ) {
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label_nodes(nodes, CELL120.LAYERS[cstr], Number(cstr));
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for (const cstr in CELLINDEX.LAYERS120 ) {
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label_nodes(nodes, CELLINDEX.LAYERS120[cstr], Number(cstr));
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}
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links.map((l) => {
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@ -393,7 +383,7 @@ export const cell120_layered = (max) => {
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for( const i of [ 0, 1, 2, 3, 4, 5, 6, 7 ] ) {
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layers.push(i);
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options.push({
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name: LAYER_NAMES[i],
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name: CELLINDEX.LAYER_NAMES[i],
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links: [...layers],
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nodes: [...layers]
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})
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@ -419,8 +409,8 @@ export const cell120_inscribed = () => {
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const nodes = make_120cell_vertices();
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const links = auto_detect_edges(nodes, 4);
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for( const cstr in CELL120.INDEX ) {
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label_nodes(nodes, CELL120.INDEX[cstr], Number(cstr));
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for( const cstr in CELLINDEX.INDEX120 ) {
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label_nodes(nodes, CELLINDEX.INDEX120[cstr], Number(cstr));
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}
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links.map((l) => l.label = 0);
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@ -450,76 +440,6 @@ export const cell120_inscribed = () => {
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// Schoute's partition via https://arxiv.org/abs/1010.4353
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const partition600 = {
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"2,0,0,0": 1,
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"0,2,0,0": 1,
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"0,0,2,0": 1,
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"0,0,0,2": 1,
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"1,1,1,1": 1,
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"1,1,-1,-1": 1,
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"1,-1,1,-1": 1,
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"1,-1,-1,1": 1,
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"1,-1,-1,-1": 1,
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"1,-1,1,1": 1,
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"1,1,-1,1": 1,
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"1,1,1,-1": 1,
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"k,0,-t,-1": 2,
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"0,k,1,-t": 2,
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"t,-1,k,0": 2,
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"1,t,0,k": 2,
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"t,k,0,-1": 2,
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"1,0,k,t": 2,
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"k,-t,-1,0": 2,
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"0,1,-t,k": 2,
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"1,k,t,0": 2,
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"t,0,-1,k": 2,
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"0,t,-k,-1": 2,
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"k,-1,0,-t": 2,
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"t,0,1,k": 3,
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"0,t,-k,1": 3,
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"1,-k,-t,0": 3,
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"k,1,0,-t": 3,
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"0,k,1,t": 3,
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"t,1,-k,0": 3,
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"k,0,t,-1": 3,
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"1,-t,0,k": 3,
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"t,-k,0,-1": 3,
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"0,1,-t,-k": 3,
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"1,0,-k,t": 3,
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"k,t,1,0": 3,
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"t,0,-1,-k": 4,
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"0,t,k,-1": 4,
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"1,-k,t,0": 4,
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"k,1,0,t": 4,
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"t,1,k,0": 4,
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"0,k,-1,-t": 4,
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"1,-t,0,-k": 4,
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"k,0,-t,1": 4,
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"0,1,t,k": 4,
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"t,-k,0,1": 4,
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"k,t,-1,0": 4,
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"1,0,k,-t": 4,
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"k,0,t,1": 5,
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"0,k,-1,t": 5,
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"t,-1,-k,0": 5,
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"1,t,0,-k": 5,
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"1,0,-k,-t": 5,
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"t,k,0,1": 5,
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"0,1,t,-k": 5,
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"k,-t,1,0": 5,
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"t,0,1,-k": 5,
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"1,k,-t,0": 5,
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"k,-1,0,t": 5,
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"0,t,k,1": 5
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};
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function partition_coord(i, coords, invert) {
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@ -584,7 +504,7 @@ export function make_600cell_vertices() {
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].flat();
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for( const n of nodes ) {
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n.label = label_vertex(n, coords, partition600);
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n.label = label_vertex(n, coords, CELLINDEX.PARTITION600);
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}
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for( const n of nodes ) {
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@ -649,6 +569,60 @@ export const cell600 = () => {
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}
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}
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export const cell600_layered = () => {
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const nodes = make_600cell_vertices();
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const links = auto_detect_edges(nodes, 12);
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nodes.map((n) => n.label = 9); // make all invisible by default
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for (const cstr in CELLINDEX.LAYERS600 ) {
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label_nodes(nodes, CELLINDEX.LAYERS600[cstr], Number(cstr));
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}
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links.map((l) => {
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const labels = link_labels(nodes, l);
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if( labels[0] >= labels[1] ) {
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l.label = labels[0];
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} else {
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l.label = labels[1];
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}
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});
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const options = [];
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const layers = [];
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for( const i of [ 0, 1, 2, 3, 4, 5, 6, 7 ] ) {
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layers.push(i);
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options.push({
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name: CELLINDEX.LAYER_NAMES[i],
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links: [...layers],
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nodes: [...layers]
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})
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}
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return {
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name: '600-cell layered',
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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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nolink2opacity: true,
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options: options
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}
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}
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function make_dodecahedron_vertices() {
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const phi = 0.5 * (1 + Math.sqrt(5));
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const phiinv = 1 / phi;
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@ -721,6 +695,7 @@ export const build_all = () => {
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tesseract(),
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cell24(),
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cell600(),
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cell600_layered(),
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cell120_inscribed(),
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cell120_layered()
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];
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