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600-cell-layers #12

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bombinans merged 2 commits from 600-cell-layers into main 2023-11-04 05:36:00 +00:00
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3 changed files with 335 additions and 91 deletions
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100
cellindex.js
View File

@ -1,4 +1,17 @@
export const INDEX = {
export const LAYER_NAMES = {
0: "North pole",
1: "Arctic circle",
2: "North temperate",
3: "Tropic of Cancer",
4: "Equator",
5: "Tropic of Capricorn",
6: "South temperate",
7: "Antarctic circle (all)"
};
export const INDEX120 = {
"1": [
27,38,48,49,61,68,74,87,95,98,105,120, 126,131,140,149,156,165,174,
179,185,200,207,210,218,223,226,231,234,239,241,248,252,253,258,263,
@ -46,7 +59,7 @@ export const INDEX = {
};
export const LAYERS = {
export const LAYERS120 = {
"0": [154,266,158,222,218,250,254,162,268,156,160,252,256,166,270,272,
164,220,224,168],
"1": [2,318,314,30,414,510,362,26,506,410,338,458,462,110,
@ -90,3 +103,86 @@ export const LAYERS = {
"7":[217,153,221,157,265,161,165,269,249,253,251,255,267,159,155,
163,219,271,223,167]
};
// Schoute's partition via https://arxiv.org/abs/1010.4353
export const PARTITION600 = {
"2,0,0,0": 1,
"0,2,0,0": 1,
"0,0,2,0": 1,
"0,0,0,2": 1,
"1,1,1,1": 1,
"1,1,-1,-1": 1,
"1,-1,1,-1": 1,
"1,-1,-1,1": 1,
"1,-1,-1,-1": 1,
"1,-1,1,1": 1,
"1,1,-1,1": 1,
"1,1,1,-1": 1,
"k,0,-t,-1": 2,
"0,k,1,-t": 2,
"t,-1,k,0": 2,
"1,t,0,k": 2,
"t,k,0,-1": 2,
"1,0,k,t": 2,
"k,-t,-1,0": 2,
"0,1,-t,k": 2,
"1,k,t,0": 2,
"t,0,-1,k": 2,
"0,t,-k,-1": 2,
"k,-1,0,-t": 2,
"t,0,1,k": 3,
"0,t,-k,1": 3,
"1,-k,-t,0": 3,
"k,1,0,-t": 3,
"0,k,1,t": 3,
"t,1,-k,0": 3,
"k,0,t,-1": 3,
"1,-t,0,k": 3,
"t,-k,0,-1": 3,
"0,1,-t,-k": 3,
"1,0,-k,t": 3,
"k,t,1,0": 3,
"t,0,-1,-k": 4,
"0,t,k,-1": 4,
"1,-k,t,0": 4,
"k,1,0,t": 4,
"t,1,k,0": 4,
"0,k,-1,-t": 4,
"1,-t,0,-k": 4,
"k,0,-t,1": 4,
"0,1,t,k": 4,
"t,-k,0,1": 4,
"k,t,-1,0": 4,
"1,0,k,-t": 4,
"k,0,t,1": 5,
"0,k,-1,t": 5,
"t,-1,-k,0": 5,
"1,t,0,-k": 5,
"1,0,-k,-t": 5,
"t,k,0,1": 5,
"0,1,t,-k": 5,
"k,-t,1,0": 5,
"t,0,1,-k": 5,
"1,k,-t,0": 5,
"k,-1,0,t": 5,
"0,t,k,1": 5
};
export const LAYERS600 = {
"0":[2,42,46,50,54,106,110,44,48,52,56,108,112],
"1":[10,12,14,16,18,20,22,24,34,36,38,40,98,102,100,104,90,92,94,96],
"2":[26,58,74,28,76,30,60,32,62,78,80,64],
"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],
"4":[25,29,27,31,57,61,59,63,73,75,77,79],
"5":[97,101,99,103,33,35,37,39,89,91,93,95,9,11,13,15,17,19,21,23],
"6":[41,105,49,43,51,45,107,47,109,53,55,111],
"7":[1]
};

173
layer600cell.js 100644
View File

@ -0,0 +1,173 @@
import * as POLYTOPES from './polytopes.js';
// face detection for the 600-cell
export function nodes_links(links, nodeid) {
return links.filter((l) => l.source === nodeid || l.target === nodeid);
}
export function linked(links, n1, n2) {
const ls = nodes_links(nodes_links(links, n1), n2);
if( ls.length ) {
return ls[0]
} else {
return false;
}
}
function fingerprint(ids) {
const sids = [...ids];
sids.sort();
return sids.join(',');
}
export function make_600cell() {
const nodes = POLYTOPES.make_600cell_vertices();
const links = POLYTOPES.auto_detect_edges(nodes, 12);
return {
nodes: nodes,
links: links
}
}
export function link_to_tetras(nodes, links, link) {
const n1 = link.source;
const n2 = link.target;
const nl1 = nodes_links(links, n1).filter((l) => l.id !== link.id);
const nl2 = nodes_links(links, n2).filter((l) => l.id !== link.id);
const p1 = new Set();
const p = new Set();
for( const nl of nl1 ) {
if( nl.source !== n1 ) {
p1.add(nl.source);
}
if( nl.target !== n1 ) {
p1.add(nl.target);
}
}
for( const nl of nl2 ) {
if( nl.source !== n2 && p1.has(nl.source) ) {
p.add(nl.source);
}
if( nl.target !== n2 && p1.has(nl.target) ) {
p.add(nl.target);
}
}
const lp = Array.from(p);
const seen = {};
const tetras = [];
for( const p1 of lp ) {
for( const p2 of lp ) {
if( p1 != p2 ) {
if( linked(links, p1, p2) ) {
const fp = fingerprint([n1, n2, p1, p2]);
if( !seen[fp] ) {
seen[fp] = true;
tetras.push({fingerprint: fp, nodes: [n1, n2, p1, p2]})
}
}
}
}
}
return tetras;
}
export function auto_600cell_cells(nodes, links) {
const seen = {};
const tetras = [];
links.map((link) => {
link_to_tetras(nodes, links, link).map((lt) => {
if( !seen[lt.fingerprint] ) {
seen[lt.fingerprint] = true;
tetras.push(lt.nodes);
}
})
});
return tetras;
}
function node_by_id(nodes, nid) {
const ns = nodes.filter((n) => n.id === nid);
return ns[0];
}
export function tetra_w(nodes, tetra) {
let w = 0;
for( const nid of tetra ) {
const node = node_by_id(nodes, nid);
w += node.w;
}
return w / 4;
}
export function sorted_600cells() {
const cell600 = make_600cell();
const tetras = auto_600cell_cells(cell600.nodes, cell600.links);
const layers = tetras.map((t) => { return { "nodes": t, w: tetra_w(cell600.nodes, t) } });
layers.sort((a, b) => b.w - a.w);
return layers;
}
// const cell600 = make_600cell();
// const layers = sorted_600cells(cell600.nodes, cell600.links);
// for( const cell of layers ) {
// // const fp = fingerprint(cell.nodes);
// console.log(`${cell.w} ${cell.nodes}`);
// }
export function make_layered_600cell() {
const tetras = sorted_600cells()
const LAYERS = [
[ "00", 20 ],
[ "01", 20 ],
[ "02", 30 ],
[ "03", 60 ],
[ "04", 60 ],
[ "05", 60 ],
[ "06", 20 ],
[ "07", 60 ],
[ "08", 20 ],
[ "09", 60 ],
[ "10", 60 ],
[ "11", 60 ],
[ "12", 30 ],
[ "13", 20 ],
[ "14", 20 ]
];
const vertices = {};
const seen = {};
let i = 0;
for( const layer of LAYERS ) {
const label = layer[0];
const n = layer[1];
vertices[label] = [];
console.log(`Layer ${label} starting at ${i}`);
for( const t of tetras.slice(i, i + n) ) {
console.log(t);
for( const n of t.nodes ) {
if( !seen[n] ) {
vertices[label].push(n);
seen[n] = true;
}
}
}
i += n;
}
return JSON.stringify(vertices);
}

153
polytopes.js
View File

@ -1,6 +1,6 @@
import * as PERMUTE from './permute.js';
import * as CELL120 from './cellindex.js';
import * as CELLINDEX from './cellindex.js';
function index_nodes(nodes, scale) {
let i = 1;
@ -22,7 +22,7 @@ function dist2(n1, n2) {
return (n1.x - n2.x) ** 2 + (n1.y - n2.y) ** 2 + (n1.z - n2.z) ** 2 + (n1.w - n2.w) ** 2;
}
function auto_detect_edges(nodes, neighbours, debug=false) {
export function auto_detect_edges(nodes, neighbours, debug=false) {
const seen = {};
const nnodes = nodes.length;
const links = [];
@ -359,23 +359,13 @@ function link_labels(nodes, link) {
// layer and the links follow that
export const cell120_layered = (max) => {
const LAYER_NAMES = {
0: "North pole",
1: "Arctic circle",
2: "North temperate",
3: "Tropic of Cancer",
4: "Equator",
5: "Tropic of Capricorn",
6: "South temperate",
7: "Antarctic circle (all)"
};
const nodes = make_120cell_vertices();
const links = auto_detect_edges(nodes, 4);
nodes.map((n) => n.label = 9); // make all invisible by default
for (const cstr in CELL120.LAYERS ) {
label_nodes(nodes, CELL120.LAYERS[cstr], Number(cstr));
for (const cstr in CELLINDEX.LAYERS120 ) {
label_nodes(nodes, CELLINDEX.LAYERS120[cstr], Number(cstr));
}
links.map((l) => {
@ -393,7 +383,7 @@ export const cell120_layered = (max) => {
for( const i of [ 0, 1, 2, 3, 4, 5, 6, 7 ] ) {
layers.push(i);
options.push({
name: LAYER_NAMES[i],
name: CELLINDEX.LAYER_NAMES[i],
links: [...layers],
nodes: [...layers]
})
@ -419,8 +409,8 @@ export const cell120_inscribed = () => {
const nodes = make_120cell_vertices();
const links = auto_detect_edges(nodes, 4);
for( const cstr in CELL120.INDEX ) {
label_nodes(nodes, CELL120.INDEX[cstr], Number(cstr));
for( const cstr in CELLINDEX.INDEX120 ) {
label_nodes(nodes, CELLINDEX.INDEX120[cstr], Number(cstr));
}
links.map((l) => l.label = 0);
@ -450,76 +440,6 @@ export const cell120_inscribed = () => {
// Schoute's partition via https://arxiv.org/abs/1010.4353
const partition600 = {
"2,0,0,0": 1,
"0,2,0,0": 1,
"0,0,2,0": 1,
"0,0,0,2": 1,
"1,1,1,1": 1,
"1,1,-1,-1": 1,
"1,-1,1,-1": 1,
"1,-1,-1,1": 1,
"1,-1,-1,-1": 1,
"1,-1,1,1": 1,
"1,1,-1,1": 1,
"1,1,1,-1": 1,
"k,0,-t,-1": 2,
"0,k,1,-t": 2,
"t,-1,k,0": 2,
"1,t,0,k": 2,
"t,k,0,-1": 2,
"1,0,k,t": 2,
"k,-t,-1,0": 2,
"0,1,-t,k": 2,
"1,k,t,0": 2,
"t,0,-1,k": 2,
"0,t,-k,-1": 2,
"k,-1,0,-t": 2,
"t,0,1,k": 3,
"0,t,-k,1": 3,
"1,-k,-t,0": 3,
"k,1,0,-t": 3,
"0,k,1,t": 3,
"t,1,-k,0": 3,
"k,0,t,-1": 3,
"1,-t,0,k": 3,
"t,-k,0,-1": 3,
"0,1,-t,-k": 3,
"1,0,-k,t": 3,
"k,t,1,0": 3,
"t,0,-1,-k": 4,
"0,t,k,-1": 4,
"1,-k,t,0": 4,
"k,1,0,t": 4,
"t,1,k,0": 4,
"0,k,-1,-t": 4,
"1,-t,0,-k": 4,
"k,0,-t,1": 4,
"0,1,t,k": 4,
"t,-k,0,1": 4,
"k,t,-1,0": 4,
"1,0,k,-t": 4,
"k,0,t,1": 5,
"0,k,-1,t": 5,
"t,-1,-k,0": 5,
"1,t,0,-k": 5,
"1,0,-k,-t": 5,
"t,k,0,1": 5,
"0,1,t,-k": 5,
"k,-t,1,0": 5,
"t,0,1,-k": 5,
"1,k,-t,0": 5,
"k,-1,0,t": 5,
"0,t,k,1": 5
};
function partition_coord(i, coords, invert) {
@ -560,7 +480,7 @@ function map_coord(i, coords, values) {
}
function make_600cell_vertices() {
export function make_600cell_vertices() {
const coords = {
0: '0',
1: '1',
@ -584,7 +504,7 @@ function make_600cell_vertices() {
].flat();
for( const n of nodes ) {
n.label = label_vertex(n, coords, partition600);
n.label = label_vertex(n, coords, CELLINDEX.PARTITION600);
}
for( const n of nodes ) {
@ -649,6 +569,60 @@ export const cell600 = () => {
}
}
export const cell600_layered = () => {
const nodes = make_600cell_vertices();
const links = auto_detect_edges(nodes, 12);
nodes.map((n) => n.label = 9); // make all invisible by default
for (const cstr in CELLINDEX.LAYERS600 ) {
label_nodes(nodes, CELLINDEX.LAYERS600[cstr], Number(cstr));
}
links.map((l) => {
const labels = link_labels(nodes, l);
if( labels[0] >= labels[1] ) {
l.label = labels[0];
} else {
l.label = labels[1];
}
});
const options = [];
const layers = [];
for( const i of [ 0, 1, 2, 3, 4, 5, 6, 7 ] ) {
layers.push(i);
options.push({
name: CELLINDEX.LAYER_NAMES[i],
links: [...layers],
nodes: [...layers]
})
}
return {
name: '600-cell layered',
nodes: nodes,
links: links,
geometry: {
node_size: 0.02,
link_size: 0.02
},
nolink2opacity: true,
options: options
}
}
function make_dodecahedron_vertices() {
const phi = 0.5 * (1 + Math.sqrt(5));
const phiinv = 1 / phi;
@ -721,6 +695,7 @@ export const build_all = () => {
tesseract(),
cell24(),
cell600(),
cell600_layered(),
cell120_inscribed(),
cell120_layered()
];