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Added a new partition of the 120-cell into layers

feature-120-cell-layers
Mike Lynch 2023-10-27 10:18:54 +11:00
parent fb1d6ddd45
commit 8c256629b1
4 changed files with 179 additions and 15 deletions
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102
cellindex.js
View File

@ -1 +1,101 @@
export const INDEX = {"1": [ 27,38,48,49,61,68,74,87,95,98,105,120, 126,131,140,149,156,165,174,179,185,200,207,210,218,223,226,231,234,239,241,248,252,253,258,263,265,272,274,279,284,285,289,296,300,301,306,311,313,320,324,325,331,334,339,342,347,350,356,357,362,367,369,376,378,383,388,389,393,400,403,406,413,414,419,420,425,427,438,440,444,448,449,453,458,460,469,471,473,474,487,488,490,494,499,503,511,512,513,514,525,527,530,532,539,543,546,550,555,558,563,566,572,573,580,581,585,592,593,600],"2":[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,28,30,31,34,35,37,40,41,44,46,47,50,51,53,56,57,60,62,63,66,67,69,72,73,76,78,79,82,83,85,88,90,91,93,96,97,100,102,103,106,107,109,112,113,116,118,119,122,123,125,128,129,132,134,135,138,139,141,144,145,148,150,151,154,155,157,160,161,164,166,167,170,171,173,176,177,180,182,183,186,187,189,192,193,196,198,199,202,203,205,208,209,212,214,215],"3":[26,39,45,52,64,65,75,86,94,99,108,117,127,130,137,152,153,168,175,178,188,197,206,211,219,222,227,230,235,238,244,245,251,254,257,264,268,269,273,280,283,286,292,293,299,302,305,312,316,317,321,328,330,335,338,343,348,349,355,358,363,366,370,375,377,384,385,392,394,399,404,405,415,416,417,418,426,428,437,439,441,445,452,456,457,459,470,472,475,476,485,486,491,495,498,502,509,510,515,516,526,528,529,531,538,542,547,551,554,559,562,567,569,576,577,584,588,589,596,597],"4":[32,33,43,54,58,71,77,84,92,101,110,115,121,136,143,146,159,162,169,184,190,195,204,213,220,221,228,229,236,237,242,247,249,256,260,261,266,271,276,277,281,288,290,295,297,304,308,309,315,318,322,327,329,336,340,341,346,351,354,359,361,368,371,374,379,382,387,390,396,397,401,408,409,410,423,424,430,432,433,435,443,447,450,454,461,463,466,468,477,478,483,484,489,493,500,504,507,508,517,518,522,524,533,535,540,544,545,549,553,560,561,568,570,575,578,583,587,590,595,598],"5":[29,36,42,55,59,70,80,81,89,104,111,114,124,133,142,147,158,163,172,181,191,194,201,216,217,224,225,232,233,240,243,246,250,255,259,262,267,270,275,278,282,287,291,294,298,303,307,310,314,319,323,326,332,333,337,344,345,352,353,360,364,365,372,373,380,381,386,391,395,398,402,407,411,412,421,422,429,431,434,436,442,446,451,455,462,464,465,467,479,480,481,482,492,496,497,501,505,506,519,520,521,523,534,536,537,541,548,552,556,557,564,565,571,574,579,582,586,591,594,599]}; export const INDEX = {
"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,
265,272,274,279,284,285,289,296,300,301,306,311,313,320,324,325,331,
334,339,342,347,350,356,357,362,367,369,376,378,383,388,389,393,400,
403,406,413,414,419,420,425,427,438,440,444,448,449,453,458,460,469,
471,473,474,487,488,490,494,499,503,511,512,513,514,525,527,530,532,
539,543,546,550,555,558,563,566,572,573,580,581,585,592,593,600
],
"2":[
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,28,
30,31,34,35,37,40,41,44,46,47,50,51,53,56,57,60,62,63,66,67,69,72,73,
76,78,79,82,83,85,88,90,91,93,96,97,100,102,103,106,107,109,112,113,
116,118,119,122,123,125,128,129,132,134,135,138,139,141,144,145,148,
150,151,154,155,157,160,161,164,166,167,170,171,173,176,177,180,182,
183,186,187,189,192,193,196,198,199,202,203,205,208,209,212,214,215
],
"3":[
26,39,45,52,64,65,75,86,94,99,108,117,127,130,137,152,153,168,175,
178,188,197,206,211,219,222,227,230,235,238,244,245,251,254,257,264,
268,269,273,280,283,286,292,293,299,302,305,312,316,317,321,328,330,
335,338,343,348,349,355,358,363,366,370,375,377,384,385,392,394,399,
404,405,415,416,417,418,426,428,437,439,441,445,452,456,457,459,470,
472,475,476,485,486,491,495,498,502,509,510,515,516,526,528,529,531,
538,542,547,551,554,559,562,567,569,576,577,584,588,589,596,597
],
"4":[
32,33,43,54,58,71,77,84,92,101,110,115,121,136,143,146,159,162,169,
184,190,195,204,213,220,221,228,229,236,237,242,247,249,256,260,261,
266,271,276,277,281,288,290,295,297,304,308,309,315,318,322,327,329,
336,340,341,346,351,354,359,361,368,371,374,379,382,387,390,396,397,
401,408,409,410,423,424,430,432,433,435,443,447,450,454,461,463,466,
468,477,478,483,484,489,493,500,504,507,508,517,518,522,524,533,535,
540,544,545,549,553,560,561,568,570,575,578,583,587,590,595,598
],
"5":[
29,36,42,55,59,70,80,81,89,104,111,114,124,133,142,147,158,163,172,
181,191,194,201,216,217,224,225,232,233,240,243,246,250,255,259,262,
267,270,275,278,282,287,291,294,298,303,307,310,314,319,323,326,332,
333,337,344,345,352,353,360,364,365,372,373,380,381,386,391,395,398,
402,407,411,412,421,422,429,431,434,436,442,446,451,455,462,464,465,
467,479,480,481,482,492,496,497,501,505,506,519,520,521,523,534,536,
537,541,548,552,556,557,564,565,571,574,579,582,586,591,594,599
]
};
export const LAYERS = {
"0": [
1,317,221,217,313,341,465,417,469,421,37,165,161,269,33,513,113,
117,517,365
],
"1": [
337,457,409,25,153,265,157,29,413,461,105,109,505,361,509,245,241,
49,177,97,433,89,41,425,169,225,321,93,101,53,437,181,45,173,429,
325,229,251,255,485,351,453,477,445,347,7,333,249,253,271,163,167,
267,155,219,223,159,481,449,349,473,345,441,329,5,529,561,81,577,
129,65,545,497,145,593,533,565,389,373,277,279,375,19,581,133,85,
69,501,549,597,149,15,367,399,39,519,583,135,487,397,579,515,35,
483,131,303,301,209,293,213
],
"2":[
521,553,385,557,525,273,275,369,17,371,569,121,73,57,489,537,585,
137,13,363,393,27,507,571,123,475,573,125,395,575,511,31,479,127,
77,61,541,493,141,589,178,226,170,174,242,230,182,246,9,322,357,
498,434,50,530,146,353,257,185,261,193,233,11,355,359,263,259,189,
237,197,326,54,438,502,150,534,335,447,455,95,103,415,319,423,239,
71,199,551,383,287,419,315,411,331,443,451,99,91,3,343,471,467,115,
119,235,67,547,195,285,381,405,309,594,390,562,294,210,82,23,406,
595,310,211,83,566,86,214,598,407,311,24,408,312,599,87,215,567,
563,295,391
],
"3":[
297,201,299,205,289,42,426,490,138,522,494,430,46,526,142,63,543,
191,283,379,339,459,463,111,107,59,187,539,377,281,546,382,286,194,
66,114,118,466,342,470,384,288,550,70,198,503,439,55,535,151,51,435,
499,147,531,212,296,302,304,216
],
"4":[
386,554,290,74,202,586,401,305,558,78,590,206,307,403,21,402,306,
587,75,203,555,79,559,207,291,387,591,308,404,22,462,338,458,110,
106,2,410,314,418,98,90,450,58,186,442,330,234,282,378,538,62,190,
238,94,102,446,334,454,284,380,542,422,414,318,495,431,327,260,264,
356,12,360,47,527,143,200,192,240,43,427,323,247,243,171,227,179,491,
523,139,183,175,231,258,262,358,354,10,196,236,188,130,578,398,596,
548,132,580,84,514,34,482,148,68,500,582,518,400,366,16,134,486,38,
600,552,88,136,584,152,72,504,20,376,392,536,568,374,278,280,532,564
],
"5":[
570,394,298,300,506,14,362,396,574,510,122,474,26,204,208,292,126,
30,478,588,540,76,124,572,140,60,492,18,370,388,524,556,372,276,274,
592,144,80,528,560,544,64,496,222,218,154,266,158,162,270,166,6,346,
350,254,250,332,452,484,444,476,8,348,336,448,480,128,352,488,456,
252,256,328,232,432,176,48,440,56,184,104,96,324,228,172,428,44,
180,52,436,248,244,92,100,516,368,36,272,164,116,520,120,468,420,
40,168,472,424,344
],
"6":[364,268,508,28,156,576,512,108,112,32,160,460,412,464,340,416,
220,224,316,320,4
]
}

68
label120cell.js
View File

@ -2,7 +2,7 @@
// code for generating the 120-cell labels // code for generating the 120-cell labels
// has some overlap with permute - FIXME // has some overlap with permute - FIXME
const THREE =require('three'); const THREE = require('three');
function pandita(a) { function pandita(a) {
const n = a.length; const n = a.length;
@ -669,11 +669,12 @@ function arctic(nodes, links, faces, startf, startn, max) {
// this is the one that works // this is the final one that works for the whole 120-cell
export function label_120cell(nodes, links, faces, startf, startn) { export function label_120cell(nodes, links, faces, startf, startn) {
const pole = face_plus_to_dodecahedron(faces, startf, startn); const pole = face_plus_to_dodecahedron(faces, startf, startn);
const dds = [ pole ]; const dds = [ pole ];
const dd_families = { "0": [ pole ] }
const seen = {}; const seen = {};
seen[dd_fingerprint(pole)] = true; seen[dd_fingerprint(pole)] = true;
@ -681,12 +682,15 @@ export function label_120cell(nodes, links, faces, startf, startn) {
const colours = colour_dodecahedron_from_face(dds[0], [ 1, 2, 3, 4, 5 ] ); const colours = colour_dodecahedron_from_face(dds[0], [ 1, 2, 3, 4, 5 ] );
const vs = dodecahedron_vertices(dds[0]); const vs = dodecahedron_vertices(dds[0]);
dd_families["1"] = [];
for( const face of pole ) { for( const face of pole ) {
const [ nextdd, ncolours ] = follow_and_colour( const [ nextdd, ncolours ] = follow_and_colour(
nodes, links, faces, colours, pole, face nodes, links, faces, colours, pole, face
); );
add_colours(colours, ncolours); add_colours(colours, ncolours);
dds.push(nextdd); dds.push(nextdd);
dd_families["1"].push(nextdd);
seen[dd_fingerprint(nextdd)] = true; seen[dd_fingerprint(nextdd)] = true;
} }
@ -695,6 +699,8 @@ export function label_120cell(nodes, links, faces, startf, startn) {
// 1, 12, 20, 12, 30 = 75 // 1, 12, 20, 12, 30 = 75
// 0 1 13, 33, 45 // 0 1 13, 33, 45
dd_families["2"] = [];
for( const a of dds.slice(1, 13) ) { for( const a of dds.slice(1, 13) ) {
for( const i of [ 6, 7, 8, 9, 10 ] ) { for( const i of [ 6, 7, 8, 9, 10 ] ) {
const [ nextdd, ncolours ] = follow_and_colour( const [ nextdd, ncolours ] = follow_and_colour(
@ -704,6 +710,7 @@ export function label_120cell(nodes, links, faces, startf, startn) {
if( !(fp in seen) ) { if( !(fp in seen) ) {
add_colours(colours, ncolours); add_colours(colours, ncolours);
dds.push(nextdd); dds.push(nextdd);
dd_families["2"].push(nextdd);
seen[fp] = true; seen[fp] = true;
} }
} }
@ -711,6 +718,7 @@ export function label_120cell(nodes, links, faces, startf, startn) {
// meridians = 45 // meridians = 45
dd_families["3"] = [];
for( const a of dds.slice(1, 13) ) { for( const a of dds.slice(1, 13) ) {
const [ nextdd, ncolours ] = follow_and_colour( const [ nextdd, ncolours ] = follow_and_colour(
nodes, links, faces, colours, a, a[11] nodes, links, faces, colours, a, a[11]
@ -719,11 +727,16 @@ export function label_120cell(nodes, links, faces, startf, startn) {
if( !(fp in seen) ) { if( !(fp in seen) ) {
add_colours(colours, ncolours); add_colours(colours, ncolours);
dds.push(nextdd); dds.push(nextdd);
dd_families["3"].push(nextdd);
seen[fp] = true; seen[fp] = true;
} }
} }
// the 30 equatorials? // the 30 equatorials?
dd_families["4"] = [];
for( const a of dds.slice(13, 46) ) { for( const a of dds.slice(13, 46) ) {
for( const i of [ 6, 7, 8, 9, 10 ] ) { for( const i of [ 6, 7, 8, 9, 10 ] ) {
const [ nextdd, ncolours ] = follow_and_colour( const [ nextdd, ncolours ] = follow_and_colour(
@ -732,12 +745,15 @@ export function label_120cell(nodes, links, faces, startf, startn) {
const fp = dd_fingerprint(nextdd); const fp = dd_fingerprint(nextdd);
if( !(fp in seen) ) { if( !(fp in seen) ) {
add_colours(colours, ncolours); add_colours(colours, ncolours);
dd_families["4"].push(nextdd);
dds.push(nextdd); dds.push(nextdd);
seen[fp] = true; seen[fp] = true;
} }
} }
} }
dd_families["5"] = [];
for( const a of dds.slice(33, 76) ) { for( const a of dds.slice(33, 76) ) {
for( const i of [ 6, 7, 8, 9, 10 ] ) { for( const i of [ 6, 7, 8, 9, 10 ] ) {
const [ nextdd, ncolours ] = follow_and_colour( const [ nextdd, ncolours ] = follow_and_colour(
@ -747,12 +763,18 @@ export function label_120cell(nodes, links, faces, startf, startn) {
if( !(fp in seen) ) { if( !(fp in seen) ) {
add_colours(colours, ncolours); add_colours(colours, ncolours);
dds.push(nextdd); dds.push(nextdd);
dd_families["5"].push(nextdd);
seen[fp] = true; seen[fp] = true;
} }
} }
} }
// this should get the rest or explode! // this should get the rest or explode!
dd_families["6"] = [];
for( const a of dds ) { for( const a of dds ) {
for( const i of [ 6, 7, 8, 9, 10 ] ) { for( const i of [ 6, 7, 8, 9, 10 ] ) {
const [ nextdd, ncolours ] = follow_and_colour( const [ nextdd, ncolours ] = follow_and_colour(
@ -761,6 +783,7 @@ export function label_120cell(nodes, links, faces, startf, startn) {
const fp = dd_fingerprint(nextdd); const fp = dd_fingerprint(nextdd);
if( !(fp in seen) ) { if( !(fp in seen) ) {
add_colours(colours, ncolours); add_colours(colours, ncolours);
dd_families["6"].push(nextdd);
dds.push(nextdd); dds.push(nextdd);
seen[fp] = true; seen[fp] = true;
} }
@ -774,7 +797,7 @@ export function label_120cell(nodes, links, faces, startf, startn) {
} }
return { dodecahedra: dds, labels: labels }; return { dodecahedra: dds, labels: labels, families: dd_families };
} }
@ -928,11 +951,44 @@ function make_dodecahedron_vertices() {
} }
// this one does the coherent indexing / partition into 600-cells
export function make_labelled_120cell() {
const nodes = make_120cell_vertices();
const links = auto_detect_edges(nodes, 4);
const faces = auto_120cell_faces(links);
const labelled = label_120cell(nodes, links, faces, faces[0], 341);
return labelled;
}
export function make_layered_120cell() {
const labelled = make_labelled_120cell();
// relabel by layer
const layer_dds = labelled["families"];
const vertices_layers = {};
const seen = {};
for( const layer of [ "0", "1", "2", "3", "4", "5", "6"] ) {
vertices_layers[layer] = [];
for( const dd of layer_dds[layer] ) {
for( const face of dd ) {
for( const n of face.nodes ) {
if( !seen[n] ) {
vertices_layers[layer].push(n);
seen[n] = true;
}
}
}
}
}
return vertices_layers;
}
// const nodes = make_120cell_vertices();
// const links = auto_detect_edges(nodes, 4);
// const faces = auto_120cell_faces(links);
// console.log("Calculating 120-cell colours") // console.log("Calculating 120-cell colours")

3
main.js
View File

@ -23,6 +23,9 @@ scene.add(light);
const amblight = new THREE.AmbientLight(0xffffff, 0.5); const amblight = new THREE.AmbientLight(0xffffff, 0.5);
scene.add(amblight); scene.add(amblight);
camera.position.set(1, 1, 3);
camera.lookAt(0, 0, 0);
camera.position.z = 4; camera.position.z = 4;
const renderer = new THREE.WebGLRenderer({antialias: true}); const renderer = new THREE.WebGLRenderer({antialias: true});

21
polytopes.js
View File

@ -339,13 +339,6 @@ function label_nodes(nodes, ids, label) {
function label_faces_120cell(nodes, faces, cfaces, label) { function label_faces_120cell(nodes, faces, cfaces, label) {
const ns = new Set(); const ns = new Set();
for( const fid of cfaces ) { for( const fid of cfaces ) {
@ -386,6 +379,14 @@ function label_120cell(nodes) {
} }
function layered_120cell(nodes) {
for (const cstr in CELL120.LAYERS ) {
label_nodes(nodes, CELL120.LAYERS[cstr], Number(cstr));
}
}
function link_labels(nodes, link) { function link_labels(nodes, link) {
const n1 = nodes.filter((n) => n.id === link.source); const n1 = nodes.filter((n) => n.id === link.source);
@ -399,7 +400,8 @@ export const cell120 = () => {
const nodes = make_120cell_vertices(); const nodes = make_120cell_vertices();
const links = auto_detect_edges(nodes, 4); const links = auto_detect_edges(nodes, 4);
label_120cell(nodes); //label_120cell(nodes);
layered_120cell(nodes);
return { return {
nodes: nodes, nodes: nodes,
@ -412,6 +414,9 @@ export const cell120 = () => {
} }
const cell120_some_inscribed = (ps) => { const cell120_some_inscribed = (ps) => {
const nodes = make_120cell_vertices(); const nodes = make_120cell_vertices();
const links = auto_detect_edges(nodes, 4); const links = auto_detect_edges(nodes, 4);