From 8c256629b10e039de4890134d9a6b4b601fcc659 Mon Sep 17 00:00:00 2001 From: Mike Lynch Date: Fri, 27 Oct 2023 10:18:54 +1100 Subject: [PATCH] Added a new partition of the 120-cell into layers --- cellindex.js | 102 +++++++++++++++++++++++++++++++++++++++++++++++- label120cell.js | 68 +++++++++++++++++++++++++++++--- main.js | 3 ++ polytopes.js | 21 ++++++---- 4 files changed, 179 insertions(+), 15 deletions(-) diff --git a/cellindex.js b/cellindex.js index 05c9d6e..782e2e4 100644 --- a/cellindex.js +++ b/cellindex.js @@ -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 + ] +} diff --git a/label120cell.js b/label120cell.js index 82a1f66..89853c8 100644 --- a/label120cell.js +++ b/label120cell.js @@ -2,7 +2,7 @@ // code for generating the 120-cell labels // has some overlap with permute - FIXME -const THREE =require('three'); +const THREE = require('three'); function pandita(a) { 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) { const pole = face_plus_to_dodecahedron(faces, startf, startn); const dds = [ pole ]; + const dd_families = { "0": [ pole ] } const seen = {}; 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 vs = dodecahedron_vertices(dds[0]); + dd_families["1"] = []; + for( const face of pole ) { const [ nextdd, ncolours ] = follow_and_colour( nodes, links, faces, colours, pole, face ); add_colours(colours, ncolours); dds.push(nextdd); + dd_families["1"].push(nextdd); seen[dd_fingerprint(nextdd)] = true; } @@ -695,6 +699,8 @@ export function label_120cell(nodes, links, faces, startf, startn) { // 1, 12, 20, 12, 30 = 75 // 0 1 13, 33, 45 + dd_families["2"] = []; + for( const a of dds.slice(1, 13) ) { for( const i of [ 6, 7, 8, 9, 10 ] ) { const [ nextdd, ncolours ] = follow_and_colour( @@ -704,6 +710,7 @@ export function label_120cell(nodes, links, faces, startf, startn) { if( !(fp in seen) ) { add_colours(colours, ncolours); dds.push(nextdd); + dd_families["2"].push(nextdd); seen[fp] = true; } } @@ -711,6 +718,7 @@ export function label_120cell(nodes, links, faces, startf, startn) { // meridians = 45 + dd_families["3"] = []; for( const a of dds.slice(1, 13) ) { const [ nextdd, ncolours ] = follow_and_colour( nodes, links, faces, colours, a, a[11] @@ -719,11 +727,16 @@ export function label_120cell(nodes, links, faces, startf, startn) { if( !(fp in seen) ) { add_colours(colours, ncolours); dds.push(nextdd); + dd_families["3"].push(nextdd); seen[fp] = true; } } // the 30 equatorials? + + + dd_families["4"] = []; + for( const a of dds.slice(13, 46) ) { for( const i of [ 6, 7, 8, 9, 10 ] ) { const [ nextdd, ncolours ] = follow_and_colour( @@ -732,12 +745,15 @@ export function label_120cell(nodes, links, faces, startf, startn) { const fp = dd_fingerprint(nextdd); if( !(fp in seen) ) { add_colours(colours, ncolours); + dd_families["4"].push(nextdd); dds.push(nextdd); seen[fp] = true; } } } + dd_families["5"] = []; + for( const a of dds.slice(33, 76) ) { for( const i of [ 6, 7, 8, 9, 10 ] ) { const [ nextdd, ncolours ] = follow_and_colour( @@ -747,12 +763,18 @@ export function label_120cell(nodes, links, faces, startf, startn) { if( !(fp in seen) ) { add_colours(colours, ncolours); dds.push(nextdd); + dd_families["5"].push(nextdd); seen[fp] = true; } } } + // this should get the rest or explode! + + dd_families["6"] = []; + + for( const a of dds ) { for( const i of [ 6, 7, 8, 9, 10 ] ) { const [ nextdd, ncolours ] = follow_and_colour( @@ -761,6 +783,7 @@ export function label_120cell(nodes, links, faces, startf, startn) { const fp = dd_fingerprint(nextdd); if( !(fp in seen) ) { add_colours(colours, ncolours); + dd_families["6"].push(nextdd); dds.push(nextdd); 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") diff --git a/main.js b/main.js index ab2abd5..e05f43a 100644 --- a/main.js +++ b/main.js @@ -23,6 +23,9 @@ scene.add(light); const amblight = new THREE.AmbientLight(0xffffff, 0.5); scene.add(amblight); +camera.position.set(1, 1, 3); + +camera.lookAt(0, 0, 0); camera.position.z = 4; const renderer = new THREE.WebGLRenderer({antialias: true}); diff --git a/polytopes.js b/polytopes.js index 1d36739..15526e9 100644 --- a/polytopes.js +++ b/polytopes.js @@ -339,13 +339,6 @@ function label_nodes(nodes, ids, label) { - - - - - - - function label_faces_120cell(nodes, faces, cfaces, label) { const ns = new Set(); 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) { const n1 = nodes.filter((n) => n.id === link.source); @@ -399,7 +400,8 @@ export const cell120 = () => { const nodes = make_120cell_vertices(); const links = auto_detect_edges(nodes, 4); - label_120cell(nodes); + //label_120cell(nodes); + layered_120cell(nodes); return { nodes: nodes, @@ -412,6 +414,9 @@ export const cell120 = () => { } + + + const cell120_some_inscribed = (ps) => { const nodes = make_120cell_vertices(); const links = auto_detect_edges(nodes, 4);