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bombinans:bugfix-colour-picker
bombinans:feature-120-cell-details
bombinans:feature-pixels
bombinans:feature-tapered-links
bombinans:broken-cursed-links
bombinans:feature-alt-projections
bombinans:feature-descriptions
bombinans:feature-node-foreshortening
bombinans:feature-snub-24-cell
bombinans:feature-120-cell-layers
bombinans:feature-3d-shapes
bombinans:feature-inscriptions
bombinans:experiments-120-cell
bombinans:feature-120-cell-index
bombinans:feature-faces
bombinans:feature-big-polytopes
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compare: bombinans:experiments-120-cell
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bombinans:main
bombinans:feature-120-cell-more-inscriptions
bombinans:bugfix-colour-picker
bombinans:feature-120-cell-details
bombinans:feature-pixels
bombinans:feature-tapered-links
bombinans:broken-cursed-links
bombinans:feature-alt-projections
bombinans:feature-descriptions
bombinans:feature-node-foreshortening
bombinans:feature-snub-24-cell
bombinans:feature-120-cell-layers
bombinans:feature-3d-shapes
bombinans:feature-inscriptions
bombinans:experiments-120-cell
bombinans:feature-120-cell-index
bombinans:feature-faces
bombinans:feature-big-polytopes

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87
600_CELL_MAPPING.md
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# 600-cell mapping
These are the nodes from a 120-cell which are on one of its inscribed 600-cells,
sorted into layers (just the first half because the second half mirror these ones)
Start: [ 27 ]
0: [ 27 ]
0.618:
[
223, 253, 265, 331,
339, 393, 419, 427,
473, 511, 539, 555
]
1
[
95, 105, 131, 140, 165, 179,
185, 207, 258, 274, 306,
313, 347, 367, 449, 471,
499, 527, 573, 585
]
1.175
[
231, 285, 289, 324,
378, 388, 413, 425,
487, 513, 543, 563
]
1.414
[
48, 49, 61, 68, 74, 87, 234,
239, 241, 248, 300, 301, 356, 357,
369, 376, 403, 406, 444, 453, 460,
469, 490, 503, 525, 532, 572, 581,
592, 593
]
## Manual mapping progress
Starting from 27 on the inscribed 600 cell and 1 on the primary 600 cell, here are
the two arctic circles
Pole: 27: 1
Arctic circle:
419: 41
223: 49
253: 45
331: 53
427: 109
339: 105
511: 51
265: 107
473: 111
539: 55
555: 43
393: 47
Next: for each face on this icosahedron, find the other vertex - these are the next 20
367
131
499
179
471
165
449
258
274
95
347
313
185
140
527
573
105
585
306
207
Then - for

28
CHANGELOG.md
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CHANGELOG
=========
## v1.3 - 7/2/2026
Went to inordinate lengths to apply the partition of the 600-cell (into five
24-cells) to the 5-cell inscription in the 120-cell, so that they could be coloured
in a way which reveals some of that symmetry.
## v1.2 - 18/1/2026
Added a second visualisation of the 120-cell's 5-cells without the 120-cell links
and with more colours added so you can get a sense of the individual 5-cells.
## v1.1 - 1/1/2026
The 120-cell now includes a visualisation of its inscribed 5-cells, which honestly
looks like less of a mess than I expected it to.
## v1.0 - 16/11/2025
It's been [two years](https://mikelynch.org/2023/Sep/02/120-cell/)</a> since
I first made this, and I haven't updated it in a while, but I got tapered links to
work without too much performance overhead, so that seemed worth a version.
The results flicker a bit at low opacities but otherwise I'm pretty happy with
it.
`

15
NOTES.md
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# NOTES
## Labelling the inscribed 600-cells in a 120-cell
I want to apply the partition of the 600-cell into five 24-cells to the inscribed
600-cells in the 120-cell, so that I can use this partition to colour the inscribed
5-cells - since each 5-cell has a vertex in each of the 600-cells, getting a
partition for just one will be enough.
The challenge is that the 600-cells in the 120-cell are rotated differently to the
coordinates for the original 600-cell. And I don't have enough maths to line them up.
What about - given one of the inscribed 600-cell, find all of the 24-cells? (there
are 25 possible ones so sorting them out will be a pain)

554
cell120_to_cell5.js
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import * as POLYTOPES from './polytopes.js';
// exploring more inscriptions of the 120-cell
function choice(a) {
const r = Math.floor(Math.random() * a.length);
return a[r];
}
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 dist(n1, n2) {
return Math.sqrt((n1.x - n2.x) ** 2 + (n1.y - n2.y) ** 2 + (n1.z - n2.z) ** 2 + (n1.w - n2.w) ** 2);
}
export function make_120cell() {
const nodes = POLYTOPES.make_120cell_vertices();
const links = POLYTOPES.auto_detect_edges(nodes, 4);
return {
nodes: nodes,
links: links
}
}
function round_dist(raw) {
return Math.floor(raw * 100000) / 100000;
}
export function distance_groups(cell120) {
// get list of other nodes by distance
// sort them and dump them out
const dists = {};
cell120.nodes.map((n) => {
const draw = dist(cell120.nodes[0], n);
const dtrunc = round_dist(draw);
if( !(dtrunc in dists) ) {
dists[dtrunc] = [];
}
dists[dtrunc].push(n);
});
return dists;
}
function distance_group(cell120, n0, chord) {
const nodes = []
cell120.nodes.map((n) => {
const d = round_dist(dist(n0, n));
if( d == chord ) {
nodes.push(n);
}
});
// filter and return those whose chord is also the same
const equidistant = [];
for( const n1 of nodes ) {
for( const n2 of nodes ) {
if( n2.id > n1.id ) {
if( round_dist(dist(n1, n2)) == chord ) {
equidistant.push([n1, n2]);
}
}
}
}
return equidistant;
}
export function chord_survey() {
const cell120 = POLYTOPES.cell120_inscribed();
const dgroups = distance_groups(cell120);
const dists = Object.keys(dgroups);
dists.sort();
for( const d of dists ) {
const g0 = dgroups[d][0];
dgroups[d].map((g) => {
console.log(`${g0.id}-${g.id}: ${round_dist(dist(g0, g))}`);
});
}
}
function overlap(c1, c2) {
for( const l in c1 ) {
if( c1[l] === c2[l] ) {
return true;
}
}
return false;
}
function c5match(c1, c2) {
for( const l in c1 ) {
if( c1[l] != c2[l] ) {
return false;
}
}
return true;
}
export function gather_5cells(cell120) {
const CHORD5 = round_dist(Math.sqrt(2.5));
const bins = [];
const all = [];
cell120.nodes.filter((n) => n.label === 1).map((n) => {
const cells = [ ];
const g = distance_group(cell120, n, CHORD5);
for( const pair of g ) {
let seen = false;
for( const cell of cells ) {
const c = Object.values(cell);
if( c.includes(pair[0].id) || c.includes(pair[1].id) ) {
if( !c.includes(pair[0].id) ) {
cell[pair[0].label] = pair[0].id;
}
if( !c.includes(pair[1].id) ) {
cell[pair[1].label] = pair[1].id;
}
seen = true;
break;
}
}
if( !seen ) {
const cell = {};
cell[1]= n.id;
cell[pair[0].label] = pair[0].id;
cell[pair[1].label] = pair[1].id;
cells.push(cell);
}
}
all.push(...cells);
});
return all;
}
function audit_5cells(cells) {
// this verifies that for each label (a 600-cell set), each of its
// vertices is in exactly 7 5-cells. It checks out.
['1','2','3','4','5'].map((l) => {
const sets = {};
for( const cell of cells ) {
const lv = cell[l];
if( !(lv in sets) ) {
sets[lv] = [];
}
sets[lv].push(cell);
}
for( const lv in sets ) {
const ok = ( sets[lv].length === 7 ) ? 'ok' : 'miss';
console.log(`${l},${lv},${sets[lv].length},${ok}`);
}
});
}
function try_120_5_cells_fails(cell120, cells, l) {
// iterate over every vertex in the 600-cell defined by label l,
// get all 7 5-cells including that vertex, and add them if they are
// disjoint with what we already have
// this always runs out of disjoint nodes early
const vertices = cell120.nodes.filter((n) => n.label === l);
const cellset = [];
for( const v of vertices ) {
console.log(`Vertex ${v.id}`);
const vcells = cells.filter((c) => c[l] === v.id);
const overlap_any = (cs, c) => {
for( const seen of cs ) {
if( overlap(seen, c) ) {
console.log("overlap");
console.log(c);
return true;
}
}
return false;
}
const disjoint = vcells.filter((c) => ! overlap_any(cellset, c));
console.log(`Found ${disjoint.length} disjoint cells`);
if( disjoint.length > 0 ) {
cellset.push(choice(disjoint));
}
}
console.log(`Found total of ${cellset.length} disjoint cells`);
//console.log(cellset);
}
function overlap_any(cs, c) {
for( const seen of cs ) {
if( overlap(seen, c) ) {
return true;
}
}
return false;
}
function explore_disjoint(cell120, all5, l) {
const a = all5[0];
const overlaps = all5.filter((c) => overlap(c, a));
console.log(a);
console.log(overlaps.length);
console.log(overlaps);
}
// select a five-cell from a starting vertex v
// find a neighbor of v vn on its 600 cell, find all of the 5-cells which include
// vn. Then see if we can find any from that set which are similiar neighbours to
// the other four vertices in the first 5-cell
// the idea is that the 600-cells are a guide to finding the right subset of
// 5-cells
function neighbours600(cell120, vid) {
const v = cell120.nodes.filter((node) => node.id === vid)[0];
const label = v.label;
const links = cell120.links.filter((l) => {
return l.label === v.label && (l.source === v.id || l.target == v.id );
});
const nodes = links.map((l) => {
if( l.source === v.id ) {
return l.target;
} else {
return l.source;
}
});
return nodes;
}
function cell120node(cell120, nid) {
return cell120.nodes.filter((n) => n.id === nid)[0];
}
function node_dist(cell120, aid, bid) {
const a = cell120node(cell120, aid);
const b = cell120node(cell120, bid);
return dist(a, b);
}
function print_row(v1, v2, p, v5) {
console.log(`${v1.id},${v2.id},${p},${v5[1]},${v5[2]},${v5[3]},${v5[4]},${v5[5]}`);
}
// for a pair of vertices which are on the same inscribed 600 cell,
// this returns all 7 pairs of 5-cells which contain v1 and v2 and
// which are also evenly spaced (ie every pair of vertices on the
// same 600-cell is one edge apart)
function find_adjoining_5cells(cell120, all5, v1, v2) {
const DIST600 = round_dist(node_dist(cell120, v1.id, v2.id));
const v15s = all5.filter((c5) => c5[v1.label] === v1.id);
const v25s = all5.filter((c5) => c5[v2.label] === v2.id);
let p = 0;
const c5pairs = [];
for( const v5a of v15s ) {
for( const v5b of v25s ) {
let match = true;
const d = {};
for( const label in v5a ) {
d[label] = round_dist(node_dist(cell120, v5a[label], v5b[label]));
if( d[label] != DIST600 ) {
match = false;
}
}
if( match ) {
c5pairs.push([ v5a, v5b ]);
}
}
}
return c5pairs;
}
function tetras(cell120, v) {
// given a vertex v, find all of the 600-cell tetras it's on
const n600s = neighbours600(cell120, v.id);
// need to find all sets of three neighbours which are neighbours: there
// should be 20 of these because they're faces of an icosahedron
const tetras = new Set;
for( const v2id of n600s ) {
// find mutual neighbours of the first two
const n2600s = neighbours600(cell120, v2id);
const mutuals = n2600s.filter((nid) => {
return nid != v2id && nid != v.id && n600s.includes(nid)
});
for( const nm of mutuals ) {
const nnms = neighbours600(cell120, nm);
const mutuals2 = nnms.filter((nid) => {
return nid != nm && nid != v2id && nid != v.id && mutuals.includes(nid)
});
for( const m2 of mutuals2 ) {
const t = [ v.id, v2id, nm, m2 ];
t.sort((a, b) => a - b);
const tstr = t.join(',');
tetras.add(tstr);
}
}
}
const tarray = [];
for( const t of tetras ) {
const ta = t.split(',').map((v) => Number(v));
tarray.push(ta);
}
return tarray;
}
function vertices(hedra) {
const v = new Set;
for ( const h of hedra) {
for( const p of h ) {
v.add(p);
}
}
return Array.from(v);
}
function str5cell(c5) {
return ["1","2","3","4","5"].map((l) => String(c5[l]).padStart(3, '0')).join('-');
}
function tetra_sets(cell120, all5, tetra) {
// given a tetrahedron on a 600-cell, find the sets of adjacent 5-cells on
// all of the pairs
// this is ass-backwards. Need to find tetras on the other 4 vertices of a 5-cell
const vs = tetra.map((tid) => cell120node(cell120, tid));
const pairs = [[0,1], [0,2], [0, 3], [1, 2], [1, 3], [2, 3]];
for( const p of pairs ) {
const v1 = vs[p[0]];
const v2 = vs[p[1]];
const c5pairs = find_adjoining_5cells(cell120, all5, v1, v2);
console.log(v1.id, v2.id);
console.log(c5pairs.map((p) => str5cell(p[0]) + " " + str5cell(p[1])));
}
}
function cell5_neighbourhoods(cell120, all5, c5) {
const neighbours = {}
for( const l in c5 ) {
const v = cell120node(cell120, c5[l]);
neighbours[l] = vertices(tetras(cell120, v));
}
// now take the set of all 5-cells and filter it to only those whose vertices
// are in the neighour sets. On first inspection there are 13?
const n5cells = all5.filter((c5) => {
for( const l in c5 ) {
if( ! neighbours[l].includes(c5[l]) ) {
return false;
}
}
return true;
});
return n5cells;
}
function cell5_tetras(cell120, all5, c5) {
const nb = cell5_neighbourhoods(cell120, all5, c5);
const v1 = cell120node(cell120, c5["1"]);
const ts = tetras(cell120, v1);
const c5s = [];
for( const t of ts ) {
const nt = nb.filter((n) => {
for( const l in n ) {
if( t.includes(n[l]) ) {
return true;
}
}
return false
});
for( const nc5 of nt ) {
const exact = c5s.filter((c) => c5match(c, nc5));
if( exact.length === 0 ) {
const o = c5s.filter((c) => overlap(c, nc5));
if( o.length > 0 ) {
console.log("Overlap", c5, o);
} else {
c5s.push(nc5);
}
}
}
}
return c5s;
}
function coherent_5cells_r(cell120, all5, c5s, c50) {
// Find next set of c5s, see if there are any we haven't seen,
// recurse into those ones
const c5ns = cell5_tetras(cell120, all5, c50);
const c5unseen = c5ns.filter((c5) => {
const matched = c5s.filter((c5b) => c5match(c5b, c5));
return matched.length === 0;
});
for( const c5u of c5unseen ) {
c5s.push(c5u);
}
for( const c5u of c5unseen ) {
coherent_5cells_r(cell120, all5, c5s, c5u);
}
}
function coherent_5cells(cell120, all5) {
// pick a starting point, collect coherent 5_cells, continue till
// there aren't any new ones
const c5set = [];
let c5 = all5[0];
const c5s = [];
coherent_5cells_r(cell120, all5, c5s, c5);
return c5s;
}
function coherent_all() {
const cell120 = POLYTOPES.cell120_inscribed();
const all5 = gather_5cells(cell120);
const c5s = coherent_5cells(cell120, all5);
const celli = c5s.map((c5) => [ "1", "2", "3", "4", "5" ].map((l) => c5[l]));
// check it because I don't believe it yet
const vertex_check = {};
for( const c5 of celli ) {
for( const l in c5 ) {
const v = c5[l];
if( v in vertex_check ) {
console.log(`Double count vertex ${v}`);
}
vertex_check[v] = 1;
}
}
for( let i = 1; i < 601; i++ ) {
if( !vertex_check[i] ) {
console.log(`v ${i} missing`);
}
}
const idict = {};
for( let i = 1; i < 121; i++ ) {
idict[i] = celli[i - 1];
}
console.log(JSON.stringify(idict, null, 2));
}
function coherent_one_set() {
const cell120 = POLYTOPES.cell120_inscribed();
const all5 = gather_5cells(cell120);
const c5ns = cell5_tetras(cell120, all5, all5[0]);
const celli = c5ns.map((c5) => [ "1", "2", "3", "4", "5" ].map((l) => c5[l]));
const idict = {};
for( let i = 0; i < celli.length; i++ ) {
idict[i + 1] = celli[i];
}
console.log(JSON.stringify(idict, null, 2));
}
function cell120_csv() {
const cell120 = POLYTOPES.cell120_inscribed();
const coords = [ 'x', 'y', 'z', 'w' ];
console.log("id,label,x,y,z,w,zeroes");
for( const n of cell120.nodes ) {
const zc = coords.filter((c) => n[c] === 0);
console.log(`${n.id},${n.label},${n.x},${n.y},${n.z},${n.w},${zc.length}`);
}
}
function cell600_links(cell600, n) {
const links = cell600.links.filter((l) => l.source === n.id || l.target === n.id);
const nbors = links.map((l) => {
if( l.source === n.id ) {
return l.target;
} else {
return l.source;
}
});
return nbors.sort((a, b) => a - b);
}
function cell600_csv() {
const cell600 = POLYTOPES.cell600();
console.log("id,label,x,y,z,w,d");
const n0 = cell600.nodes[0];
for( const n of cell600.nodes ) {
const d = dist(n0, n);
const nbors = cell600_links(cell600, n);
const nids = nbors.join(',');
console.log(`${n.id},${n.label},${n.x},${n.y},${n.z},${n.w},${d},${nids}`);
}
}
cell600_csv();

2602
cellindex.js
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23
colours.js
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@ -1,29 +1,12 @@
import ColorScheme from 'color-scheme'; import ColorScheme from 'color-scheme';
import Color from 'color';
export const get_colours = (basis) => { export const get_colours = (basis) => {
const basis_c = Color(basis);
const hslb = basis_c.hsl();
const hue = hslb['color'][0];
const saturation = hslb['color'][1];
const luminance = hslb['color'][2];
const scheme = new ColorScheme; const scheme = new ColorScheme;
scheme.from_hue(hue).scheme("tetrade").distance(0.75); const hexbasis = basis.toString(16).padStart(6, "0");
const colours = scheme.colors(); scheme.from_hex(hexbasis).scheme("tetrade").variation("hard").distance(0.5);
colours.reverse(); return scheme.colors().map((cs) => parseInt('0x' + cs));
const hsl = colours.map((c) => Color("#" + c).hsl());
const resaturated = hsl.map((hslc) => hslc.saturationl(saturation).rgbNumber());
resaturated.unshift(basis);
return resaturated;
} }
// basic colours where 0 = blue
// 1 - dark blue
// 2 - white
// 3 - light cyan
// 4 - light orange
// 5 - dark orange
export const get_plain_colours = (basis) => { export const get_plain_colours = (basis) => {
return [ return [
basis, basis,

1
explore_120
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104
fourDShape.js
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@ -1,10 +1,7 @@
import * as THREE from 'three'; import * as THREE from 'three';
import { TaperedLink } from './taperedLink.js';
const HYPERPLANE = 2.0; const HYPERPLANE = 2.0;
const W_FORESHORTENING = 0.04;
class FourDShape extends THREE.Group { class FourDShape extends THREE.Group {
@ -18,10 +15,11 @@ class FourDShape extends THREE.Group {
this.nodes3 = {}; this.nodes3 = {};
this.links = structure.links; this.links = structure.links;
this.faces = ( "faces" in structure ) ? structure.faces : []; this.faces = ( "faces" in structure ) ? structure.faces : [];
this.node_size = structure.geometry.node_size;
this.link_size = structure.geometry.link_size;
this.node_scale = 1; this.node_scale = 1;
this.link_scale = 1; this.link_scale = 1;
this.hyperplane = HYPERPLANE; this.hyperplane = HYPERPLANE;
this.foreshortening = W_FORESHORTENING;
this.initShapes(); this.initShapes();
} }
@ -29,15 +27,15 @@ class FourDShape extends THREE.Group {
// if a node/link has no label, use the 0th material // if a node/link has no label, use the 0th material
getMaterialLabel(entity) { getMaterial(entity, materials) {
if( "label" in entity ) { if( "label" in entity ) {
return entity.label return materials[entity.label];
} else { } else {
return 0; return materials[0];
} }
} }
makeNode(material, v3, scale) { makeNode(material, v3) {
const geometry = new THREE.SphereGeometry(this.node_size); const geometry = new THREE.SphereGeometry(this.node_size);
const sphere = new THREE.Mesh(geometry, material); const sphere = new THREE.Mesh(geometry, material);
sphere.position.copy(v3); sphere.position.copy(v3);
@ -45,24 +43,34 @@ class FourDShape extends THREE.Group {
return sphere; return sphere;
} }
makeLink(materialLabel, link) { makeLink(material, link) {
const n1 = this.nodes3[link.source]; const n1 = this.nodes3[link.source].v3;
const n2 = this.nodes3[link.target]; const n2 = this.nodes3[link.target].v3;
const s1 = this.link_scale * n1.scale; const length = n1.distanceTo(n2);
const s2 = this.link_scale * n2.scale; const centre = new THREE.Vector3();
const basematerial = this.link_ms[materialLabel]; centre.lerpVectors(n1, n2, 0.5);
const edge = new TaperedLink(basematerial, materialLabel, n1, n2, s1, s2); const geometry = new THREE.CylinderGeometry(this.link_size, this.link_size, 1);
this.add( edge ); const cyl = new THREE.Mesh(geometry, material);
const edge = new THREE.Group();
edge.add(cyl);
edge.position.copy(centre);
edge.scale.copy(new THREE.Vector3(1, 1, length));
edge.lookAt(n2);
cyl.rotation.x = Math.PI / 2.0;
this.add(edge);
return edge; return edge;
} }
updateLink(link, links_show) { updateLink(link) {
const n1 = this.nodes3[link.source]; const n1 = this.nodes3[link.source].v3;
const n2 = this.nodes3[link.target]; const n2 = this.nodes3[link.target].v3;
const s1 = this.link_scale * n1.scale; const length = n1.distanceTo(n2);
const s2 = this.link_scale * n2.scale; const centre = new THREE.Vector3();
link.object.update(n1, n2, s1, s2); centre.lerpVectors(n1, n2, 0.5);
link.object.visible = (!links_show || links_show.includes(link.label)); link.object.scale.copy(new THREE.Vector3(this.link_scale, this.link_scale, length));
link.object.position.copy(centre);
link.object.lookAt(n2);
link.object.children[0].rotation.x = Math.PI / 2.0;
} }
@ -91,62 +99,47 @@ class FourDShape extends THREE.Group {
} }
fourDscale(w) { fourDtoV3(x, y, z, w, rotations) {
return this.hyperplane / ( this.hyperplane + w );
}
fourDrotate(x, y, z, w, rotations) {
const v4 = new THREE.Vector4(x, y, z, w); const v4 = new THREE.Vector4(x, y, z, w);
for ( const m4 of rotations ) { for ( const m4 of rotations ) {
v4.applyMatrix4(m4); v4.applyMatrix4(m4);
} }
return v4; const k = this.hyperplane / (this.hyperplane + v4.w);
}
fourDtoV3(v4) {
const k = this.fourDscale(v4.w);
return new THREE.Vector3(v4.x * k, v4.y * k, v4.z * k); return new THREE.Vector3(v4.x * k, v4.y * k, v4.z * k);
} }
initShapes() { initShapes() {
for( const n of this.nodes4 ) { for( const n of this.nodes4 ) {
const k = this.fourDscale(n.w); const v3 = this.fourDtoV3(n.x, n.y, n.z, n.w, []);
const v3 = new THREE.Vector3(n.x * k, n.y * k, n.z * k); const material = this.getMaterial(n, this.node_ms);
const material = this.node_ms[this.getMaterialLabel(n)];
this.nodes3[n.id] = { this.nodes3[n.id] = {
v3: v3, v3: v3,
scale: k, object: this.makeNode(material, v3)
label: n.label,
object: this.makeNode(material, v3, k)
}; };
} }
for( const l of this.links ) { for( const l of this.links ) {
const mLabel = this.getMaterialLabel(l); const material = this.getMaterial(l, this.link_ms);
l.object = this.makeLink(mLabel, l); l.object = this.makeLink(material, l);
} }
for( const f of this.faces ) { for( const f of this.faces ) {
const material = this.face_ms(this.getMaterialLabel(f)); const material = this.getMaterial(f, this.face_ms);
f.object = this.makeFace(material, f); f.object = this.makeFace(material, f);
} }
} }
render3(rotations, nodes_show, links_show) { render3(rotations) {
this.scalev3 = new THREE.Vector3(this.node_scale, this.node_scale, this.node_scale); this.scalev3 = new THREE.Vector3(this.node_scale, this.node_scale, this.node_scale);
for( const n of this.nodes4 ) { for( const n of this.nodes4 ) {
const v4 = this.fourDrotate(n.x, n.y, n.z, n.w, rotations); const v3 = this.fourDtoV3(n.x, n.y, n.z, n.w, rotations);
const k = this.fourDscale(v4.w);
const v3 = new THREE.Vector3(v4.x * k, v4.y * k, v4.z * k);
const s4 = k * this.node_scale * this.foreshortening;
const s3 = new THREE.Vector3(s4, s4, s4);
this.nodes3[n.id].v3 = v3; this.nodes3[n.id].v3 = v3;
this.nodes3[n.id].scale = k * this.foreshortening;
this.nodes3[n.id].object.position.copy(v3); this.nodes3[n.id].object.position.copy(v3);
this.nodes3[n.id].object.scale.copy(s3); this.nodes3[n.id].object.scale.copy(this.scalev3);
this.nodes3[n.id].object.visible = ( !nodes_show || nodes_show.includes(n.label) );
} }
for( const l of this.links ) { for( const l of this.links ) {
this.updateLink(l, links_show); this.updateLink(l);
} }
for( const f of this.faces ) { for( const f of this.faces ) {
@ -154,6 +147,7 @@ class FourDShape extends THREE.Group {
} }
} }
} }
export { FourDShape }; export { FourDShape };

120
gui.js
View File

@ -1,26 +1,18 @@
import { GUI } from 'lil-gui'; import { GUI } from 'lil-gui';
const DEFAULTS = { const DEFAULTS = {
nodesize: 0.6, thickness: 0.25,
nodeopacity: 1, nodesize: 1.25,
linksize: 1.0, linkopacity: 0.5,
linkopacity: 0.75, shape: '120-cell',
shape: '600-cell', color: 0x3293a9,
link2opacity: 0.75,
option: 'none',
visibility: 5,
inscribed: false,
inscribe_all: false,
colour: 0x3293a9,
background: 0xd4d4d4, background: 0xd4d4d4,
hyperplane: 0.93, hyperplane: 2,
zoom: 1, xRotate: 'YW',
xRotate: 'YZ',
yRotate: 'XZ', yRotate: 'XZ',
dtheta: 0, dtheta: 0,
damping: false,
captions: true,
dpsi: 0, dpsi: 0,
} }
@ -28,82 +20,41 @@ const DEFAULTS = {
class FourDGUI { class FourDGUI {
constructor(funcs) { constructor(createShape, setColor, setBackground, setLinkOpacity) {
this.shapes = funcs.shapes;
this.gui = new GUI(); this.gui = new GUI();
const SHAPE_NAMES = this.shapes.map((s) => s.name);
this.parseLinkParams(); this.parseLinkParams();
const guiObj = this; const guiObj = this;
this.params = { this.params = {
shape: this.link['shape'], shape: this.link['shape'],
option: this.link['option'], thickness: this.link['thickness'],
inscribed: this.link['inscribed'],
inscribe_all: this.link['inscribe_all'],
linksize: this.link['linksize'],
linkopacity: this.link['linkopacity'], linkopacity: this.link['linkopacity'],
link2opacity: this.link['link2opacity'],
nodesize: this.link['nodesize'], nodesize: this.link['nodesize'],
nodeopacity: this.link['nodeopacity'], color: this.link['color'],
depth: this.link['depth'],
colour: this.link['colour'],
background: this.link['background'], background: this.link['background'],
hyperplane: this.link['hyperplane'], hyperplane: this.link['hyperplane'],
zoom: this.link['zoom'],
xRotate: this.link['xRotate'], xRotate: this.link['xRotate'],
yRotate: this.link['yRotate'], yRotate: this.link['yRotate'],
damping: false, damping: false,
captions: true,
dtheta: this.link['dtheta'], dtheta: this.link['dtheta'],
dpsi: this.link['dpsi'], dpsi: this.link['dpsi'],
"copy link": function () { guiObj.copyUrl() }, "copy link": function () { guiObj.copyUrl() }
}; };
if( funcs.extras ) {
for( const label in funcs.extras ) { this.gui.add(this.params, 'shape',
this.params[label] = funcs.extras[label]; [ '5-cell', '16-cell', 'tesseract', '24-cell', '600-cell', '120-cell', '120-cell-inscribed' ]
} ).onChange(createShape)
}
let options_ctrl; this.gui.add(this.params, 'hyperplane', 1.5, 2.25);
this.gui.add(this.params, 'shape', SHAPE_NAMES).onChange((shape) => { this.gui.add(this.params, 'thickness', 0.1, 2);
const options = this.getShapeOptions(shape); this.gui.add(this.params, 'linkopacity', 0, 1).onChange(setLinkOpacity);
options_ctrl = options_ctrl.options(options).onChange((option) => { this.gui.add(this.params, 'nodesize', 0.1, 4);
funcs.setVisibility(option) this.gui.addColor(this.params, 'color').onChange(setColor);
}); this.gui.addColor(this.params, 'background').onChange(setBackground);
options_ctrl.setValue(options[0])
funcs.changeShape(shape)
});
const options = this.getShapeOptions(this.params['shape']);
options_ctrl = this.gui.add(this.params, 'option').options(options).onChange((option) => {
funcs.setVisibility(option)
});
this.gui.add(this.params, 'hyperplane', 0.5, 1 / 0.8);
this.gui.add(this.params, 'zoom', 0.1, 2.0);
this.gui.add(this.params, 'nodesize', 0, 1.5);
this.gui.add(this.params, 'nodeopacity', 0, 1).onChange(funcs.setNodeOpacity);
this.gui.add(this.params, 'linksize', 0, 2);
this.gui.add(this.params, 'linkopacity', 0, 1).onChange((v) => funcs.setLinkOpacity(v, true));
this.gui.add(this.params, 'link2opacity', 0, 1).onChange((v) => funcs.setLinkOpacity(v, false));
this.gui.addColor(this.params, 'colour').onChange(funcs.setColours);
this.gui.addColor(this.params, 'background').onChange(funcs.setBackground);
this.gui.add(this.params, 'xRotate', [ 'YW', 'YZ', 'ZW' ]); this.gui.add(this.params, 'xRotate', [ 'YW', 'YZ', 'ZW' ]);
this.gui.add(this.params, 'yRotate', [ 'XZ', 'XY', 'XW' ]); this.gui.add(this.params, 'yRotate', [ 'XZ', 'XY', 'XW' ]);
this.gui.add(this.params, 'captions').onChange(this.showDocs);
this.gui.add(this.params, 'damping'); this.gui.add(this.params, 'damping');
this.gui.add(this.params, 'copy link'); this.gui.add(this.params, 'copy link');
if( funcs.extras ) {
for( const label in funcs.extras ) {
this.gui.add(this.params, label);
}
}
}
getShapeOptions(shape) {
const spec = this.shapes.filter((s) => s.name === shape);
if( spec && spec[0].options ) {
return spec[0].options.map((o) => o.name);
} else {
return [];
}
} }
@ -131,10 +82,9 @@ class FourDGUI {
parseLinkParams() { parseLinkParams() {
this.linkUrl = new URL(window.location.toLocaleString()); this.linkUrl = new URL(window.location.toLocaleString());
this.link = {}; this.link = {};
const guiObj = this;
this.urlParams = this.linkUrl.searchParams; this.urlParams = this.linkUrl.searchParams;
for( const param of [ "shape", "xRotate", "yRotate", "option" ]) { for( const param of [ "shape", "xRotate", "yRotate" ]) {
const value = this.urlParams.get(param); const value = this.urlParams.get(param);
if( value ) { if( value ) {
this.link[param] = value; this.link[param] = value;
@ -142,17 +92,12 @@ class FourDGUI {
this.link[param] = DEFAULTS[param]; this.link[param] = DEFAULTS[param];
} }
} }
for( const param of [ "inscribed", "inscribe_all"] ) { const guiObj = this;
this.link[param] = ( this.urlParams.get(param) === 'y' );
}
this.link['hyperplane'] = this.numParam('hyperplane', parseFloat); this.link['hyperplane'] = this.numParam('hyperplane', parseFloat);
this.link['zoom'] = this.numParam('zoom', parseFloat); this.link['thickness'] = this.numParam('thickness', parseFloat);
this.link['linksize'] = this.numParam('linksize', parseFloat);
this.link['linkopacity'] = this.numParam('linkopacity', parseFloat); this.link['linkopacity'] = this.numParam('linkopacity', parseFloat);
this.link['link2opacity'] = this.numParam('link2opacity', parseFloat);
this.link['nodesize'] = this.numParam('nodesize', parseFloat); this.link['nodesize'] = this.numParam('nodesize', parseFloat);
this.link['nodeopacity'] = this.numParam('nodeopacity', parseFloat); this.link['color'] = this.numParam('color', (s) => guiObj.stringToHex(s));
this.link['colour'] = this.numParam('colour', (s) => guiObj.stringToHex(s));
this.link['background'] = this.numParam('background', (s) => guiObj.stringToHex(s)); this.link['background'] = this.numParam('background', (s) => guiObj.stringToHex(s));
this.link['dpsi'] = this.numParam('dpsi', parseFloat); this.link['dpsi'] = this.numParam('dpsi', parseFloat);
this.link['dtheta'] = this.numParam('dtheta', parseFloat); this.link['dtheta'] = this.numParam('dtheta', parseFloat);
@ -162,17 +107,11 @@ class FourDGUI {
copyUrl() { copyUrl() {
const url = new URL(this.linkUrl.origin + this.linkUrl.pathname); const url = new URL(this.linkUrl.origin + this.linkUrl.pathname);
url.searchParams.append("shape", this.params.shape); url.searchParams.append("shape", this.params.shape);
url.searchParams.append("option", this.params.option); url.searchParams.append("thickness", this.params.thickness.toString());
url.searchParams.append("inscribed", this.params.inscribed ? 'y': 'n');
url.searchParams.append("inscribe_all", this.params.inscribe_all ? 'y': 'n');
url.searchParams.append("linksize", this.params.linksize.toString());
url.searchParams.append("nodesize", this.params.nodesize.toString()); url.searchParams.append("nodesize", this.params.nodesize.toString());
url.searchParams.append("nodeopacity", this.params.nodesize.toString()); url.searchParams.append("color", this.hexToString(this.params.color));
url.searchParams.append("linkopacity", this.params.nodeopacity.toString());
url.searchParams.append("colour", this.hexToString(this.params.colour));
url.searchParams.append("background", this.hexToString(this.params.background)); url.searchParams.append("background", this.hexToString(this.params.background));
url.searchParams.append("hyperplane", this.params.hyperplane.toString()); url.searchParams.append("hyperplane", this.params.hyperplane.toString());
url.searchParams.append("zoom", this.params.zoom.toString());
url.searchParams.append("xRotate", this.params.xRotate); url.searchParams.append("xRotate", this.params.xRotate);
url.searchParams.append("yRotate", this.params.yRotate); url.searchParams.append("yRotate", this.params.yRotate);
url.searchParams.append("dtheta", this.params.dtheta.toString()); url.searchParams.append("dtheta", this.params.dtheta.toString());
@ -187,6 +126,7 @@ class FourDGUI {
return; return;
} }
navigator.clipboard.writeText(text).then(function() { navigator.clipboard.writeText(text).then(function() {
console.log('Async: Copying to clipboard was successful!');
}, function(err) { }, function(err) {
console.error('Async: Could not copy text: ', err); console.error('Async: Could not copy text: ', err);
}); });

31
index.html
View File

@ -5,40 +5,9 @@
<title>FourD</title> <title>FourD</title>
<style> <style>
body { margin: 0; } body { margin: 0; }
div#description {
position: fixed;
top: 0;
left: 0;
width: 20%;
z-index: 2;
font-family: sans-serif;
padding: 1em;
}
div#release_notes {
position: fixed;
top: 0;
left: 0;
width: 20%;
z-index: 2;
padding: 1em;
font-family: sans-serif;
}
div#info {
position: fixed;
bottom:0;
right: 0;
z-index: 2;
border:0.5em;
font-family: sans-serif }
</style> </style>
</head> </head>
<body> <body>
<script type="module" src="/main.js"></script> <script type="module" src="/main.js"></script>
<div id="description"></div>
<div id="release_notes"></div>
<div id="info"><a href="#" id="show_notes">release 1.3</a> |
by <a target="_blank" href="https://mikelynch.org/">Mike Lynch</a> |
<a target="_blank" href="https://git.tilde.town/bombinans/fourdjs">source</a></div>
</body> </body>
</html> </html>

409
label_inscribed_600cell.js
View File

@ -1,409 +0,0 @@
import * as POLYTOPES from './polytopes.js';
import * as CELLINDEX from './cellindex.js';
// script to help me label the vertices of one of the inscribed 600-cells of a 120-cell
// with Schoute's partition (which is used to label the main 600-cell)
function choice(a) {
const r = Math.floor(Math.random() * a.length);
return a[r];
}
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;
}
}
export function dist(n1, n2) {
return Math.sqrt((n1.x - n2.x) ** 2 + (n1.y - n2.y) ** 2 + (n1.z - n2.z) ** 2 + (n1.w - n2.w) ** 2);
}
function round_dist(raw) {
return Math.floor(raw * 1000) / 1000;
}
export function make_one_600cell() {
const nodes = POLYTOPES.make_120cell_vertices();
const links = POLYTOPES.auto_detect_edges(nodes, 4);
for( const cstr in CELLINDEX.INDEX120 ) {
POLYTOPES.label_nodes(nodes, CELLINDEX.INDEX120[cstr], Number(cstr));
}
links.map((l) => l.label = 0);
const nodes600 = nodes.filter((n) => n.label === 1);
const links600 = POLYTOPES.auto_detect_edges(nodes600, 12);
links600.map((l) => l.label = 1);
return {
nodes: nodes600,
links: links600
}
}
export function base_600cell() {
const nodes = POLYTOPES.make_600cell_vertices();
const links = POLYTOPES.auto_detect_edges(nodes, 12);
links.map((l) => l.label = 0);
for( const p of [1, 2, 3, 4, 5]) {
const nodes24 = nodes.filter((n) => n.label === p);
}
return {
nodes: nodes,
links: links,
};
}
export function distance_groups(shape) {
// get list of other nodes by distance
// sort them and dump them out
const dists = {};
shape.nodes.map((n) => {
const draw = dist(shape.nodes[0], n);
const dtrunc = round_dist(draw);
if( !(dtrunc in dists) ) {
dists[dtrunc] = [];
}
dists[dtrunc].push(n.id);
});
return dists;
}
export function insc600_layers(cell600) {
const layers = distance_groups(cell600);
/* const sorted = Object.keys(layers).sort((a,b) => a - b);
for( const d of sorted ) {
const ids = layers[d].map((n) => n.id);
console.log(`Layer at distance ${d}`);
console.log(ids);
} */
return layers;
}
export function neighbours(shape, nid) {
const links = shape.links.filter((l) => l.source === nid || l.target == nid );
const nodes = links.map((l) => {
if( l.source === nid ) {
return l.target;
} else {
return l.source;
}
});
return nodes;
}
export function neighbours_in_subset(shape, subset, nid) {
// shape = nodes, links
// subset = a list of ids
// n = an id
// returns all of n's neighbours which are in subset
const all_nbors = neighbours(shape, nid);
return all_nbors.filter((n) => subset.includes(n));
}
export function face_vertices(shape, f1, f2, f3) {
// for f1/f2/f3 forming a triangular face, return the two vertices of the
// adjacent tetrahedra
const n1 = neighbours(shape, f1).filter((n) => n !== f2 && n !== f3);
const n2 = neighbours(shape, f2).filter((n) => n !== f1 && n !== f3);
const n3 = neighbours(shape, f3).filter((n) => n !== f1 && n !== f2);
const ns = n1.filter((n) => n2.includes(n) && n3.includes(n));
return ns;
}
export function shared_neighbours(shape, nodes) {
let ns = shape.nodes.map((n) => n.id);
for( const n of nodes ) {
ns = neighbours_in_subset(shape, ns, n);
}
return ns;
}
export function layer_neighbours(cell600, layer) {
console.log("Layer neighbours");
for( const n of layer ) {
console.log(`n = ${n}`);
const nbors = neighbours_in_subset(cell600, layer, n);
console.log(` Vertex ${n} neighbours: ` + JSON.stringify(nbors));
}
}
const ARCTIC_I_FACES = [
[ 419, 223, 253 ],
[ 419, 253, 331 ],
[ 419, 331, 427 ],
[ 419, 427, 339 ],
[ 419, 339, 223 ],
[ 253, 223, 265 ],
[ 331, 253, 473 ],
[ 427, 331, 539 ],
[ 339, 427, 555 ],
[ 511, 339, 223 ],
[ 223, 511, 265 ],
[ 253, 265, 473 ],
[ 331, 473, 539 ],
[ 427, 539, 555 ],
[ 339, 555, 511 ],
[ 393, 265, 511 ],
[ 393, 473, 265 ],
[ 393, 539, 473 ],
[ 393, 555, 539 ],
[ 393, 555, 511 ]
];
export const ARCTIC_FACES = ARCTIC_I_FACES.map((f) => {
return f.map((nid) => CELLINDEX.CELL600_METAMAP[nid]);
});
export const TEMPERATE_PENTAGONS_I = [
[ 499, 179, 471, 367, 131 ],
[ 131, 367, 165, 313, 449 ],
[ 131, 449, 185, 258, 499 ],
[ 499, 258, 140, 274, 179 ],
[ 179, 274, 527, 95, 471 ],
[ 471, 95, 347, 165, 367 ],
[ 347, 573, 105, 313, 165 ],
[ 313, 105, 585, 185, 449 ],
[ 185, 585, 306, 140, 258 ],
[ 140, 306, 207, 527, 274 ],
[ 527, 207, 573, 347, 95 ],
[ 105, 573, 207, 306, 585 ],
];
export const TEMPERATE_PENTAGONS = TEMPERATE_PENTAGONS_I.map((f) => {
return f.map((nid) => CELLINDEX.CELL600_METAMAP[nid])
});
export function layer_two(cell600, centre, faces) {
for ( const face of faces ) {
const n2 = face_vertices(cell600, face[0], face[1], face[2]);
console.log(face, n2);
}
}
export function layer_three(shape, pentagons) {
for ( const pentagon of pentagons ) {
console.log(pentagon);
const s = shared_neighbours(shape, pentagon);
console.log(s);
console.log("\n");
}
}
export const TEMPERATE_APICES = [
563,
513,
285,
324,
231,
487,
413,
425,
378,
388,
543,
289,
];
// this one generates the mapping to the base 600 cell as well, unlike
// previous versions where I did the mapping by hand
export function equator(i600, b600, apices) {
const pairs = [];
// get all 30 of the edges on the temperate dodeca
for( let i = 0; i < 11; i++ ) {
for( let j = i + 1; j < 12; j++ ) {
const s = shared_neighbours(i600, [ apices[i], apices[j] ]);
if( s.length > 0 ) {
const e = s.filter((n) => !(n in CELLINDEX.CELL600_METAMAP));
pairs.push([apices[i], apices[j], e]);
}
}
}
const MAPPED = Object.values(CELLINDEX.CELL600_METAMAP);
const eq = {};
for( const pair of pairs ) {
const b1 = CELLINDEX.CELL600_METAMAP[pair[0]];
const b2 = CELLINDEX.CELL600_METAMAP[pair[1]];
const s = shared_neighbours(b600, [ b1, b2 ]);
const e = s.filter((n) => !MAPPED.includes(n));
if( e.length !== 1 ) {
console.log(`Bad value at ${pair}`);
} else {
eq[pair[2]] = e[0];
}
}
return eq;
}
export function antipode(shape, nid) {
const n0 = shape.nodes.filter((n) => n.id === nid)[0];
if( !n0 ) {
throw new Error(`antipodes error: couldn't find node ${nid} in shape`);
}
const dists = shape.nodes.map((n) => [ dist(n, n0), n ]);
dists.sort((a, b) => b[0] - a[0]);
return dists[0][1];
}
export function check_antipodes() {
const c600 = base_600cell();
const seen = {};
c600.nodes.map((n) => {
const a = antipode(c600, n.id);
if( !seen[a.id] && !seen[n.id] ) {
seen[a.id] = true;
seen[n.id] = true;
console.log(`${n.id} - ${n.label} / ${a.id} - ${a.label}`);
if( n.label !== a.label ) {
console.lot("MISMATCH");
}
}
});
}
export function meta600_label(b600, iid) {
const bid = CELLINDEX.CELL600_METAMAP[iid];
const bn = b600.nodes.filter((n) => bid === n.id);
return bn[0].label;
}
export function map_antipodes() {
const b600 = base_600cell();
const i600 = make_one_600cell();
const already = [];
const antimap = {};
for( const inid in CELLINDEX.CELL600_METAMAP ) {
const bnid = CELLINDEX.CELL600_METAMAP[inid];
const banti = antipode(b600, Number(bnid));
const ianti = antipode(i600, Number(inid));
if( CELLINDEX.CELL600_METAMAP[ianti.id] ) {
//console.log(`Anti ${ianti.id} is already mapped`);
already.push(ianti.id);
const l1 = meta600_label(b600, inid);
const l2 = meta600_label(b600, Number(ianti.id));
//console.log(`labels: ${l1} ${l2}`);
} else {
antimap[ianti.id] = banti.id;
}
}
console.log(JSON.stringify(antimap, null, 2));
}
export function check_metamap_completeness() {
const b600 = base_600cell();
const i600 = make_one_600cell();
const labels = {};
const bids = {};
const mm = CELLINDEX.CELL600_METAMAP;
for( const i of i600.nodes ) {
if( i.id in mm ) {
const ml = meta600_label(b600, i.id);
if( !(ml in labels) ) {
labels[ml] = [];
}
labels[ml].push(i.id);
bids[mm[i.id]] = 1;
} else {
console.log(`inscribed node ${i.id} is not in metamap`);
}
}
for( const b of b600.nodes ) {
if( !(b.id in bids) ) {
console.log(`base mode ${b.id} is not mapped`);
}
}
for ( const label in labels ) {
console.log(`label ${label} has ${labels[label].length} nodes`);
}
}
// this gives a mapping from cell-120-ids of one inscribed 600-cell to the
// metamap labels, which I can then [checks notes] use to colour the 5-cells.
export function metamap_to_labels() {
const b600 = base_600cell();
const i600 = make_one_600cell();
const mapping = {};
for( const inode of i600.nodes ) {
mapping[inode.id] = meta600_label(b600, inode.id);;
}
return mapping;
}
export function cell5_labels() {
const labels = metamap_to_labels();
// now build a dict of the 120 cell5s with the colours from the above
const cell5map = {};
const CELL5S = CELLINDEX.CELL120_CELL5.cell5s;
for( const c5i in CELL5S ) {
const n1 = CELL5S[c5i][0]; // label 1 node;
const ml = labels[n1];
cell5map[c5i] = ml;
}
return cell5map;
}
export function rebuild_cell5_index() {
const labels = metamap_to_labels();
const new_cell5s = {};
const CELL5S = CELLINDEX.CELL120_CELL5;
for( const c5i in CELL5S ) {
const n1 = CELL5S[c5i][0]; // label 1 node;
const ml = labels[n1];
new_cell5s[c5i] = {
nodes: CELL5S[c5i],
label: ml
}
}
return new_cell5s;
}
const nc5 = rebuild_cell5_index();
console.log(JSON.stringify(nc5, null, 4));

173
layer600cell.js
View File

@ -1,173 +0,0 @@
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);
}

119
linktest.js
View File

@ -1,119 +0,0 @@
import * as THREE from 'three';
import { OrbitControls } from 'three/addons/controls/OrbitControls.js';
import { GUI } from 'lil-gui';
import { TaperedLink } from './taperedLink.js';
const FACE_OPACITY = 0.3;
const CAMERA_K = 5;
// scene, lights and camera
const scene = new THREE.Scene();
const camera = new THREE.PerspectiveCamera( 75, window.innerWidth / window.innerHeight, 0.1, 1000 );
const light = new THREE.PointLight(0xffffff, 2);
light.position.set(10, 10, 10);
scene.add(light);
const light2 = new THREE.PointLight(0xffffff, 2);
light2.position.set(-10, 5, 10);
scene.add(light);
const amblight = new THREE.AmbientLight(0xffffff, 0.5);
scene.add(amblight);
camera.position.set(0, 0, CAMERA_K / 2);
camera.lookAt(0, 0, 0);
camera.position.z = 8;
const renderer = new THREE.WebGLRenderer({antialias: true});
renderer.setSize( window.innerWidth, window.innerHeight );
renderer.localClippingEnabled = true;
const controls = new OrbitControls( camera, renderer.domElement );
controls.autoRotate = true;
document.body.appendChild( renderer.domElement );
const NODEC = 0x3293a9;
const LINKC = 0x00ff88;
const BACKGROUNDC = 0xd4d4d4;
scene.background = new THREE.Color(BACKGROUNDC);
const material = new THREE.MeshStandardMaterial({ color: LINKC });
material.transparent = true;
material.opacity = 0.7;
const node_mat = new THREE.MeshStandardMaterial({ color: NODEC });
node_mat.transparent = true;
node_mat.opacity = 0.5;
const params = {
r1: 0.5,
r2: 0.6,
sync: false,
l: 9,
rotx: 1,
roty: 0,
rotz: 0,
};
const gui = new GUI();
gui.add(params, "r1", 0.01, 1.5);
gui.add(params, "r2", 0.01, 1.5);
gui.add(params, "sync");
gui.add(params, "l", 0, 10);
gui.add(params, "rotx", 0, 4);
gui.add(params, "roty", 0, 4);
gui.add(params, "rotz", 0, 4);
function makeNode(material, pos, r) {
const geometry = new THREE.SphereGeometry(1);
const sphere = new THREE.Mesh(geometry, material);
const node = {
v3: pos,
object: sphere
};
updateNode(node, pos, r);
return node;
}
function updateNode(node, pos, r) {
node.v3 = pos;
node.object.scale.copy(new THREE.Vector3(r, r, r));
node.object.position.copy(pos);
}
const n1 = makeNode(node_mat, new THREE.Vector3(-params["l"], -1, -1), params["r1"]);
const n2 = makeNode(node_mat, new THREE.Vector3(params["l"], 1, 1), params["r2"]);
const tl = new TaperedLink(material, n1, n2, params["r1"], params["r2"]);
scene.add(n1.object);
scene.add(n2.object);
scene.add(tl);
function animate() {
requestAnimationFrame(animate);
const r1 = params["r1"];
const r2 = params["sync"] ? r1 : params["r2"]
updateNode(n1, new THREE.Vector3(- params["l"], -1, -1), r1);
updateNode(n2, new THREE.Vector3(params["l"], 1, 1), r2);
tl.update(n1, n2, r1, r2, params["rotx"], params["roty"], params["rotz"]);
controls.update();
renderer.render(scene, camera);
}
animate();

201
main.js
View File

@ -1,31 +1,5 @@
import * as THREE from 'three'; import * as THREE from 'three';
const RELEASE_NOTES = `
<p><b>v1.3 - 7/2/2026</b></p>
<p>Went to inordinate lengths to apply the partition of the 600-cell (into five
24-cells) to the 5-cell inscription in the 120-cell, so that they could be coloured
in a way which reveals some of that symmetry.</p>
<p><b>v1.2 - 18/1/2026</b></p>
<p>Added a second visualisation of the 120-cell's 5-cells without the 120-cell links and with more colours added so you can get a sense of the individual 5-cells.</p>
<p><b>v1.1 - 1/1/2026</b></p>
<p>The 120-cell now includes a visualisation of its inscribed 5-cells, which honestly
looks like less of a mess than I expected it to.</p>
<p><b>v1.0 - 16/11/2025</b></p>
<p>It's been <a target="_blank" href="https://mikelynch.org/2023/Sep/02/120-cell/">two years</a> since
I first made this, and I haven't updated it in a while, but I got tapered links to
work without too much performance overhead, so that seemed worth a version.</p>
<p>The results flicker a bit at low opacities but otherwise I'm pretty happy with
it.</p>
`;
import * as POLYTOPES from './polytopes.js'; import * as POLYTOPES from './polytopes.js';
@ -35,7 +9,6 @@ import { FourDShape } from './fourDShape.js';
import { get_colours } from './colours.js'; import { get_colours } from './colours.js';
const FACE_OPACITY = 0.3; const FACE_OPACITY = 0.3;
const CAMERA_K = 5;
// scene, lights and camera // scene, lights and camera
@ -50,44 +23,34 @@ 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(0, 0, CAMERA_K / 2); camera.position.z = 4;
camera.lookAt(0, 0, 0);
//camera.position.z = 4;
const renderer = new THREE.WebGLRenderer({antialias: true}); const renderer = new THREE.WebGLRenderer({antialias: true});
renderer.setSize( window.innerWidth, window.innerHeight ); renderer.setSize( window.innerWidth, window.innerHeight );
renderer.localClippingEnabled = true;
document.body.appendChild( renderer.domElement ); document.body.appendChild( renderer.domElement );
// set up colours and materials for gui callbacks // set up colours and materials for gui callbacks
scene.background = new THREE.Color(DEFAULTS.background); scene.background = new THREE.Color(DEFAULTS.background);
const node_colours = get_colours(DEFAULTS.colour); const material = new THREE.MeshStandardMaterial({ color: DEFAULTS.color });
const node_colours = get_colours(DEFAULTS.color);
material.transparent = true;
material.opacity = 0.5;
const node_ms = node_colours.map((c) => new THREE.MeshStandardMaterial({color: c})); const node_ms = node_colours.map((c) => new THREE.MeshStandardMaterial({color: c}));
const link_ms = node_colours.map((c) => new THREE.MeshStandardMaterial({color: c})); const link_ms = node_colours.map((c) => new THREE.MeshStandardMaterial({color: c}));
node_ms.map((m) => {
m.transparent = true;
m.opacity = 1.0;
}
);
link_ms.map((m) => { link_ms.map((m) => {
m.transparent = true; m.transparent = true;
m.opacity = 0.5; m.opacity = 0.5;
} }
); )
const face_ms = [ const face_ms = [
new THREE.MeshStandardMaterial( { color: 0x44ff44 } ) new THREE.MeshLambertMaterial( { color: 0x44ff44 } )
]; ];
for( const face_m of face_ms ) { for( const face_m of face_ms ) {
@ -96,141 +59,54 @@ for( const face_m of face_ms ) {
} }
const STRUCTURES = POLYTOPES.build_all(); const STRUCTURES = {
'5-cell': POLYTOPES.cell5(),
const STRUCTURES_BY_NAME = {}; '16-cell': POLYTOPES.cell16(),
'tesseract': POLYTOPES.tesseract(),
STRUCTURES.map((s) => STRUCTURES_BY_NAME[s.name] = s); '24-cell': POLYTOPES.cell24(),
'120-cell': POLYTOPES.cell120(),
'120-cell-inscribed': POLYTOPES.cell120_inscribed(),
'600-cell': POLYTOPES.cell600()
};
let shape = false; let shape = false;
let structure = false;
let node_show = [];
let link_show = [];
function createShape(name) {
function createShape(name, option) {
if( shape ) { if( shape ) {
scene.remove(shape); scene.remove(shape);
} }
structure = STRUCTURES_BY_NAME[name]; shape = new FourDShape(node_ms, link_ms, face_ms, STRUCTURES[name]);
shape = new FourDShape(node_ms, link_ms, face_ms, structure);
scene.add(shape); scene.add(shape);
setVisibility(option ? option : structure.options[0].name);
} }
function displayDocs(name) {
const docdiv = document.getElementById("description");
const description = STRUCTURES_BY_NAME[name].description;
if( description ) {
docdiv.innerHTML =`<p>${name}</p><p>${description}</p>`;
} else {
docdiv.innerHTML =`<p>${name}</p>`;
}
}
function showDocs(visible) {
const docdiv = document.getElementById("description");
if( visible ) {
docdiv.style.display = '';
} else {
docdiv.style.display = 'none';
}
}
function releaseNotes() {
showDocs(false);
const reldiv = document.getElementById("release_notes");
reldiv.style.display = '';
reldiv.innerHTML = RELEASE_NOTES + '<p><a id="no_notes" href="#">[hide]</a>';
const goaway = document.getElementById("no_notes");
goaway.addEventListener('click', noNotes);
}
function noNotes() {
const reldiv = document.getElementById("release_notes");
reldiv.style.display = 'none';
}
const relnotes = document.getElementById('show_notes');
relnotes.addEventListener('click', releaseNotes);
// initialise gui and read params from URL // initialise gui and read params from URL
// callbacks to do things which are triggered by controls: reset the shape, // callbacks to do things which are triggered by controls: reset the shape,
// change the colors. Otherwise we just read stuff from gui.params. // change the colors. Otherwise we just read stuff from gui.params.
function setColours(c) { function setColors(c) {
const nc = get_colours(c); const nc = get_colours(c);
for( let i = 0; i < node_ms.length; i++ ) { for( let i = 0; i < node_ms.length; i++ ) {
node_ms[i].color = new THREE.Color(nc[i]); node_ms[i].color = new THREE.Color(nc[i]);
link_ms[i].color = new THREE.Color(nc[i]); link_ms[i].color = new THREE.Color(nc[i]);
} }
if( shape ) { material.color = new THREE.Color(c);
// taperedLink.set_color updates according to the link index
shape.links.map((l) => l.object.set_colour(nc));
}
} }
function setBackground(c) { function setBackground(c) {
scene.background = new THREE.Color(c) scene.background = new THREE.Color(c)
} }
// taperedLinks have their own materials so we have to set opacity function setLinkOpacity(o) {
// on them individually. And also set the base materials as they for( const lm of link_ms ) {
// will get updated from it when the shape changes lm.opacity = o;
function setLinkOpacity(o, primary) {
link_ms.map((lm) => lm.opacity = o);
if( shape ) {
shape.links.map((l) => {
if( (primary && l.label == 0) || (!primary && l.label !== 0) ) {
l.object.material.opacity = o
}
});
}
}
function setNodeOpacity(o) {
node_ms.map((nm) => nm.opacity = o);
}
let gui;
function changeShape() {
createShape(gui.params.shape);
displayDocs(gui.params.shape);
}
function setVisibility(option_name) {
const option = structure.options.filter((o) => o.name === option_name);
if( option.length ) {
node_show = option[0].nodes;
link_show = option[0].links;
} else {
console.log(`Error: option '${option_name}' not found`);
} }
} }
const gui = new FourDGUI(createShape, setColors, setBackground, setLinkOpacity);
gui = new FourDGUI(
{
shapes: STRUCTURES,
changeShape: changeShape,
setColours: setColours,
setBackground: setBackground,
setNodeOpacity: setNodeOpacity,
setLinkOpacity: setLinkOpacity,
setVisibility: setVisibility,
showDocs: showDocs,
}
);
// these are here to pick up colour settings from the URL params // these are here to pick up colour settings from the URL params
setColours(gui.params.colour); setColors(gui.params.color);
setBackground(gui.params.background); setBackground(gui.params.background);
const dragK = 0.005; const dragK = 0.005;
@ -270,8 +146,7 @@ renderer.domElement.addEventListener("pointerup", (event) => {
dragging = false; dragging = false;
}) })
createShape(gui.params.shape, gui.params.option); createShape(gui.params.shape);
displayDocs(gui.params.shape);
function animate() { function animate() {
requestAnimationFrame( animate ); requestAnimationFrame( animate );
@ -289,14 +164,10 @@ function animate() {
rotfn[gui.params.xRotate](theta), rotfn[gui.params.xRotate](theta),
rotfn[gui.params.yRotate](psi) rotfn[gui.params.yRotate](psi)
]; ];
shape.hyperplane = 1 / gui.params.hyperplane; shape.hyperplane = gui.params.hyperplane;
camera.position.set(0, 0, gui.params.zoom * CAMERA_K * gui.params.hyperplane); shape.link_scale = gui.params.thickness;
shape.node_scale = gui.params.nodesize; shape.node_scale = gui.params.nodesize;
shape.link_scale = gui.params.linksize * gui.params.nodesize * 0.5; shape.render3(rotations);
shape.render3(rotations, node_show, link_show);
renderer.render( scene, camera ); renderer.render( scene, camera );
} }

270
package-lock.json generated
View File

@ -4,11 +4,9 @@
"requires": true, "requires": true,
"packages": { "packages": {
"": { "": {
"name": "fourdjs",
"dependencies": { "dependencies": {
"color": "^4.2.3",
"color-scheme": "^1.0.1", "color-scheme": "^1.0.1",
"lil-gui": "^0.19.0", "lil-gui": "^0.18.2",
"three": "^0.154.0" "three": "^0.154.0"
}, },
"devDependencies": { "devDependencies": {
@ -16,9 +14,9 @@
} }
}, },
"node_modules/@esbuild/android-arm": { "node_modules/@esbuild/android-arm": {
"version": "0.18.20", "version": "0.18.15",
"resolved": "https://registry.npmjs.org/@esbuild/android-arm/-/android-arm-0.18.20.tgz", "resolved": "https://registry.npmjs.org/@esbuild/android-arm/-/android-arm-0.18.15.tgz",
"integrity": "sha512-fyi7TDI/ijKKNZTUJAQqiG5T7YjJXgnzkURqmGj13C6dCqckZBLdl4h7bkhHt/t0WP+zO9/zwroDvANaOqO5Sw==", "integrity": "sha512-wlkQBWb79/jeEEoRmrxt/yhn5T1lU236OCNpnfRzaCJHZ/5gf82uYx1qmADTBWE0AR/v7FiozE1auk2riyQd3w==",
"cpu": [ "cpu": [
"arm" "arm"
], ],
@ -32,9 +30,9 @@
} }
}, },
"node_modules/@esbuild/android-arm64": { "node_modules/@esbuild/android-arm64": {
"version": "0.18.20", "version": "0.18.15",
"resolved": "https://registry.npmjs.org/@esbuild/android-arm64/-/android-arm64-0.18.20.tgz", "resolved": "https://registry.npmjs.org/@esbuild/android-arm64/-/android-arm64-0.18.15.tgz",
"integrity": "sha512-Nz4rJcchGDtENV0eMKUNa6L12zz2zBDXuhj/Vjh18zGqB44Bi7MBMSXjgunJgjRhCmKOjnPuZp4Mb6OKqtMHLQ==", "integrity": "sha512-NI/gnWcMl2kXt1HJKOn2H69SYn4YNheKo6NZt1hyfKWdMbaGadxjZIkcj4Gjk/WPxnbFXs9/3HjGHaknCqjrww==",
"cpu": [ "cpu": [
"arm64" "arm64"
], ],
@ -48,9 +46,9 @@
} }
}, },
"node_modules/@esbuild/android-x64": { "node_modules/@esbuild/android-x64": {
"version": "0.18.20", "version": "0.18.15",
"resolved": "https://registry.npmjs.org/@esbuild/android-x64/-/android-x64-0.18.20.tgz", "resolved": "https://registry.npmjs.org/@esbuild/android-x64/-/android-x64-0.18.15.tgz",
"integrity": "sha512-8GDdlePJA8D6zlZYJV/jnrRAi6rOiNaCC/JclcXpB+KIuvfBN4owLtgzY2bsxnx666XjJx2kDPUmnTtR8qKQUg==", "integrity": "sha512-FM9NQamSaEm/IZIhegF76aiLnng1kEsZl2eve/emxDeReVfRuRNmvT28l6hoFD9TsCxpK+i4v8LPpEj74T7yjA==",
"cpu": [ "cpu": [
"x64" "x64"
], ],
@ -64,9 +62,9 @@
} }
}, },
"node_modules/@esbuild/darwin-arm64": { "node_modules/@esbuild/darwin-arm64": {
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"resolved": "https://registry.npmjs.org/@esbuild/darwin-arm64/-/darwin-arm64-0.18.20.tgz", "resolved": "https://registry.npmjs.org/@esbuild/darwin-arm64/-/darwin-arm64-0.18.15.tgz",
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"resolved": "https://registry.npmjs.org/fsevents/-/fsevents-2.3.3.tgz", "resolved": "https://registry.npmjs.org/fsevents/-/fsevents-2.3.2.tgz",
"integrity": "sha512-5xoDfX+fL7faATnagmWPpbFtwh/R77WmMMqqHGS65C3vvB0YHrgF+B1YmZ3441tMj5n63k0212XNoJwzlhffQw==", "integrity": "sha512-xiqMQR4xAeHTuB9uWm+fFRcIOgKBMiOBP+eXiyT7jsgVCq1bkVygt00oASowB7EdtpOHaaPgKt812P9ab+DDKA==",
"dev": true, "dev": true,
"hasInstallScript": true, "hasInstallScript": true,
"optional": true, "optional": true,
@ -460,15 +421,10 @@
"node": "^8.16.0 || ^10.6.0 || >=11.0.0" "node": "^8.16.0 || ^10.6.0 || >=11.0.0"
} }
}, },
"node_modules/is-arrayish": {
"version": "0.3.2",
"resolved": "https://registry.npmjs.org/is-arrayish/-/is-arrayish-0.3.2.tgz",
"integrity": "sha512-eVRqCvVlZbuw3GrM63ovNSNAeA1K16kaR/LRY/92w0zxQ5/1YzwblUX652i4Xs9RwAGjW9d9y6X88t8OaAJfWQ=="
},
"node_modules/lil-gui": { "node_modules/lil-gui": {
"version": "0.19.0", "version": "0.18.2",
"resolved": "https://registry.npmjs.org/lil-gui/-/lil-gui-0.19.0.tgz", "resolved": "https://registry.npmjs.org/lil-gui/-/lil-gui-0.18.2.tgz",
"integrity": "sha512-02/Z7rPng3GXWFwkQVj1hQaJYo2fIEYctqe0ima5uI/N2HEagB9ZGCQKkVWr3UuKfTr0arto3Q9prTB8sxtJJw==" "integrity": "sha512-DgdrLy3/KGC0PiQLKgOcJMPItP4xY4iWgJ9+91Zaxfr8GCTmMps05QS9w9jW7yspILlbscbquwjOwxmWnSx5Uw=="
}, },
"node_modules/nanoid": { "node_modules/nanoid": {
"version": "3.3.6", "version": "3.3.6",
@ -495,9 +451,9 @@
"dev": true "dev": true
}, },
"node_modules/postcss": { "node_modules/postcss": {
"version": "8.4.31", "version": "8.4.27",
"resolved": "https://registry.npmjs.org/postcss/-/postcss-8.4.31.tgz", "resolved": "https://registry.npmjs.org/postcss/-/postcss-8.4.27.tgz",
"integrity": "sha512-PS08Iboia9mts/2ygV3eLpY5ghnUcfLV/EXTOW1E2qYxJKGGBUtNjN76FYHnMs36RmARn41bC0AZmn+rR0OVpQ==", "integrity": "sha512-gY/ACJtJPSmUFPDCHtX78+01fHa64FaU4zaaWfuh1MhGJISufJAH4cun6k/8fwsHYeK4UQmENQK+tRLCFJE8JQ==",
"dev": true, "dev": true,
"funding": [ "funding": [
{ {
@ -523,9 +479,9 @@
} }
}, },
"node_modules/rollup": { "node_modules/rollup": {
"version": "3.29.4", "version": "3.26.3",
"resolved": "https://registry.npmjs.org/rollup/-/rollup-3.29.4.tgz", "resolved": "https://registry.npmjs.org/rollup/-/rollup-3.26.3.tgz",
"integrity": "sha512-oWzmBZwvYrU0iJHtDmhsm662rC15FRXmcjCk1xD771dFDx5jJ02ufAQQTn0etB2emNk4J9EZg/yWKpsn9BWGRw==", "integrity": "sha512-7Tin0C8l86TkpcMtXvQu6saWH93nhG3dGQ1/+l5V2TDMceTxO7kDiK6GzbfLWNNxqJXm591PcEZUozZm51ogwQ==",
"dev": true, "dev": true,
"bin": { "bin": {
"rollup": "dist/bin/rollup" "rollup": "dist/bin/rollup"
@ -538,14 +494,6 @@
"fsevents": "~2.3.2" "fsevents": "~2.3.2"
} }
}, },
"node_modules/simple-swizzle": {
"version": "0.2.2",
"resolved": "https://registry.npmjs.org/simple-swizzle/-/simple-swizzle-0.2.2.tgz",
"integrity": "sha512-JA//kQgZtbuY83m+xT+tXJkmJncGMTFT+C+g2h2R9uxkYIrE2yy9sgmcLhCnw57/WSD+Eh3J97FPEDFnbXnDUg==",
"dependencies": {
"is-arrayish": "^0.3.1"
}
},
"node_modules/source-map-js": { "node_modules/source-map-js": {
"version": "1.0.2", "version": "1.0.2",
"resolved": "https://registry.npmjs.org/source-map-js/-/source-map-js-1.0.2.tgz", "resolved": "https://registry.npmjs.org/source-map-js/-/source-map-js-1.0.2.tgz",
@ -561,14 +509,14 @@
"integrity": "sha512-Uzz8C/5GesJzv8i+Y2prEMYUwodwZySPcNhuJUdsVMH2Yn4Nm8qlbQe6qRN5fOhg55XB0WiLfTPBxVHxpE60ug==" "integrity": "sha512-Uzz8C/5GesJzv8i+Y2prEMYUwodwZySPcNhuJUdsVMH2Yn4Nm8qlbQe6qRN5fOhg55XB0WiLfTPBxVHxpE60ug=="
}, },
"node_modules/vite": { "node_modules/vite": {
"version": "4.5.3", "version": "4.4.6",
"resolved": "https://registry.npmjs.org/vite/-/vite-4.5.3.tgz", "resolved": "https://registry.npmjs.org/vite/-/vite-4.4.6.tgz",
"integrity": "sha512-kQL23kMeX92v3ph7IauVkXkikdDRsYMGTVl5KY2E9OY4ONLvkHf04MDTbnfo6NKxZiDLWzVpP5oTa8hQD8U3dg==", "integrity": "sha512-EY6Mm8vJ++S3D4tNAckaZfw3JwG3wa794Vt70M6cNJ6NxT87yhq7EC8Rcap3ahyHdo8AhCmV9PTk+vG1HiYn1A==",
"dev": true, "dev": true,
"dependencies": { "dependencies": {
"esbuild": "^0.18.10", "esbuild": "^0.18.10",
"postcss": "^8.4.27", "postcss": "^8.4.26",
"rollup": "^3.27.1" "rollup": "^3.25.2"
}, },
"bin": { "bin": {
"vite": "bin/vite.js" "vite": "bin/vite.js"

3
package.json
View File

@ -1,8 +1,7 @@
{ {
"dependencies": { "dependencies": {
"color": "^4.2.3",
"color-scheme": "^1.0.1", "color-scheme": "^1.0.1",
"lil-gui": "^0.19.0", "lil-gui": "^0.18.2",
"three": "^0.154.0" "three": "^0.154.0"
}, },
"devDependencies": { "devDependencies": {

826
polytopes.js
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File diff suppressed because it is too large Load Diff

67
taperedLink.js
View File

@ -1,67 +0,0 @@
import * as THREE from 'three';
const EPSILON = 0.001;
class TaperedLink extends THREE.Group {
constructor(baseMaterial, colour_i, n1, n2, r1, r2) {
super();
const geometry = new THREE.ConeGeometry( 1, 1, 16, true );
const cplane = new THREE.Plane(new THREE.Vector3(0, -1, 0), 0.5);
this.colour_i = colour_i;
this.material = baseMaterial.clone();
this.material.clippingPlanes = [ cplane ];
this.object = new THREE.Mesh( geometry, this.material );
this.add( this.object );
this.update(n1, n2, r1, r2);
}
update(n1, n2, r1, r2) {
const kraw = r1 - r2;
let k = ( Math.abs(kraw) < EPSILON ) ? EPSILON : kraw;
let nbase = n1.v3;
let napex = n2.v3;
let rbase = r1;
let rapex = r2;
if( k < 0 ) {
nbase = n2.v3;
napex = n1.v3;
rbase = r2;
rapex = r1;
k = -k;
}
const l = nbase.distanceTo(napex);
const lapex = l * rapex / k;
const h = l + lapex;
this.scale.copy(new THREE.Vector3(rbase, rbase, h));
const h_offset = 0.5 * h / l;
const pos = new THREE.Vector3();
pos.lerpVectors(nbase, napex, h_offset);
this.position.copy(pos); // the group, not the cone!!
this.lookAt(nbase);
this.children[0].rotation.x = 3 * Math.PI / 2.0;
this.visible = true;
const clipnorm = new THREE.Vector3();
clipnorm.copy(napex);
clipnorm.sub(nbase);
clipnorm.negate();
clipnorm.normalize();
this.material.clippingPlanes[0].setFromNormalAndCoplanarPoint(
clipnorm, napex
);
}
set_colour(colours) {
console.log(`taperedLink.set_colour {this.colour_i} {colours[this.colour_i]}`);
this.material.color = new THREE.Color(colours[this.colour_i]);
}
}
export { TaperedLink };

322
label120cell.js → testbed.js
View File

@ -1,8 +1,7 @@
// code for generating the 120-cell labels //testbed for playing with stuff in node repl
// 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;
@ -134,7 +133,7 @@ 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; return (n1.x - n2.x) ** 2 + (n1.y - n2.y) ** 2 + (n1.z - n2.z) ** 2 + (n1.w - n2.w) ** 2;
} }
export function auto_detect_edges(nodes, neighbours, debug=false) { function auto_detect_edges(nodes, neighbours, debug=false) {
const seen = {}; const seen = {};
const nnodes = nodes.length; const nnodes = nodes.length;
const links = []; const links = [];
@ -169,7 +168,7 @@ export function auto_detect_edges(nodes, neighbours, debug=false) {
export function make_120cell_vertices() { function make_120cell_vertices() {
const phi = 0.5 * (1 + Math.sqrt(5)); const phi = 0.5 * (1 + Math.sqrt(5));
const r5 = Math.sqrt(5); const r5 = Math.sqrt(5);
const phi2 = phi * phi; const phi2 = phi * phi;
@ -231,7 +230,7 @@ function fingerprint(ids) {
export function auto_120cell_faces(links) { function auto_120cell_faces(links) {
const faces = []; const faces = [];
const seen = {}; const seen = {};
let id = 1; let id = 1;
@ -487,7 +486,7 @@ function colour_next_dodeca_maybe(nodes, links, faces, colours, dd, nextf, nextd
const nextvs = dodecahedron_vertices(nextdd); const nextvs = dodecahedron_vertices(nextdd);
// get the initial colour permutations from the existing labels; // get the initial colour permutations from the existing labels;
const p = []; const p = [];
for( let i = 0; i < 5; i ++ ) { for( i = 0; i < 5; i ++ ) {
p[i] = colours[nextvs[i]]; p[i] = colours[nextvs[i]];
} }
const nlabels = colour_dodecahedron_from_face(nextdd, p); const nlabels = colour_dodecahedron_from_face(nextdd, p);
@ -530,33 +529,6 @@ function meridian(nodes, links, faces, startf, startn, dir=11, max=10) {
} }
function meridian_bump(nodes, links, faces, startf, startn, bumpdir=6) {
const o = face_plus_to_dodecahedron(faces, startf, startn);
const dir = 11;
const max = 10;
const colours = colour_dodecahedron_from_face(o, [ 1, 2, 3, 4, 5 ] );
const dds = follow_meridian(nodes, links, faces, colours, o, dir, max);
const dd4 = dds[4];
const nextf = dd4[bumpdir];
const bump = follow_face_to_dodeca(faces, dd4, nextf);
const ncolours = colour_next_dodeca_maybe(nodes, links, faces, colours, dd4, nextf, bump);
add_colours(colours, ncolours);
const labels = { 1: [], 2:[], 3:[], 4:[], 5:[] };
for( const vstr in colours ) {
labels[colours[vstr]].push(Number(vstr));
}
return { dodecahedra: dds, labels: labels };
}
function all_meridians(nodes, links, faces, startf, startn) { function all_meridians(nodes, links, faces, startf, startn) {
const o = face_plus_to_dodecahedron(faces, startf, startn); const o = face_plus_to_dodecahedron(faces, startf, startn);
@ -696,9 +668,8 @@ function arctic(nodes, links, faces, startf, startn, max) {
// this is the final one that works for the whole 120-cell
export function label_120cell(nodes, links, faces, startf, startn) { function arctic_two(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 ];
@ -717,6 +688,10 @@ export function label_120cell(nodes, links, faces, startf, startn) {
seen[dd_fingerprint(nextdd)] = true; seen[dd_fingerprint(nextdd)] = true;
} }
// go around all of the arctic circle and grow all faces
// 1, 12, 20, 12, 30 = 75
// 0 1 13, 33, 45
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 ] ) {
@ -747,8 +722,6 @@ export function label_120cell(nodes, links, faces, startf, startn) {
} }
// the 30 equatorials? // the 30 equatorials?
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(
@ -777,10 +750,7 @@ export function label_120cell(nodes, links, faces, startf, startn) {
} }
} }
// this should get the rest or explode! // this should get the rest or explode!
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(
@ -808,124 +778,6 @@ export function label_120cell(nodes, links, faces, startf, startn) {
export function cell120_layers(nodes, links, faces, startf, startn, max_layer) {
const pole = face_plus_to_dodecahedron(faces, startf, startn);
const dds = [ pole ];
const dd_families = { "0": [ pole ] }
const seen = {};
seen[dd_fingerprint(pole)] = true;
const colours = colour_dodecahedron_from_face(dds[0], [ 1, 2, 3, 4, 5 ] );
const vs = dodecahedron_vertices(dds[0]);
// arctic
if( max_layer > 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;
}
}
// subarctic - interstitial
if( max_layer > 1 ) {
dd_families["2"] = [];
for( const a of dd_families["1"] ) {
for( const i of [ 6, 7, 8, 9, 10 ] ) {
const [ nextdd, ncolours ] = follow_and_colour(
nodes, links, faces, colours, a, a[i]
);
const fp = dd_fingerprint(nextdd);
if( !(fp in seen) ) {
add_colours(colours, ncolours);
dds.push(nextdd);
dd_families["2"].push(nextdd);
seen[fp] = true;
}
}
}
}
// tropic of cancer
if( max_layer > 2 ) {
dd_families["3"] = [];
for( const a of dd_families["1"] ) {
const [ nextdd, ncolours ] = follow_and_colour(
nodes, links, faces, colours, a, a[11]
);
const fp = dd_fingerprint(nextdd);
if( !(fp in seen) ) {
add_colours(colours, ncolours);
dds.push(nextdd);
dd_families["3"].push(nextdd);
seen[fp] = true;
}
}
}
if( max_layer > 3 ) {
// equator
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(
nodes, links, faces, colours, a, a[i]
);
const fp = dd_fingerprint(nextdd);
if( !(fp in seen) ) {
add_colours(colours, ncolours);
dd_families["4"].push(nextdd);
dds.push(nextdd);
seen[fp] = true;
}
}
}
}
if( max_layer > 4 ) {
dd_families["5"] = [];
for( const a of dd_families["4"] ) {
for( const i of [ 6, 7, 8, 9, 10 ] ) {
const [ nextdd, ncolours ] = follow_and_colour(
nodes, links, faces, colours, a, a[i]
);
const fp = dd_fingerprint(nextdd);
if( !(fp in seen) ) {
add_colours(colours, ncolours);
dds.push(nextdd);
dd_families["5"].push(nextdd);
seen[fp] = true;
}
}
}
}
const labels = { 1: [], 2:[], 3:[], 4:[], 5:[] };
for( const vstr in colours ) {
labels[colours[vstr]].push(Number(vstr));
}
return { dodecahedra: dds, labels: labels, families: dd_families };
}
// for a face, pick an edge, and then find the other two faces which // for a face, pick an edge, and then find the other two faces which
// share this edge. These can be used as the starting points for the // share this edge. These can be used as the starting points for the
// first face's two dodecahedra // first face's two dodecahedra
@ -963,6 +815,7 @@ function make_120cell_cells(faces) {
for( const dd of dds ) { for( const dd of dds ) {
const fp = dd_fingerprint(dd); const fp = dd_fingerprint(dd);
if( ! (fp in seen) ) { if( ! (fp in seen) ) {
//console.log(`added dodeca ${fp}`);
const d = { const d = {
id: i, id: i,
faces: dd, faces: dd,
@ -1042,7 +895,7 @@ function meridian_label_120cell(nodes) {
//label_nodes(nodes, [313], 6); //label_nodes(nodes, [313], 6);
} }
1
function check_120cell_nodes(nodes) { function check_120cell_nodes(nodes) {
nodes.map((n) => { nodes.map((n) => {
const vs = find_adjacent_labels(nodes, links, n.id); const vs = find_adjacent_labels(nodes, links, n.id);
@ -1055,153 +908,24 @@ function check_120cell_nodes(nodes) {
}); });
} }
function make_dodecahedron_vertices() {
const phi = 0.5 * (1 + Math.sqrt(5));
const phiinv = 1 / phi;
const nodes = [ const nodes = make_120cell_vertices();
{ x: 1, y: 1, z: 1, w: 0 }, const links = auto_detect_edges(nodes, 4);
{ x: 1, y: 1, z: -1, w: 0 }, const faces = auto_120cell_faces(links);
{ x: 1, y: -1, z: 1, w: 0 },
{ x: 1, y: -1, z: -1, w: 0 },
{ x: -1, y: 1, z: 1, w: 0 },
{ x: -1, y: 1, z: -1, w: 0 },
{ x: -1, y: -1, z: 1, w: 0 },
{ x: -1, y: -1, z: -1, w: 0 }
].flat();
scale_nodes(nodes, 0.5);
return nodes;
}
// this one does the coherent indexing / partition into 600-cells console.log("Calculating 120-cell colours")
export function make_labelled_120cell() { const a2 = arctic_two(nodes, links, faces, faces[0], 341)
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); console.log(`got ${a2.dodecahedra.length}`);
return labelled;
}
// calculate the w-distance of a dodecahedron's centroid const labels = a2.labels;
export function dd_w_distance(nodes, dd) { console.log("labelling nodes");
const vertices = new Set(); for( const cstr in labels ) {
dd.map((f) => f.nodes.map((n) => vertices.add(n))); label_nodes(nodes, labels[cstr], Number(cstr));
let w = 0;
for( const nid of vertices ) {
const node = node_by_id(nodes, nid);
w += node.w;
}
return w / 20;
}
export function sort_dds_w(nodes, dds) {
dds.sort((a, b) => {
return dd_w_distance(nodes, a) - dd_w_distance(nodes, b)
})
} }
export function find_antipode_dd(nodes, links, dd) {
}
// notes because I'm too sick to continue working on this today
// the vertices which aren't counted by the layers are showing
// up in the visualisation because they are labelled "0" by default -
// for this to work better there needs to be a value which is never
// displayed.
// in the current layer algorithm, layer '5' (the one after the equator)
// is too greedy
export function make_layered_120cell(max_layer) {
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[628], 250, max_layer);
// get layers from sorted w-distance order
const dds = labelled.dodecahedra;
dds.sort((a, b) => dd_w_distance(nodes, b) - dd_w_distance(nodes, a));
const LAYERS = [
[ "0", 1 ],
[ "1", 12 ],
[ "2", 20 ],
[ "3", 12 ],
[ "4", 30 ],
[ "5", 12 ],
[ "6", 20 ],
[ "7", 12 ],
[ "8", 1]
];
const layer_dds = labelled["families"];
const vertices_layers = {};
const seen = {};
let i = 0;
for( const layer of LAYERS ) {
const label = layer[0];
const n = layer[1];
vertices_layers[label] = [];
console.log(`Layer ${label} starting at ${i}`);
for( const dd of dds.slice(i, i + n) ) {
console.log(dd_w_distance(nodes, dd));
for( const face of dd ) {
for( const n of face.nodes ) {
if( !seen[n] ) {
vertices_layers[label].push(n);
seen[n] = true;
}
}
}
}
i += n;
}
return JSON.stringify(vertices_layers);
}
export function make_meridians(bumpdir) {
const nodes = make_120cell_vertices();
const links = auto_detect_edges(nodes, 4);
const faces = auto_120cell_faces(links);
const mbs ={}
for( const bumpdir of [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 ] ) {
mbs[bumpdir] = meridian_bump(nodes, links, faces, faces[0], 341, bumpdir)
}
return mbs;
//
}
// console.log("Calculating 120-cell colours")
// const a2 = arctic_two(nodes, links, faces, faces[0], 341)
// console.log(`got ${a2.dodecahedra.length}`);
// const labels = a2.labels;
// console.log("labelling nodes");
// for( const cstr in labels ) {
// label_nodes(nodes, labels[cstr], Number(cstr));
// }

11
vite.config.js
View File

@ -3,14 +3,5 @@
import { defineConfig, loadEnv } from 'vite'; import { defineConfig, loadEnv } from 'vite';
export default defineConfig({ export default defineConfig({
base: '/fourjs/', base: '/fourjs/'
build: {
rollupOptions: {
output: {
manualChunks: {
threejs: [ 'three' ]
}
}
}
}
}) })