Added dodecahedron with compound of five cubes, refactored the

inscribed polytopes into one function

gui.js

@@ -7,7 +7,7 @@ const DEFAULTS = {
 	nodesize: 1.25,
 	linkopacity: 0.5,
 	link2opacity: 0.5,
-	shape: '120-cell',
+	shape: 'five-cubes',
 	inscribed: false,
 	inscribe_all: false,
 	color: 0x3293a9,
@@ -45,7 +45,7 @@ class FourDGUI {
 		};
 
 		this.gui.add(this.params, 'shape',
-			[ 'dodecahedron', '5-cell', '16-cell', 'tesseract',
+			[ 'dodecahedron', 'five-cubes', '5-cell', '16-cell', 'tesseract',
 				'24-cell', '600-cell', '120-cell' ]
 		).onChange(changeShape)
 		this.gui.add(this.params, 'inscribed').onChange(changeShape);

main.js

@@ -65,6 +65,7 @@ const STRUCTURES = {
 	'tesseract': POLYTOPES.tesseract(),
 	'24-cell': POLYTOPES.cell24(),
 	'dodecahedron': POLYTOPES.dodecahedron(),
+	'five-cubes': POLYTOPES.five_cubes(),
 	'120-cell': POLYTOPES.cell120(),
 	'600-cell': POLYTOPES.cell600(),
 };
@@ -75,6 +76,7 @@ const INSCRIBED = {
 	'120-cell': POLYTOPES.cell120_inscribed(),
 	'600-cell': POLYTOPES.cell600_inscribed(),
 	'dodecahedron': POLYTOPES.dodecahedron_inscribed(),
+	'five-cubes': POLYTOPES.five_cubes_inscribed(),
 };
 
 const ALL_INSCRIBED = {
@@ -83,6 +85,7 @@ const ALL_INSCRIBED = {
 	'120-cell': POLYTOPES.cell120_all_inscribed(),
 	'600-cell': POLYTOPES.cell600_all_inscribed(),
 	'dodecahedron': POLYTOPES.dodecahedron_all_inscribed(),
+	'five-cubes': POLYTOPES.five_cubes_all_inscribed(),
 }
 
 let shape = false;

polytopes.js

@@ -327,6 +327,8 @@ function make_120cell_vertices() {
 		].flat();
 	index_nodes(nodes);
 	scale_nodes(nodes, 0.5);
+	label_120cell(nodes);
+
 	return nodes;
 }
 
@@ -413,20 +415,18 @@ export const cell120 = () => {
 }
 
 
-const cell120_some_inscribed = (ps) => {
+const inscribed_polytope = (vertex_fn, edges, inscr_edges, parts) => {
-	const nodes  = make_120cell_vertices();
+	const nodes  = vertex_fn();
-	const links = auto_detect_edges(nodes, 4);
+	const links = auto_detect_edges(nodes, edges);
-
-	label_120cell(nodes);
 
 	const all_links = links;
 	all_links.map((l) => l.label = 0);
 
-	for( const p of ps) {
+	for( const p of parts ) {
-		const nodes600 = nodes.filter((n) => n.label === p);
+		const nodes_in = nodes.filter((n) => n.label === p);
-		const links600 = auto_detect_edges(nodes600, 12);
+		const links_in = auto_detect_edges(nodes_in, inscr_edges);
-		links600.map((l) => l.label = p);
+		links_in.map((l) => l.label = p);
-		all_links.push(...links600);
+		all_links.push(...links_in);
 	}
 
 	return {
@@ -439,8 +439,13 @@ const cell120_some_inscribed = (ps) => {
 	}
 }
 
-export const cell120_inscribed = () => cell120_some_inscribed([1]);
+
-export const cell120_all_inscribed = () => cell120_some_inscribed([1,2,3,4,5]);
+export const cell120_inscribed = () => inscribed_polytope(
+	make_120cell_vertices, 4, 12, [1]
+);
+export const cell120_all_inscribed = () => inscribed_polytope(
+	make_120cell_vertices, 4, 12, [1,2,3,4,5]
+);
 
 
 // Schoute's partition via https://arxiv.org/abs/1010.4353
@@ -628,36 +633,12 @@ export const cell600 = () => {
 	}
 }
 
-
+export const cell600_inscribed = () => inscribed_polytope(
-
+	make_600cell_vertices, 12, 8, [1]
-const cell600_some_inscribed = (ps) => {
+);
-	const nodes  = make_600cell_vertices();
+export const cell600_all_inscribed = () => inscribed_polytope(
-	const links = auto_detect_edges(nodes, 12);
+	make_600cell_vertices, 12, 8, [1,2,3,4,5]
-
+);
-	const all_links = links;
-	all_links.map((l) => l.label = 0);
-
-	for( const p of ps) {
-		const nodes24 = nodes.filter((n) => n.label === p);
-		const links24 = auto_detect_edges(nodes24, 8);
-		links24.map((l) => l.label = p);
-		all_links.push(...links24);
-	}
-
-	return {
-		nodes: nodes,
-		links: all_links,
-		geometry: {
-			node_size: 0.02,
-			link_size: 0.02
-		},
-	}
-}
-
-
-export const cell600_inscribed = () => cell600_some_inscribed([1]);
-export const cell600_all_inscribed = () => cell600_some_inscribed([1,2,3,4,5]);
-
 
 
 function make_dodecahedron_vertices() {
@@ -708,18 +689,42 @@ export const dodecahedron = () => {
 	}
 }
 
-const dodecahedron_some_inscribed = (ps) => {
+export const dodecahedron_inscribed = () => inscribed_polytope(
+	make_dodecahedron_vertices, 3, 3, [1]
+);
+export const dodecahedron_all_inscribed = () => inscribed_polytope(
+	make_dodecahedron_vertices, 3, 3, [1,2,3,4,5]
+);
+
+
+// this can't be done with inscribed_polytope because each vertex
+// belongs to two cubes
+
+export const dodecahedron_five_cubes = (parts) => {
 	const nodes  = make_dodecahedron_vertices();
 	const links = auto_detect_edges(nodes, 3);
 	const all_links = links;
 	all_links.map((l) => l.label = 0);
 
-	for( const p of ps) {
+	const CUBES = { 
-		const tetran = nodes.filter((n) => n.label === p);
+		1: [ 1, 2, 3, 4, 5, 6, 7, 8 ],
-		const tetral = auto_detect_edges(tetran, 3);
+		2: [ 4, 5, 10, 11, 13, 16, 17, 20],
-		tetral.map((l) => l.label = p);
+		3: [ 2, 7, 9, 12, 13, 16, 18, 19],
-		all_links.push(...tetral);
+		4: [ 1, 8, 10, 11, 14, 15, 18, 19],
-	}
+		5: [ 3, 6, 9, 12, 14, 15, 17, 20]
+	};
+	if( parts.length > 0 ) {
+	//	console.log(parts);
+		//console.log(parts.map(String));
+		//nodes.map((n) => n.label = 0);
+		for( const label of parts.map(String) ) {
+			console.log(`label = ${label}`);
+			const cube = nodes.filter((n) => CUBES[label].includes(n.id));
+			const cubel = auto_detect_edges(cube, 3);
+			cubel.map((l) => l.label = Number(label));
+			all_links.push(...cubel);
+ 		}
+ 	}
 
 	return {
 		nodes: nodes,
@@ -727,11 +732,11 @@ const dodecahedron_some_inscribed = (ps) => {
 		geometry: {
 			node_size: 0.02,
 			link_size: 0.02
-		},
+		}
 	}
 }
 
-
+export const five_cubes = () => dodecahedron_five_cubes([]);
-export const dodecahedron_inscribed = () => dodecahedron_some_inscribed([1]);
+export const five_cubes_inscribed = () => dodecahedron_five_cubes([1]);
-export const dodecahedron_all_inscribed = () => dodecahedron_some_inscribed([1,2,3,4,5]);
+export const five_cubes_all_inscribed = () => dodecahedron_five_cubes([1,2,3,4,5]);
 

testbed.js

@@ -913,16 +913,32 @@ function make_dodecahedron_vertices() {
 	const phiinv = 1 / phi;    
 
 	const nodes = [
-			{ x: 1, y: 1, z: 1, w: 0 },
+			{ x: 1, y: 1, z: 1, w: 0, 			label: 4 },
-			{ x: 1, y: 1, z: -1, w: 0 },
+			{ x: 1, y: 1, z: -1, w: 0, 			label: 3 },
-			{ x: 1, y: -1, z: 1, w: 0 },
+			{ x: 1, y: -1, z: 1, w: 0, 			label: 3 },
-			{ x: 1, y: -1, z: -1, w: 0 },
+			{ x: 1, y: -1, z: -1, w: 0, 		label: 2 },
-			{ x: -1, y: 1, z: 1, w: 0 },
+
-			{ x: -1, y: 1, z: -1, w: 0 },
+			{ x: -1, y: 1, z: 1, w: 0, 			label: 3 },
-			{ x: -1, y: -1, z: 1, w: 0 },
+			{ x: -1, y: 1, z: -1, w: 0, 		label: 1 },
-			{ x: -1, y: -1, z: -1, w: 0 }
+			{ x: -1, y: -1, z: 1, w: 0, 		label: 5 },
-		].flat();
+			{ x: -1, y: -1, z: -1, w: 0, 		label: 3 },
-	scale_nodes(nodes, 0.5);
+
+			{ x: 0, y: phi, z: phiinv, w: 0, 	label: 5 },
+			{ x: 0, y: phi, z: -phiinv, w: 0 , 	label: 2 },
+			{ x: 0, y: -phi, z: phiinv, w: 0, 	label: 4 },
+			{ x: 0, y: -phi, z: -phiinv, w: 0 , label: 1 },
+
+			{ x: phiinv, y: 0, z: phi, w: 0 , 	label: 2},
+			{ x: phiinv, y: 0, z: -phi, w: 0 , 	label: 4},
+			{ x: -phiinv, y: 0, z: phi, w: 0 , 	label: 1},
+			{ x: -phiinv, y: 0, z: -phi, w: 0 , label: 5},
+
+			{ x: phi, y: phiinv, z:0, w: 0 , 	label: 1},
+			{ x: phi, y: -phiinv, z:0, w: 0 , 	label: 5},
+			{ x: -phi, y: phiinv, z:0, w: 0 , 	label: 4},
+			{ x: -phi, y: -phiinv, z:0, w: 0 , 	label: 2},
+		];
+	index_nodes(nodes);
 	return nodes;
 }