Exploratory code which seems to be able to pick out four 5-cells which connect

five tetrahedra on the 600-cells

explore_120cell.js

@@ -1,14 +1,4 @@
 
-// TODO - try visualising the 5-cells from a vertex on the layered 120-cell
-// and get an intuition for how they work with the dodecahedral structure
-
-// Another new approach -
-// pick a starting 5-cell
-// look at the neighbours on the 120-cell of all of its 5 vertices
-// try to find abother 5-cell with these neighbours
-// if there's only one, add that to the list and keep going
-// if there's more than one, are they disjoint with each other?
-
 import * as POLYTOPES from './polytopes.js';
 
 // exploring more inscriptions of the 120-cell
@@ -302,15 +292,12 @@ function find_adjoining_5cells(cell120, all5, v1, v2) {
     return c5pairs;
 }
 
-
-
-function tetras(cell120, all5, v) {
+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
-    console.log(v.id);
     const tetras = new Set;
     for( const v2id of n600s ) {
         // find mutual neighbours of the first two
@@ -331,14 +318,23 @@ function tetras(cell120, all5, v) {
             }
         }
     }
-    console.log(tetras);
+    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);
 }
-/*    // find mutuals which are mutuals of each other
-    const m0 = mutuals[0];
-    const mn = neighbours600(cell120, m0);
-    const mm = mn.filter((nid) => nid != m0 && mutuals.includes(nid));
-    return [ v1.id, v2id, m0, mm[0] ];
-}*/
 
 function str5cell(c5) {
     return ["1","2","3","4","5"].map((l) => String(c5[l]).padStart(3, '0')).join('-');
@@ -360,11 +356,62 @@ function tetra_sets(cell120, all5, tetra) {
     }
 }
 
+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;
+}
+
+
+// pick a 5-cell, and then pick the nearest neighbours to its vertices on their
+// respective inscribed 600-cells
+
 const cell120 = POLYTOPES.cell120_inscribed();
 const all5 = gather_5cells(cell120);
 
-const v1 = cell120.nodes[0];
+const c5 = all5[0]
 
-tetras(cell120, all5, v1);
-tetras(cell120, all5, cell120.nodes[1]);
+const nb = cell5_neighbourhoods(cell120, all5, c5);
 
+// trying for all tetras
+
+// let's pick a tetra on the first vertex of the primary 5cell...
+
+const v1 = cell120node(cell120, c5["1"]);
+const ts = tetras(cell120, v1);
+
+for( const t of ts ) {
+
+    console.log(t);
+
+    // ... and then see which of the neighbourhood 5-cells have at least one
+    // of its vertices
+
+    const nt = nb.filter((n) => {
+        for( const l in n ) {
+            if( t.includes(n[l]) ) {
+                return true;
+            }
+        }
+        return false
+    });
+
+    console.log(nt);
+    console.log("\n");
+}