Special cuts of 600-cell
-
600-cell is a regular polytope with 120 vertices whose facets are 600 tetrahedra.
-
A special cut is a family S of vertices of 600-cells such that no two vertices in S are adjacent.
-
Given a special cut, one obtains a regular faced polytope by taking the convex hull of vertices not in S. The vertices in S correspond to icosahedra in this convex hull.
-
The symmetry group of 600-cell is the coxeter group H4. It has 14400 elements. Two special cuts, which are equivalent under this group correspond to isometric corresponding regular faced polytopes.
-
The number of vertices in S is at most 24. The case of 24 corresponds to a special semiregular polytope named snub 24-cell.
We enumerated the orbits of special cuts up to isomorphism. In the list below s is the number of vertices of S:
Additional data and programs:
- The vertices of the orbits are indicated with respect to the following adjacency matrix.
- The elements of the group are listed here.
- The program used for the enumeration are here.
- Some Case analysis here.
The program used here is good for enumerating cliques in graph up to symmetry. It scales well to parallel computers. But it is not recommended if one is only interested in the cliques of maximal size.