The vertex coordinate set for the contact polytope of the Leech lattice listed on Wikipedia contains all permutations of:
- $\{4,-4,0^{22}\}$
- $\{-3,1^{23}\}$
- $\{3,-1^{23}\}$
The convex hull of these 600 vertices is an expanded 24-simplex, meaning that there is a compound of expanded 24-simplices using the vertices and long edges of the Leech lattice’s contact polytope. How many expanded simplices are in this compound?
