The vertex coordinate set for the contact polytope of the Leech lattice listed on [Wikipedia][1] 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-sinplex, 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? [1]: https://en.m.wikipedia.org/wiki/Leech_lattice