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Daniel Sebald
Daniel Sebald
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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-sinplexsimplex, 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?

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-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?

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?

Source Link
Daniel Sebald
Daniel Sebald
  • 2.8k
  • 6
  • 19

Expanded 24-simplices in the Leech polytope

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-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?