More polytope experiments

Anand has been visiting for the weekend and we have been working on enhancing the visualizer he has written to see the high dimensional polytopes. The enumeration software has also been enhanced and is much faster now.

Here is an example:This is the 4-prism generated from the 4-simplex by deleting any vertex. Now if we move a hyperplane to truncate vertices 3 and 7 we get

The final cut is 4 vertices, { 4, 8, 11, 14 }. Truncating these gets us the beautiful 4-cube which I had alluded to in an earlier post.

The actual face-lattice for the 4-cube produced by this cut is
VERTICES_IN_FACETS
{ 0 1 2 3 4 5 6 7}
{ 0 2 4 6 8 10 12 14}
{ 1 3 5 7 9 11 13 15}
{ 0 1 2 3 8 9 10 11}
{ 0 1 4 5 8 9 12 13}
{ 2 3 6 7 10 11 14 15}
{ 4 5 6 7 12 13 14 15}
{ 8 9 10 11 12 13 14 15}

If that is not poetry, I dont know what is. As Hardy had said "It must be true, as no one will have the imagination to invent something as beautiful....".

Cut sequence for the interactive enumerator are;
1
0
1
2
1 5
1
4
4 8 11 14
0