Closed sashakolpakov closed 1 year ago
@sashakolpakov Can you include here the CoxIter file? The download link is not valid anymore.
@rgugliel Please check this link. The test examples that I use all come as facets of the 21-dimensional Borcherds polytope. They are computed in SageMath using (pretty basic) linear algebra. It is known that they are finite-volume, and I think my computation of their normals / Coxeter diagrams is correct (I tested same code on smaller polytopes, and it worked fine, and also I got correct results when using CoxIter on them).
Closing this issue, as I don't have material to reproduce.
Polytope's Coxeter diagram (colour code: red=3, blue=4):
This polytope is known to me to have finite volume, since it is a 13-dimensional face of the 21-dimensional Borcherds polytope. It is obtained by successive projections of its normals to hyperplanes of its faces, and this computation has been verified.
CoxIter tries to enhance the elliptic sub-diagram below (edge):
It reports that it succeeds to enhance it in 3 ways, and therefore the polytope is not finite volume.
1st enhancement to an affine (ideal vertex) sub-diagram:
2nd enhancement to an affine (ideal vertex) sub-diagram:
3rd enhancement: here we have 3 \tilde{F}_4 diagrams with overlaps, which does not give us an affine sub-diagram.
Seemingly, there is no difference made between a union of subgraphs and an induced subgraph isomorphic to 3 disjoint \tilde{F}_4's.
Here are the input file for CoxIter, and the output in "debug" mode (all vertices are indexed +1 in CoxIter files): download link.