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rgugliel / CoxIter

CoxIter is a computer program designed to compute invariants of hyperbolic Coxeter groups.
GNU General Public License v3.0
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False negative for finite volume test #23

Closed sashakolpakov closed 1 year ago

sashakolpakov commented 4 years ago

Polytope's Coxeter diagram (colour code: red=3, blue=4):

d13-10

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):

d13-10-0

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:

d13-10-1

2nd enhancement to an affine (ideal vertex) sub-diagram:

d13-10-2

3rd enhancement: here we have 3 \tilde{F}_4 diagrams with overlaps, which does not give us an affine sub-diagram.

d13-10-3

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.

rgugliel commented 4 years ago

@sashakolpakov Can you include here the CoxIter file? The download link is not valid anymore.

sashakolpakov commented 4 years ago

@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).

rgugliel commented 1 year ago

Closing this issue, as I don't have material to reproduce.