On faces of quasi-arithmetic Coxeter polytopes
Abstract
We prove that each lower-dimensional face of a quasi-arithmetic Coxeter polytope, which happens to be itself a Coxeter polytope, is also quasi-arithmetic. We also provide a sufficient condition for a codimension $1$ face to be actually arithmetic, as well as a few computed examples.
- Publication:
-
arXiv e-prints
- Pub Date:
- February 2020
- DOI:
- 10.48550/arXiv.2002.11445
- arXiv:
- arXiv:2002.11445
- Bibcode:
- 2020arXiv200211445B
- Keywords:
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- Mathematics - Geometric Topology;
- Mathematics - Group Theory;
- Mathematics - Metric Geometry;
- Mathematics - Number Theory;
- 20F55;
- 20H10;
- 22E40
- E-Print:
- 14 pages, 3 figures