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arXiv · 2002.11445

On faces of quasi-arithmetic Coxeter polytopes

Nikolay Bogachev·Alexander Kolpakov
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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.

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Nikolay Bogachev, Alexander Kolpakov. 2020-11-01. On faces of quasi-arithmetic Coxeter polytopes. https://doi.org/10.1093/imrn%2Frnaa278

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