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.

14 pages, 3 figures; ancillary files available at https://github.com/sashakolpakov/plof