Spherical simplices generating discrete reflection groups

Details Spherical simplices generating discrete reflection groups Spherical simplices generating discrete reflection groups

2002-12-18

arxiv.org/abs/math/0212244v1

Mathematics

Metric Geometry

21 pages, 3 figures, 4 tables

Scientific paper

Let $P$ be a simplex in $S^n$ and $G_P$ be a group generated by the reflections with respect to the facets of $P$. We are interested in the case when the group $G_P$ is discrete. In this case we say that $G$ generates the discrete reflection group $G_P$. We develop the criteria for a simplex generating a discrete reflection group. We also describe all indecomposable spherical simplices generating discrete reflection groups.

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