Consortium of Swiss Academic Libraries

The Inradius of a Hyperbolic Truncated $$n$$ n -Simplex

Jacquemet, Matthieu

In: Discrete & Computational Geometry, 2014, vol. 51, no. 4, p. 997-1016

Université de Fribourg

Commensurability of hyperbolic Coxeter groups: theory and computation

Guglielmetti, Rafael ; Jacquemet, Matthieu ; Kellerhals, Ruth

In: RIMS Kôkyûroku Bessatsu, 2017, vol. B66, p. 057-113

For hyperbolic Coxeter groups of finite covolume we review and present new theoretical and computational aspects of wide commensurability. We discuss separately the arithmetic and the non-arithmetic cases. Some worked examples are added as well as a panoramic viewto hyperbolic Coxeter groups and their classification.

Université de Fribourg

On commensurable hyperbolic Coxeter groups

Guglielmetti, Rafael ; Jacquemet, Matthieu ; Kellerhals, Ruth

In: Geometriae Dedicata, 2016, vol. 183, no. 1, p. 143–167

For Coxeter groups acting non-cocompactly but with finite covolume on real hyperbolic space Hn, new methods are presented to distinguish them up to (wide) commensurability. We exploit these ideas and determine the commensurability classes of all hyperbolic Coxeter groups whose fundamental polyhedra are pyramids over a product of two simplices of positive dimensions.

Université de Fribourg

The Inradius of a Hyperbolic Truncated $$n$$-Simplex

Jacquemet, Matthieu

In: Discrete & Computational Geometry, 2014, vol. 51, no. 4, p. 997-1016

Hyperbolic truncated simplices are polyhedra bounded by at most $$2n+2$$hyperplanes in hyperbolic $$n$$-space. They provide important models in the context of hyperbolic space forms of small volume. In this work, we derive an explicit formula for their inradius by algebraic means and by using the concept of reduced Gram matrix. As an illustration, we discuss implications for some polyhedra ...