In: Discrete & Computational Geometry, 2014, vol. 51, no. 4, p. 997-1016
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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.
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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.
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Thèse de doctorat : Université de Fribourg, 2015 ; no. 1929.
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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 ...
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