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

Jacquemet, Matthieu

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

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    Title
    • The Inradius of a Hyperbolic Truncated $$n$$ n -Simplex
    Author
    • Jacquemet, Matthieu. Université de Fribourg, Chemin du Musée 23, CH-1700, Fribourg, Switzerland
    Document Type
    • Postprint
    Language
    • English
    Published in
    • Discrete & Computational Geometry, 2014, vol. 51, no. 4, p. 997-1016. Springer US; http://www.springer-ny.com
    Other Version
    OAI-PMH Identifier
    • oai:doc.rero.ch:324855
    Summary
    Hyperbolic truncated simplices are polyhedra bounded by at most $$2n+2$$ 2 n + 2 hyperplanes in hyperbolic $$n$$ 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 related to small volume arithmetic orientable hyperbolic orbifolds.