The inradius of a hyperbolic truncated \(n\)-simplex
type: Item
instance of: scholarly article
title: The inradius of a hyperbolic truncated \(n\)-simplex
zbMATH Open document ID: 1319.52021
author: Matthieu Jacquemet
published in: Discrete \& Computational Geometry
publication date: 2014-09-12T00:00:00Z
review text: For a hyperbolic simplex \(T\), some of whose vertices lie outside the hyperbolic space, the intersection of \(T\) with the half-spaces polar to some of the ultra-ideal vertices is called a hyperbolic truncated simplex. This class of polytopes includes many interesting members such as simplices, rectangular hexagons, Lambert cubes, straight simplicial prisms and, most notably, provides a way to construct hyperbolic Coxeter polytopes, in particular those giving rise to ``smallest'' hyperbolic orbifolds in various senses (see e.g. [\textit{R. Kellerhals}, Comput. Methods Funct. Theory 14, No. 2--3, 465--481 (2014; Zbl 1307.57001)]). The author computes the radius of a maximal sphere contained in an arbitrary truncated simplex (see Section 3.2). In Section 4.2, he applies this result to numerically compute the answer for some Coxeter polytopes that give rise to ``small'' hyperbolic orbifolds. This computation is motivated by the observation that the inradii of such small Coxeter polytopes are related to hyperbolic ball packings of large density.
reviewed by: Alexander Esterov
Mathematics Subject Classification ID: 52B11
Mathematics Subject Classification ID: 51M25
Mathematics Subject Classification ID: 51F15
Mathematics Subject Classification ID: 52C17
Mathematics Subject Classification ID: 51M10
zbMATH DE Number: 6343931
zbMATH Keywords: hyperbolic polarly truncated simplices
zbMATH Keywords: gram matrix
zbMATH Keywords: inradius
zbMATH Keywords: hyperbolic orbifolds
zbMATH Keywords: small volume
MaRDI profile type: Publication
full work available at URL: s00454-014-9600-y
OpenAlex ID: W2155514577
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DOI: 10.1007/S00454-014-9600-Y
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description: scientific article; zbMATH DE number 6343931