On hyperbolic Coxeter n-cubes. (January 2017)

• Record Type: Journal Article
• Authors: Jacquemet, Matthieu
• Is Part Of: European journal of combinatorics. Volume 59(2017)
• Page Start: 192
• Page End: 203
• Publication Date: 2017-01
• Subjects: Combinatorial analysis -- Periodicals; Analyse combinatoire -- Périodiques; Combinatorial analysis; Periodicals; Electronic journals; 511.6
• DOI: 10.1016/j.ejc.2016.08.008
• Languages: English
• ISSNs: 0195-6698

Abstract

Abstract: Besides simplices, n -cubes form an important class of simple polyhedra. Unlike hyperbolic Coxeter simplices, hyperbolic Coxeter n -cubes are not classified. In this work, we first show that there are no Coxeter n -cubes in H n for n ≥ 10 . Then, we show that the ideal ones exist only for n = 2 and 3, and provide a classification. The methods used are of combinatorial and algebraic nature, using properties of a Coxeter graph, its Schläfli matrix, and the Gram matrix of a polyhedron.