文摘
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 Hn for b5067a2bd379c5654e58144240e0f6c" title="Click to view the MathML source">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.