All hyperbolic Coxeter $n$-cubes

Matthieu Jacquemet; Steven T. Tschantz

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arXiv · 1803.10462

All hyperbolic Coxeter $n$-cubes

Matthieu Jacquemet·Steven T. Tschantz

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Abstract

Beside simplices, $n$-cubes form an important class of simple polyhedra. Unlike hyperbolic Coxeter simplices, hyperbolic Coxeter $n$-cubes are not classified. We show that there is no hyperbolic Coxeter $n$-cube for $n\geq~6$, and provide a full classification for $n\leq 5$. Our methods, which are essentially of combinatorial and algebraic nature, can be (and have been successfully) implemented in a symbolic computation software such as Mathematica$^\circledR$.

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BibTeX RIS

Matthieu Jacquemet, Steven T. Tschantz. 2018-03-28. All hyperbolic Coxeter $n$-cubes. https://arxiv.org/abs/1803.10462

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