2018/03/28 by Jacquemet, Matthieu, Tschantz, Steven T. · 1 citation
#05C30 #20F55 #51M09 #52B11 #57M15 #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #Metric Geometry (math.MG)
paper · doi:10.48550/arxiv.1803.10462
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≥~6, and provide a full classification for n≤ 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.