Volume formulae for regular hyperbolic cubes

We express the volume of a regular cube in hyperbolic n n -space as an integral on [ 0 , ∞ ) [0, \infty ) , and derive from this an asymptotic volume formula for the regular ideal hyperbolic n n -cube. This in turn is applied to finding an asymptotic lower bound for the least number of simplices into which a Euclidean n n -cube can be triangulated.