The minimal covolume right-angled Coxeter group in hyperbolic 3-space
Abstract
We prove that among all right-angled Coxeter groups in hyperbolic 3-space, the group generated by reflections in the faces of a right-angled triangular bipyramid with three ideal and two finite vertices has the smallest covolume. The group is arithmetic and its covolume equals Catalan's constant G = 0.915965....
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