Abstract
A Lambert cube Q(α,β,γ) is a combinatorial cube with dihedral angles α, β, and γ assigned to the three mutually noncomplanar edges and right angles at the remaining edges. In this paper, we classify the Lambert cubes in S3, \(\mathbb{E}^3 \), and \(\mathbb{H}^3 \) such that the group GQ generated by the reflections with respect to the faces of a cube Q is discrete.
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