On manifolds defined by 4-colourings of simple 3-polytopes
On manifolds defined by 4-colourings of simple 3-polytopes
Let $\mathcal{P}$ be the class of combinatorial 3-dimensional simple polytopes $P$, different from a tetrahedron, without 3- and 4-belts of facets. By the results of Pogorelov and Andreev, a polytope $P$ admits a realisation in Lobachevsky space $\mathbb{L}^3$ with right dihedral angles if and only if $P \in \mathcal{P}$. We …