  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 consider two families of smooth manifolds defined by
regular 4-colourings of Pogorelov polytopes P: six-dimensional quasitoric
manifolds over $P$ and three-dimensional small covers of $P$; the latter are
also known as three-dimensional hyperbolic manifolds of Loebell type. We prove
that two manifolds from either of the families are diffeomorphic if and only if
the corresponding 4-colourings are equivalent.

Algebraic Topology;General Topology