Hyperbolic 3-manifolds with totally geodesic boundary which are decomposed into hyperbolic truncated tetrahedra
Gluing the hexagonal faces of hyperbolic truncated tetrahedra by isometries, the author proves the following main result: Theorem 3.1. There are exactly eight mutually non-isometric compact oriented hyperbolic 3-manifolds with totally geodesic boundary such that they can be decomposed into two hyperbolic truncated tetrahedra and their boundaries are closed surfaces of genus 2. We remark that the hyperbolic volume of these manifolds (\(\approx 6.452)\) is the minimal one among all compact oriented hyperbolic 3-manifolds with totally geodesic closed boundary [\textit{S. Kojima} and \textit{Y. Miyamoto}, The smallest hyperbolic 3-manifolds with totally geodesic boundary, Preprint]. Uniqueness of these eight manifolds follows from \textit{E. M. Andreev}'s classification theorem on hyperbolic polyhedra [Mat. Sb., Nov. Ser. 81, 445-478 (1970; Zbl 0194.232); see also \textit{W. Thurston}, The geometry and topology of 3-manifolds, Princeton Lecture Notes, Ch.13].
scientific article; zbMATH DE number 4205407