Abstract: We consider a three-parameter family of tetrahedra in the hyperbolic space, whose three edges at one vertex are pairwise orthogonal. It is convenient to determine such tetrahedra by the lengths of these edges. We obtain a relatively simple formulas for them expressing the volume and the surface area. This allows us to find normalised volume and investigate its asymptotics.

Cite: Abrosimov N.V.
The volume of a hyperbolic tetrahedron with right angles at one vertex
International conference «Knot theory and applications» 29 Jun - 5 Jul 2022