On application of contemporary proof of the Sforza formula to computation of volumes of hyperbolic tetrahedra of special kind
The research for volume formulas for hyperbolic tetrahedra began with the discovery of hyperbolic geometry, and many researchers have been making partial refinements of the formulas until now. The volume of a hyperbolic polyhedron determines its shape in hyperbolic geometry, and it is one of the crucial formulas in low-dimensional topology. Since it is a natural occurrence that volume formulas are formulated in terms of integral formulas, it is essential from the viewpoint of application to be able to obtain simple formulas under certain conditions. In this paper, from an old theorem known as Sforza's formula, a relatively simple integral formula by a dihedral angle is derived for the case of tetrahedra with some special conditions (orthoschemes and tetrahedra with the symmetry group \(S^4\)).
scientific article; zbMATH DE number 7599124