A trick for calculating volumes of non-Euclidean polyhedra
type: Item
instance of: scholarly article
title: A trick for calculating volumes of non-Euclidean polyhedra
zbMATH Open document ID: 1468.51009
DOI: 10.1134/S0001434621030366
author: Vladimir Aleksandrovich Krasnov
published in: Mathematical Notes
publication date: 2021-07-08T00:00:00Z
review text: Using the proof idea for a formula for the volume of a compact tetrahedron in three-dimensional hyperbolic space \({\mathbb H}^3\) proposed by \textit{G. Sforza} [Modena Mem. (3) 8, 21--66 (1907; JFM 38.0675.01)], the author establishes alternative formulas for the volumes of hyperbolic orthoschemes, of hyperbolic octahedra with \(4|m\)-symmetry (invariant under the rotation about the axis joining the pyramid vertices through an angle of \(\frac{\pi}{2}\) and reflection with respect to the plane perpendicular to it) whose dihedral angles satisfy a certain system of inequalities, and of spherical octahedra with \(4|m\)-symmetry.
reviewed by: Victor V. Pambuccian
Mathematics Subject Classification ID: 51M25
Mathematics Subject Classification ID: 51M20
Mathematics Subject Classification ID: 51M10
zbMATH DE Number: 7369743
zbMATH Keywords: volume
zbMATH Keywords: \((4|m)\)-octahedron
zbMATH Keywords: orthoscheme
zbMATH Keywords: non-Euclidean space
zbMATH Keywords: Sforza's formula
Wikidata QID: Q114075417
MaRDI profile type: Publication
cites work: On the volume of hyperbolic octahedra with nontrivial symmetry
full work available at URL: s0001434621030366
OpenAlex ID: W3177744151
description: scientific article; zbMATH DE number 7369743