Some applications of the formula for the volume of an octahedron
type: Item
instance of: scholarly article
title: Some applications of the formula for the volume of an octahedron
zbMATH Open document ID: 1075.52006
author: R. V. Galiulin
author: S. N. Mikhalev
author: I. Kh Sabitov
published in: Mathematical Notes
publication date: 2004-12-07T00:00:00Z
review text: Referring to a simplicial complex \(K\), first the authors introduce three types of symmetry: combinatorial symmetry (if there exists an automorphism of the vertex set of \(K\) preserving the occuring incidences), metrical symmetry (if in addition the edge-lengths are preserved), and spatial symmetry of polyhedra in 3-space (if there is a motion taking these polyhedra into themselves, preserving or reversing the orientaion). In earlier contributions, the authors confirmed the existence of polynomials related to the combinatorial structure, squared edge-lengths and volume of a polyhedron in 3-space. Here they give explicit forms of canonical polynomials determining the volume of octahedral polyhedra having certain types of symmetry. These results are also interesting from the viewpoint of crystallography.
reviewed by: Horst Martini
Mathematics Subject Classification ID: 52B10
Mathematics Subject Classification ID: 52B12
zbMATH DE Number: 2121440
zbMATH Keywords: symmetries of polyhedra
zbMATH Keywords: symmetric octahedra
zbMATH Keywords: canonical polynomials for volumes
zbMATH Keywords: simplicial complex
zbMATH Keywords: crystallography
MaRDI profile type: Publication
full work available at URL: b:matn.0000036739.35916.ae
OpenAlex ID: W1999133280
DOI: 10.1023/B:MATN.0000036739.35916.AE
description: scientific article; zbMATH DE number 2121440