Regular projective polyhedra with planar faces. II
type: Item
instance of: scholarly article
title: Regular projective polyhedra with planar faces. II
zbMATH Open document ID: 0952.52012
DOI: 10.1007/PL00000122
published in: Aequationes Mathematicae
publication date: 2001-01-11T00:00:00Z
review text: This paper is a sequel to the paper ibid., 55-73 (2000; Zbl 0952.52011 above) by \textit{J. L. Arocha}, \textit{J. Bracho} and \textit{L. Montejano}. The author studies in full generality projective polyhedra with planar faces and skew vertex figures. After recalling some of the terminology of polyhedra in the projective context, the author also gives the definition of various operations on polyhedra in the projective context: the mixing operator, the dual, the Petrie operator, the \(j\)-hole operator. Using these operations he is able to produce a list consisting of an infinite family of tori and of 84 special projective polyhedra. To complete the classification he establishes that the preceding list is complete, using separate arguments for the case of polyhedra with antiprismatic and the case of polyhedra with skew-prismatic vertex figures.
reviewed by: Charles Leytem
Mathematics Subject Classification ID: 52B11
Mathematics Subject Classification ID: 51M20
Mathematics Subject Classification ID: 51F15
zbMATH DE Number: 1436173
zbMATH Keywords: regular polyhedron
zbMATH Keywords: operation on polyhedron
zbMATH Keywords: waist equation
zbMATH Keywords: projective polyhedra
zbMATH Keywords: vertex figures
Wikidata QID: Q56580497
author: Javier Bracho
MaRDI profile type: Publication
full work available at URL: pl00000122
OpenAlex ID: W4240376641
description: scientific article; zbMATH DE number 1436173