Simplices whose dihedral angles are all rational multiples of \(\pi\), and related topics
type: Item
instance of: scholarly article
title: Simplices whose dihedral angles are all rational multiples of \(\pi\), and related topics
zbMATH Open document ID: 1413.51012
author: Horst Martini
author: H. Maehara
published in: Acta Mathematica Hungarica
publication date: 2018-07-23T00:00:00Z
review text: This interesting paper deals with the dihedral angles of \(n\)-simplices. It is proved (Theorem 2.5) that for every \(n \geq 2\), there are infinitely many, mutually non-similar \(n\)-dimensional Hill-simplices whose dihedral angles are all rational multiples of \(\pi\). The following problem is raised. Problem 2.6. If the dihedral angles of an \(n\)-simplex are all rational multiples of \(\pi\), is this simplex then a space-filler? Using the theorem concerning fairly-inscribed \(n\)-symplices (Theorem 4.2) and the outer normal transformation among others, it is showed (Theorem 5.3) that for every \(n \geq 3\), there are uncountably many, mutually non-similar \(n\) simplices whose dihedral angles are \(\pi\)-independent.
Mathematics Subject Classification ID: 51M20
Mathematics Subject Classification ID: 52B11
Mathematics Subject Classification ID: 52C20
Mathematics Subject Classification ID: 05B45
zbMATH DE Number: 6909523
zbMATH Keywords: Hill-simplex
zbMATH Keywords: outer normal transformation
zbMATH Keywords: dihedral angle
zbMATH Keywords: \(\pi\)-independent number
zbMATH Keywords: elementary function
zbMATH Keywords: identity theorem
reviewed by: Ágota H. Temesvári
MaRDI profile type: Publication
full work available at URL: s10474-018-0813-z
OpenAlex ID: W2790018309
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cites work: Q5287551
DOI: 10.1007/S10474-018-0813-Z
description: scientific article; zbMATH DE number 6909523