Classifying Simplicial Dissections of Convex Polyhedra with Symmetry

A convex polyhedron is the convex hull of a finite set of points in [Formula: see text] A triangulation of a convex polyhedron is a decomposition into a finite number of 3-simplices such that any two intersect in a common face or are disjoint. A simplicial dissection is a decomposition into a finite...

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Detalles Bibliográficos
Autores principales: Betten, Anton, Mukthineni, Tarun
Formato: Online Artículo Texto
Lenguaje:English
Publicado: 2020
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7340891/
http://dx.doi.org/10.1007/978-3-030-52200-1_14
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author Betten, Anton
Mukthineni, Tarun
author_facet Betten, Anton
Mukthineni, Tarun
author_sort Betten, Anton
collection PubMed
description A convex polyhedron is the convex hull of a finite set of points in [Formula: see text] A triangulation of a convex polyhedron is a decomposition into a finite number of 3-simplices such that any two intersect in a common face or are disjoint. A simplicial dissection is a decomposition into a finite number of 3-simplices such that no two share an interior point. We present an algorithm to classify the simplicial dissections of a regular polyhedron under the symmetry group of the prolyhedron.
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spelling pubmed-73408912020-07-08 Classifying Simplicial Dissections of Convex Polyhedra with Symmetry Betten, Anton Mukthineni, Tarun Mathematical Software – ICMS 2020 Article A convex polyhedron is the convex hull of a finite set of points in [Formula: see text] A triangulation of a convex polyhedron is a decomposition into a finite number of 3-simplices such that any two intersect in a common face or are disjoint. A simplicial dissection is a decomposition into a finite number of 3-simplices such that no two share an interior point. We present an algorithm to classify the simplicial dissections of a regular polyhedron under the symmetry group of the prolyhedron. 2020-06-06 /pmc/articles/PMC7340891/ http://dx.doi.org/10.1007/978-3-030-52200-1_14 Text en © Springer Nature Switzerland AG 2020 This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.
spellingShingle Article
Betten, Anton
Mukthineni, Tarun
Classifying Simplicial Dissections of Convex Polyhedra with Symmetry
title Classifying Simplicial Dissections of Convex Polyhedra with Symmetry
title_full Classifying Simplicial Dissections of Convex Polyhedra with Symmetry
title_fullStr Classifying Simplicial Dissections of Convex Polyhedra with Symmetry
title_full_unstemmed Classifying Simplicial Dissections of Convex Polyhedra with Symmetry
title_short Classifying Simplicial Dissections of Convex Polyhedra with Symmetry
title_sort classifying simplicial dissections of convex polyhedra with symmetry
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7340891/
http://dx.doi.org/10.1007/978-3-030-52200-1_14
work_keys_str_mv AT bettenanton classifyingsimplicialdissectionsofconvexpolyhedrawithsymmetry
AT mukthinenitarun classifyingsimplicialdissectionsofconvexpolyhedrawithsymmetry

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