The orthogonal connectedness of polyhedral surfaces
Julia Q. Du, Xuemei He, Xiaotian Song, Daniela Stiller, Liping Yuan, Tudor Zamfirescu
TL;DR
This paper introduces the concept of orthogonal connectedness to analyze the orthogonal decomposability of convex polytopes, focusing on Platonic and Archimedean solids, and identifies polytopes that are not orthogonally decomposable.
Contribution
It defines orthogonal decomposability for convex polytopes and explores this property in well-known classes of polyhedra, revealing new insights into their structure.
Findings
Identifies which Platonic and Archimedean solids are orthogonally decomposable.
Discovers polytopes that are not orthogonally decomposable.
Provides a framework for analyzing polytope decomposability using orthogonal connectedness.
Abstract
Using the orthogonal connectedness, we introduce the notion of orthogonal decomposability of convex polytopes and study it in the case of Platonic and Archimedean solids. While doing so, we also encounter polytopes which are not orthogonally decomposable.
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Taxonomy
TopicsMathematics and Applications · Homotopy and Cohomology in Algebraic Topology · Polynomial and algebraic computation