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On inside-out Dissections of Polygons and Polyhedra

2024/11/10 by Reymond Akpanya, Akpanya, Reymond, Adi Rivkin +3
Engineering · Computer Science · #Advanced Materials and Mechanics #Architecture and Computational Design #Computational Geometry and Mesh Generation

paper · pdf · doi:10.48550/arxiv.2411.06584

Abstract

In this work we study inside-out dissections of polygons and polyhedra. We first show that an arbitrary polygon can be inside-out dissected with 2n+1 pieces, thereby improving the best previous upper bound of 4(n-2) pieces. Additionally, we establish that a regular polygon can be inside-out dissected with at most 6 pieces. Lastly, we prove that any polyhedron that can be decomposed into finitely many regular tetrahedra and octahedra can be inside-out dissected.

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