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arXiv · 2411.06584

On inside-out Dissections of Polygons and Polyhedra

Reymond Akpanya·Adi Rivkin·Frederick Stock
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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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Reymond Akpanya, Adi Rivkin, Frederick Stock. 2024-11-10. On inside-out Dissections of Polygons and Polyhedra. https://arxiv.org/abs/2411.06584

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