On inside-out Dissections of Polygons and Polyhedra

arXiv (Cornell University)

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.

Authors 3

1. Reymond Akpanya Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University , Aachen , Germany,

2. Adi Rivkin

   Technion – Israel Institute of Technology

   Affiliation as printed

   Dept. of Computer Science , Technion-Israel Institute of Technology , Haifa , Israel,

3. Frederick Stock

   University of Massachusetts Lowell

   Affiliation as printed

   Miner School of Computer & Information Sciences , Lowell , MA . USA , Frederick