Unfolding and dissection of multiple cubes

With Zachary Abel*, Brad Ballinger, Erik D. Demaine, Martin L. Demaine, Adam Hesterberg*, Hiro Ito, Irina Kostitsyna, Jayson Lynch*, and Ryuhei Uehara.

Journal of Information Processing 25:610–615, 2017.
Special issue of discrete and computational geometry, graphs, and games.

Extended abstract in Abstracts of the 19th Japan Conference on Discrete and Computational Geometry, Graphs, and Games, 42—43, 2016.

In this paper, we introduce the notion of “rep-cube”: a net of a cube that can be divided into multiple polygons, each of which can be folded into a cube. This notion is inspired by the notion of polyomino and rep-tile; both are introduced by Solomon W. Golomb, and well investigated in the recreational mathematics society. We prove that there are infinitely many distinct rep-cubes. We also extend this notion to doubly covered squares and regular tetrahedra.

Publications - Jeff Erickson (jeffe@illinois.edu) 16 Aug 2017