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.


Abstract:
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