@article{5ccbe6519c334fefb3a05450c3027834,
title = "Unfolding and dissection of multiple cubes, tetrahedra, and doubly covered squares",
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 SolomonW. 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.",
keywords = "Dissection, Folding and unfolding, Polyomino, Rep-cube, Rep-tile",
author = "Zachary Abel and Brad Ballinger and Demaine, {Erik D.} and Demaine, {Martin L.} and Jeff Erickson and Adam Hesterberg and Hiro Ito and Irina Kostitsyna and Jayson Lynch and Ryuhei Uehara",
note = "Funding Information: Acknowledgments This work was initiated at the 31st Bellairs Winter Workshop on Computational Geometry, co-organized by Erik Demaine and Godfried Toussaint, held on March 18–25, 2016, in Holetown, Barbados. We thank the other participants of that workshop for providing a stimulating research environment. Parts of this paper were presented at JCD-CGGG [2], and WAAC 2016 [1]. This work was partly supported by JSPS/MEXT KAKENHI Grant Numbers 23300001, 24106003, 24106004, 26330009, 15K11985. Publisher Copyright: {\textcopyright} 2017 Information Processing Society of Japan.",
year = "2017",
month = aug,
doi = "10.2197/ipsjjip.25.610",
language = "English (US)",
volume = "25",
pages = "610--615",
journal = "Journal of Information Processing",
issn = "0387-6101",
publisher = "Information Processing Society of Japan",
}