Unfolding and Dissection of Multiple Cubes, Tetrahedra, and Doubly Covered Squares

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  • Abel Zachary
    Mathematics Department, MIT
  • Ballinger Brad
    Department of Mathematics, Humboldt State University
  • Demaine Erik D.
    Computer Science and Artificial Intelligence Laboratory, MIT
  • Demaine Martin L.
    Computer Science and Artificial Intelligence Laboratory, MIT
  • Erickson Jeff
    Department of Computer Science, University of Illinois at Urbana-Champaign
  • Hesterberg Adam
    Computer Science and Artificial Intelligence Laboratory, MIT
  • Ito Hiro
    Graduate School of Informatics and Engineering, the University of Electro-Communications
  • Kostitsyna Irina
    Computer Science Department, Université libre de Bruxelles
  • Lynch Jayson
    Computer Science and Artificial Intelligence Laboratory, MIT
  • Uehara Ryuhei
    School of Information Science, Japan Advanced Institute of Science and Technology

Abstract

<p>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.</p>

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