Folding Polyominoes into (Poly) Cubes
Name
1712.09317.pdf
Description
Accepted version
Size
900.54 KB
Format
Adobe PDF
Checksum (MD5)
951029347ba98c100cdd56adcb0f8a5c
Author(s)
Aichholzer, Oswin
Biro, Michael
Demaine, Erik D.
Demaine, Martin L.
Eppstein, David
Fekete, Sándor P.
Hesterberg, Adam
Kostitsyna, Irina
Schmidt, Christiane
Date Issued
2015
Citation
Aichholzer, Oswin, Biro, Michael, Demaine, Erik D., Demaine, Martin L., Eppstein, David et al. 2018. "Folding Polyominoes into (Poly) Cubes."
Version
Author's final manuscript
Abstract
© 2015 Queen's University Ontario Canada. All rights reserved. We study the problem of folding a given polyomino S into a polycube C under different folding models, allowing faces of C to be covered multiple times. First, we define a variety of folding models according to whether the folds (a) must be along grid lines ofPor can divide squares in half(diagonally and/or orthogonally), (b) must be mountain or can be both mountain and valley, (c) can remain flat (forming an angle of 180◦), and (d) must lie on just the polycube surface or can have interior faces as well. Second, we give all the inclusion relations among all models that fold on the grid lines of P. Third, we characterize all polyominoes that can fold into a unit cube, in some models. Fourth, we give a linear-time dynamic programming algorithm to fold a tree-shaped polyomino into a constant-size polycube, in some models. Finally, we consider the triangular version of the problem,characterizing which polyiamonds fold into a regular tetrahedron.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
http://research.cs.queensu.ca/cccg2015/
