{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,3,6]],"date-time":"2023-03-06T14:15:50Z","timestamp":1678112150130},"reference-count":4,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Comput. Geom. Appl."],"published-print":{"date-parts":[[2018,9]]},"abstract":" We study the problem of folding a polyomino [Formula: see text] into a polycube [Formula: see text], allowing faces of [Formula: see text] to be covered multiple times. First, we define a variety of folding models according to whether the folds (a) must be along grid lines of [Formula: see text] or 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 [Formula: see text]), 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 [Formula: see text]. 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. <\/jats:p>","DOI":"10.1142\/s0218195918500048","type":"journal-article","created":{"date-parts":[[2018,11,16]],"date-time":"2018-11-16T00:53:15Z","timestamp":1542329595000},"page":"197-226","source":"Crossref","is-referenced-by-count":2,"title":["Folding Polyominoes into (Poly)Cubes"],"prefix":"10.1142","volume":"28","author":[{"given":"Oswin","family":"Aichholzer","sequence":"first","affiliation":[{"name":"Institute for Software Technology, Graz University of Technology, Austria"}]},{"given":"Michael","family":"Biro","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Swarthmore College, USA"}]},{"given":"Erik D.","family":"Demaine","sequence":"additional","affiliation":[{"name":"Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology, USA"}]},{"given":"Martin L.","family":"Demaine","sequence":"additional","affiliation":[{"name":"Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology, USA"}]},{"given":"David","family":"Eppstein","sequence":"additional","affiliation":[{"name":"Computer Science Department, University of California, Irvine, USA"}]},{"given":"S\u00e1ndor P.","family":"Fekete","sequence":"additional","affiliation":[{"name":"Department of Computer Science, TU Braunschweig, Germany"}]},{"given":"Adam","family":"Hesterberg","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Massachusetts Institute of Technology, USA"}]},{"given":"Irina","family":"Kostitsyna","sequence":"additional","affiliation":[{"name":"Computer Science Department, Universit\u00e9 Libre de Bruxelles, Belgium"}]},{"given":"Christiane","family":"Schmidt","sequence":"additional","affiliation":[{"name":"Communications and Transport Systems, ITN, Link\u00f6ping University, Sweden"}]}],"member":"219","published-online":{"date-parts":[[2018,11,15]]},"reference":[{"key":"S0218195918500048BIB007","doi-asserted-by":"publisher","DOI":"10.1007\/s00373-011-1024-3"},{"key":"S0218195918500048BIB008","doi-asserted-by":"publisher","DOI":"10.1016\/S0925-7721(99)00056-5"},{"key":"S0218195918500048BIB009","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511735172"},{"key":"S0218195918500048BIB013","doi-asserted-by":"publisher","DOI":"10.1142\/S0218195913500040"}],"container-title":["International Journal of Computational Geometry & Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218195918500048","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T16:54:39Z","timestamp":1565110479000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218195918500048"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,9]]},"references-count":4,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2018,11,15]]},"published-print":{"date-parts":[[2018,9]]}},"alternative-id":["10.1142\/S0218195918500048"],"URL":"http:\/\/dx.doi.org\/10.1142\/s0218195918500048","relation":{},"ISSN":["0218-1959","1793-6357"],"issn-type":[{"value":"0218-1959","type":"print"},{"value":"1793-6357","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,9]]}}}
