Rep-Cubes: Dissection of a Cube into Nets

Dawei XU  Jinfeng HUANG  Yuta NAKANE  Tomoo YOKOYAMA  Takashi HORIYAMA  Ryuhei UEHARA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E101-A   No.9   pp.1420-1430
Publication Date: 2018/09/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E101.A.1420
Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
cube,  net,  polyomino,  pythagorean triple,  rep-cube,  rep-tile,  

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Last year, a new notion of rep-cube was proposed. A rep-cube is a polyomino that is a net of a cube, and it can be divided into some polyominoes such that each of them can be folded into a cube. This notion was inspired by the notions of polyomino and rep-tile, which were introduced by Solomon W. Golomb. It was proved that there are infinitely many distinct rep-cubes. In this paper, we investigate this new notion and show further results.