Rep-Cubes: Dissection of a Cube into Nets

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

doi:10.1587/transfun.E101.A.1420

Special Section on Discrete Mathematics and Its Applications

Rep-Cubes: Dissection of a Cube into Nets

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

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Keywords: cube, net, polyomino, pythagorean triple, rep-cube, rep-tile

JOURNAL RESTRICTED ACCESS

2018 Volume E101.A Issue 9 Pages 1420-1430

DOI https://doi.org/10.1587/transfun.E101.A.1420

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Abstract

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.

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