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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 invented in 2017, which is inspired by the notions of polyomino and rep-tile, which were introduced by Solomon W. Golomb. A rep-cube is called regular if it can be divided into the nets of the same area. A regular rep-cube is of order *k* if it is divided into *k* nets. Moreover, it is called uniform if it can be divided into the congruent nets. In this paper, we focus on these special rep-cubes and solve several open problems.

- Publication
- IEICE TRANSACTIONS on Information Vol.E105-D No.3 pp.459-465

- Publication Date
- 2022/03/01

- Publicized
- 2021/10/22

- Online ISSN
- 1745-1361

- DOI
- 10.1587/transinf.2021FCP0004

- Type of Manuscript
- Special Section PAPER (Special Section on Foundations of Computer Science - New Trends of Theory of Computation and Algorithm -)

- Category

Tamami OKADA

Japan Advanced Institute of Science and Technology (JAIST)

Ryuhei UEHARA

Japan Advanced Institute of Science and Technology (JAIST)

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Tamami OKADA, Ryuhei UEHARA, "Research on Dissections of a Net of a Cube into Nets of Cubes" in IEICE TRANSACTIONS on Information,
vol. E105-D, no. 3, pp. 459-465, March 2022, doi: 10.1587/transinf.2021FCP0004.

Abstract: 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 invented in 2017, which is inspired by the notions of polyomino and rep-tile, which were introduced by Solomon W. Golomb. A rep-cube is called regular if it can be divided into the nets of the same area. A regular rep-cube is of order *k* if it is divided into *k* nets. Moreover, it is called uniform if it can be divided into the congruent nets. In this paper, we focus on these special rep-cubes and solve several open problems.

URL: https://global.ieice.org/en_transactions/information/10.1587/transinf.2021FCP0004/_p

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@ARTICLE{e105-d_3_459,

author={Tamami OKADA, Ryuhei UEHARA, },

journal={IEICE TRANSACTIONS on Information},

title={Research on Dissections of a Net of a Cube into Nets of Cubes},

year={2022},

volume={E105-D},

number={3},

pages={459-465},

abstract={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 invented in 2017, which is inspired by the notions of polyomino and rep-tile, which were introduced by Solomon W. Golomb. A rep-cube is called regular if it can be divided into the nets of the same area. A regular rep-cube is of order *k* if it is divided into *k* nets. Moreover, it is called uniform if it can be divided into the congruent nets. In this paper, we focus on these special rep-cubes and solve several open problems.},

keywords={},

doi={10.1587/transinf.2021FCP0004},

ISSN={1745-1361},

month={March},}

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TY - JOUR

TI - Research on Dissections of a Net of a Cube into Nets of Cubes

T2 - IEICE TRANSACTIONS on Information

SP - 459

EP - 465

AU - Tamami OKADA

AU - Ryuhei UEHARA

PY - 2022

DO - 10.1587/transinf.2021FCP0004

JO - IEICE TRANSACTIONS on Information

SN - 1745-1361

VL - E105-D

IS - 3

JA - IEICE TRANSACTIONS on Information

Y1 - March 2022

AB - 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 invented in 2017, which is inspired by the notions of polyomino and rep-tile, which were introduced by Solomon W. Golomb. A rep-cube is called regular if it can be divided into the nets of the same area. A regular rep-cube is of order *k* if it is divided into *k* nets. Moreover, it is called uniform if it can be divided into the congruent nets. In this paper, we focus on these special rep-cubes and solve several open problems.

ER -