IEICE TRANSACTIONS on Information
Research on Dissections of a Net of a Cube into Nets of Cubes
Summary :
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
Authors
Tamami OKADA
Japan Advanced Institute of Science and Technology (JAIST)
Ryuhei UEHARA
Japan Advanced Institute of Science and Technology (JAIST)
Keyword
Latest Issue
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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},}
Copy
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 -
English
