The search functionality is under construction.

The search functionality is under construction.

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.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E101-A No.9 pp.1420-1430

- Publication Date
- 2018/09/01

- Publicized

- 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)

- Category

Dawei XU

JAIST

Jinfeng HUANG

JAIST

Yuta NAKANE

Nagoya Institute of Technology

Tomoo YOKOYAMA

Kyoto University of Education

Takashi HORIYAMA

Saitama University

Ryuhei UEHARA

JAIST

The copyright of the original papers published on this site belongs to IEICE. Unauthorized use of the original or translated papers is prohibited. See IEICE Provisions on Copyright for details.

Copy

Dawei XU, Jinfeng HUANG, Yuta NAKANE, Tomoo YOKOYAMA, Takashi HORIYAMA, Ryuhei UEHARA, "Rep-Cubes: Dissection of a Cube into Nets" in IEICE TRANSACTIONS on Fundamentals,
vol. E101-A, no. 9, pp. 1420-1430, September 2018, doi: 10.1587/transfun.E101.A.1420.

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.

URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E101.A.1420/_p

Copy

@ARTICLE{e101-a_9_1420,

author={Dawei XU, Jinfeng HUANG, Yuta NAKANE, Tomoo YOKOYAMA, Takashi HORIYAMA, Ryuhei UEHARA, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={Rep-Cubes: Dissection of a Cube into Nets},

year={2018},

volume={E101-A},

number={9},

pages={1420-1430},

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.},

keywords={},

doi={10.1587/transfun.E101.A.1420},

ISSN={1745-1337},

month={September},}

Copy

TY - JOUR

TI - Rep-Cubes: Dissection of a Cube into Nets

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 1420

EP - 1430

AU - Dawei XU

AU - Jinfeng HUANG

AU - Yuta NAKANE

AU - Tomoo YOKOYAMA

AU - Takashi HORIYAMA

AU - Ryuhei UEHARA

PY - 2018

DO - 10.1587/transfun.E101.A.1420

JO - IEICE TRANSACTIONS on Fundamentals

SN - 1745-1337

VL - E101-A

IS - 9

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - September 2018

AB - 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.

ER -