Unfolding and dissection of multiple cubes, tetrahedra, and doubly covered squares

Z. Abel; B. Ballinger; E.D. Demaine; M.L. Demaine; J. Erickson; A. Hesterberg; H. Ito; I. Kostitsyna; J. Lynch; R. Uehara

doi:10.2197/ipsjjip.25.610

Unfolding and dissection of multiple cubes, tetrahedra, and doubly covered squares

Z. Abel, B. Ballinger, E.D. Demaine, M.L. Demaine, J. Erickson, A. Hesterberg, H. Ito, I. Kostitsyna, J. Lynch, R. Uehara

Research output: Contribution to journal › Article › Academic › peer-review

5 Citations (Scopus)

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Abstract

In this paper, we introduce the notion of “rep-cube”: a net of a cube that can be divided into multiple polygons, each of which can be folded into a cube. This notion is inspired by the notion of polyomino and rep-tile; both are introduced by Solomon W. Golomb, and well investigated in the recreational mathematics society. We prove that there are infinitely many distinct rep-cubes. We also extend this notion to doubly covered squares and regular tetrahedra.

Original language	English
Pages (from-to)	610-615
Number of pages	6
Journal	Journal of Information Processing
Volume	25
DOIs	https://doi.org/10.2197/ipsjjip.25.610
Publication status	Published - Aug 2017
Externally published	Yes

Keywords

Dissection
Folding and unfolding
Polyomino
Rep-cube
Rep-tile

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10.2197/ipsjjip.25.610

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AU - Abel, Z.

AU - Ballinger, B.

AU - Demaine, E.D.

AU - Demaine, M.L.

AU - Erickson, J.

AU - Hesterberg, A.

AU - Ito, H.

AU - Kostitsyna, I.

AU - Lynch, J.

AU - Uehara, R.

PY - 2017/8

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AB - In this paper, we introduce the notion of “rep-cube”: a net of a cube that can be divided into multiple polygons, each of which can be folded into a cube. This notion is inspired by the notion of polyomino and rep-tile; both are introduced by Solomon W. Golomb, and well investigated in the recreational mathematics society. We prove that there are infinitely many distinct rep-cubes. We also extend this notion to doubly covered squares and regular tetrahedra.

KW - Dissection

KW - Folding and unfolding

KW - Polyomino

KW - Rep-cube

KW - Rep-tile

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SP - 610

EP - 615

JO - Journal of Information Processing

JF - Journal of Information Processing

ER -

Unfolding and dissection of multiple cubes, tetrahedra, and doubly covered squares

Abstract

Keywords

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