No acute tetrahedron is an 8-reptile

H.J. Haverkort

doi:10.1016/j.disc.2017.10.010

No acute tetrahedron is an 8-reptile

H.J. Haverkort

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Abstract

An r-gentiling is a dissection of a shape into r ≥ 2 parts which are all similar to the original shape. An r-reptiling is an r-gentiling of which all parts are mutually congruent. The complete characterization of all reptile tetrahedra has been a long-standing open problem. This note concerns acute tetrahedra in particular. We find that no acute tetrahedron is an r-gentile or r-reptile for any r < 10. The proof is based on showing that no acute spherical diangle can be dissected into less than ten acute spherical triangles.

Original language	English
Pages (from-to)	1131-1135
Number of pages	5
Journal	Discrete Mathematics
Volume	341
Issue number	4
Early online date	10 Nov 2017
DOIs	https://doi.org/10.1016/j.disc.2017.10.010
Publication status	Published - Apr 2018

Keywords

Tessellation;
Tetrahedron
Reptile
Tessellation

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10.1016/j.disc.2017.10.010

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abstract = "An r-gentiling is a dissection of a shape into r ≥ 2 parts which are all similar to the original shape. An r-reptiling is an r-gentiling of which all parts are mutually congruent. The complete characterization of all reptile tetrahedra has been a long-standing open problem. This note concerns acute tetrahedra in particular. We find that no acute tetrahedron is an r-gentile or r-reptile for any r < 10. The proof is based on showing that no acute spherical diangle can be dissected into less than ten acute spherical triangles.",

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KW - Reptile

KW - Tessellation

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JF - Discrete Mathematics

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No acute tetrahedron is an 8-reptile

Abstract

Keywords

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