No acute tetrahedron is an 8-reptile

H.J. Haverkort

Research output: Contribution to journalArticleAcademicpeer-review

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 languageEnglish
Pages (from-to)1131-1135
Number of pages5
JournalDiscrete Mathematics
Volume341
Issue number4
Early online date10 Nov 2017
DOIs
Publication statusPublished - 2018

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Reptile
Dissection
Triangular pyramid
Acute
Spherical triangle
Congruent
Open Problems

Keywords

  • Tessellation;
  • Tetrahedron
  • Reptile

Cite this

Haverkort, H.J. / No acute tetrahedron is an 8-reptile. In: Discrete Mathematics. 2018 ; Vol. 341, No. 4. pp. 1131-1135.
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No acute tetrahedron is an 8-reptile. / Haverkort, H.J.

In: Discrete Mathematics, Vol. 341, No. 4, 2018, p. 1131-1135.

Research output: Contribution to journalArticleAcademicpeer-review

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PY - 2018

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AB - 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

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