No acute tetrahedron is an 8-reptile

H.J. Haverkort

Uittreksel

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.
Taal Engels 1131-1135 5 Discrete Mathematics 341 4 10 nov 2017 10.1016/j.disc.2017.10.010 Gepubliceerd - 2018

Vingerafdruk

Reptile
Triangular pyramid
Acute
Spherical triangle
Dissection
Congruent
Open Problems

Citeer dit

Haverkort, H.J./ No acute tetrahedron is an 8-reptile. In: Discrete Mathematics. 2018 ; Vol. 341, Nr. 4. blz. 1131-1135
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Haverkort, HJ 2018, 'No acute tetrahedron is an 8-reptile' Discrete Mathematics, vol. 341, nr. 4, blz. 1131-1135. DOI: 10.1016/j.disc.2017.10.010

No acute tetrahedron is an 8-reptile. / Haverkort, H.J.

In: Discrete Mathematics, Vol. 341, Nr. 4, 2018, blz. 1131-1135.

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N2 - 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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Haverkort HJ. No acute tetrahedron is an 8-reptile. Discrete Mathematics. 2018;341(4):1131-1135. Beschikbaar vanaf, DOI: 10.1016/j.disc.2017.10.010