No acute tetrahedron is an 8-reptile

H.J. Haverkort

Research output: Book/ReportReportAcademic

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Abstract

An $r$-gentiling is a dissection of a shape into $r \geq 2$ parts which are all similar to the original shape. An $r$-reptiling is an $r$-gentiling of which all parts are mutually congruent. This article shows that no acute tetrahedron is an $r$-gentile or $r$-reptile for any $r <9$, by showing that no acute spherical diangle can be dissected into less than nine acute spherical triangles.
Original languageEnglish
Publishers.n.
Number of pages6
Publication statusPublished - 2015

Publication series

NamearXiv
Volume1508.03773 [cs.CG]

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Reptile
Triangular pyramid
Acute
Spherical triangle
Dissection
Congruent

Cite this

Haverkort, H. J. (2015). No acute tetrahedron is an 8-reptile. (arXiv; Vol. 1508.03773 [cs.CG]). s.n.
Haverkort, H.J. / No acute tetrahedron is an 8-reptile. s.n., 2015. 6 p. (arXiv).
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Haverkort, HJ 2015, No acute tetrahedron is an 8-reptile. arXiv, vol. 1508.03773 [cs.CG], s.n.

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

s.n., 2015. 6 p. (arXiv; Vol. 1508.03773 [cs.CG]).

Research output: Book/ReportReportAcademic

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Haverkort HJ. No acute tetrahedron is an 8-reptile. s.n., 2015. 6 p. (arXiv).