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arXiv · 1508.03773

No acute tetrahedron is an 8-reptile

Herman Haverkort
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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.

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Herman Haverkort. 2015-08-15. No acute tetrahedron is an 8-reptile. https://arxiv.org/abs/1508.03773

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