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 language | English |
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| Publisher | s.n. |
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| Number of pages | 6 |
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| Publication status | Published - 2015 |
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| Name | arXiv |
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| Volume | 1508.03773 [cs.CG] |
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