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An $r$-gentiling is a dissection of a shape into $r \geq 2$ parts which areall similar to the original shape. An $r$-reptiling is an $r$-gentiling ofwhich all parts are mutually congruent. This article shows that no acutetetrahedron is an $r$-gentile or $r$-reptile for any $r < 9$, by showing thatno acute spherical diangle can be dissected into less than nine acute sphericaltriangles.

No acute tetrahedron is an 8-reptile