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.
|Number of pages||6|
|Publication status||Published - 2015|