No acute tetrahedron is an 8-reptile

An r-gentiling is a dissection of a shape into r≥2 parts which are all similar to the original shape. An r-reptiling is an r-gentiling of which all parts are mutually congruent. The complete characterization of all reptile tetrahedra has been a long-standing open problem. This note concerns acute tetrahedra in particular. We find that no acute tetrahedron is an r-gentile or r-reptile for any r<10. The proof is based on showing that no acute spherical diangle can be dissected into less than ten acute spherical triangles.