2015/08/15 by Herman Haverkort, Haverkort, Herman
Computer Science · Mathematics · #Computational Geometry (cs.CG) #FOS: Computer and information sciences #FOS: Mathematics #Metric Geometry (math.MG) #cs.CG #math.MG
paper · pdf · doi:10.48550/arxiv.1508.03773
updated text, as in press with Discrete Mathematics, Discrete Mathematics Available online 10 November 2017
arxiv created 2018/01/29 · arxiv updated 2018/01/30
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. 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.