No acute tetrahedron is an 8-reptile

H.J. Haverkort

Research output: Contribution to journalArticleAcademicpeer-review


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.
Original languageEnglish
Pages (from-to)1131-1135
Number of pages5
JournalDiscrete Mathematics
Issue number4
Early online date10 Nov 2017
Publication statusPublished - Apr 2018


  • Tessellation;
  • Tetrahedron
  • Reptile
  • Tessellation


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