English

No acute tetrahedron is an 8-reptile

Computational Geometry 2018-01-30 v2 Metric Geometry

Abstract

An rr-gentiling is a dissection of a shape into r2r \geq 2 parts which are all similar to the original shape. An rr-reptiling is an rr-gentiling of which all parts are mutually congruent. This article shows that no acute tetrahedron is an rr-gentile or rr-reptile for any r<9r < 9, by showing that no acute spherical diangle can be dissected into less than nine acute spherical triangles.

Keywords

Cite

@article{arxiv.1508.03773,
  title  = {No acute tetrahedron is an 8-reptile},
  author = {Herman Haverkort},
  journal= {arXiv preprint arXiv:1508.03773},
  year   = {2018}
}

Comments

updated text, as in press with Discrete Mathematics, Discrete Mathematics Available online 10 November 2017