| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 8903070 | Discrete Mathematics | 2018 | 5 Pages |
Abstract
An r-gentiling is a dissection of a shape into râ¥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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Herman Haverkort,