### Abstract

Original language | English |
---|---|

Pages (from-to) | 1131-1135 |

Number of pages | 5 |

Journal | Discrete Mathematics |

Volume | 341 |

Issue number | 4 |

Early online date | 10 Nov 2017 |

DOIs | |

Publication status | Published - 2018 |

### Fingerprint

### Keywords

- Tessellation;
- Tetrahedron
- Reptile

### Cite this

*Discrete Mathematics*,

*341*(4), 1131-1135. https://doi.org/10.1016/j.disc.2017.10.010

}

*Discrete Mathematics*, vol. 341, no. 4, pp. 1131-1135. https://doi.org/10.1016/j.disc.2017.10.010

**No acute tetrahedron is an 8-reptile.** / Haverkort, H.J.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - No acute tetrahedron is an 8-reptile

AU - Haverkort, H.J.

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

KW - Tessellation;

KW - Tetrahedron

KW - Reptile

U2 - 10.1016/j.disc.2017.10.010

DO - 10.1016/j.disc.2017.10.010

M3 - Article

VL - 341

SP - 1131

EP - 1135

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 4

ER -