2021/03/15

Tetrahexes are figures made of four hexagons connected at their sides. There are 10 one-sided pieces with a total area of 40 hexagons, which can be used to construct various symmetric patterns. Two parallelograms and one kind of oval are shown on the Poly Pages and some other constructions are here. You can cut or print these pieces with the provided SVG file.

Jared McComb suggested taking three sets of these pieces with different colors. For construction he demanded that same colored pieces shoudn't touch and same shapes shoudn't touch either. I only took the first condition for my patterns and tried to find solutions with my old program for front and back colored polyforms. Unfortunately the source code was lost and the program failed solving larger problems. So I had to write a new one.

A solution for a size 15 triangle is shown above. Click the number of pieces of some other sets to get more constructions.

Number of Hexagons | Properties | Uncolored Pieces | Number of Colored Pieces | Total Number of Hexagons |
---|---|---|---|---|

3 | - | 3 | 9 | 27 |

4 | two-sided | 7 | 21 | 84 |

one-sided | 10 | 30 | 120 | |

3..4 | two-sided | 10 | 30 | 111 |

one-sided | 13 | 39 | 147 | |

5 | two-sided | 22 | 66 | 330 |

one-sided | 33 | 99 | 495 |

To get a physical puzzle I printed three sets of one-sided tetrahexes, colored one side of the pieces and attached magnetic foils to the other one. This way a construction is fixed and can easily be moved around.