# Trihing Compatibility

## Introduction

A *trihing* is a figure made of three equal regular hexagons
joined along edges or at vertexes in parallel.
There are 8 trihings, not distinguishing reflections and rotations.
The *compatibility problem*
is to find a figure that can be tiled with each of a set of polyforms.
Here are minimal known compatibility figures for pairs of trihings.

## Enumeration

## Table of Results

| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |

1 | * | 3 | 2 | × | 2 | 3 | × | 2 |

2 | 3 | * | 2 | 2 | 2 | 3 | 2 | 2 |

3 | 2 | 2 | * | × | 2 | × | × | 6 |

4 | × | 2 | × | * | × | 2 | 2 | 2 |

5 | 2 | 2 | 2 | × | * | × | × | 2 |

6 | 3 | 3 | × | 2 | × | * | 2 | 2 |

7 | × | 2 | × | 2 | × | 2 | * | 6 |

8 | 2 | 2 | 6 | 2 | 2 | 2 | 6 | * |

## 2 Tiles

## 3 Tiles

## 6 Tiles

Last revised 2014-12-08.

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Polyform Compatibility
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Polyform Curiosities

Col. George Sicherman
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