# Cell Shifts for Polyhexes

## Introduction

Two figures can be tiled with copies of the same polyhex.
The figures differ in only one cell.
How near can the unmatched cells lie?
Over all such pairs of figures,
a minimal vector from one unmatched cell to the other
is called a *minimal shift vector*.
Here I show minimal shift vectors
for polyiamonds up to order 5.
The minimal values were established by Mike Reid,
using
Tile Homotopy Theory.

For hexahexes, see Cell Shifts for Hexahexes.

### Monohex

| 1 | |

### Dihex

| 1 | |

### Trihexes

### Tetrahexes

### Pentahexes

| 5 | |

| 1 | |

| 1 | |

| √3 | |

| 1 | |

| 1 | |

| 2√3 | |

| 1 | |

| 1 | |

| 1 | |

| 1 | |

| 1 | |

| 1 | |

| 1 | |

| √3 | |

| 1 | |

| 5√3 | |

| 1 | |

| 1 | |

| 1 | |

| 5 | |

| 2√3 | |

### Dihex

| 2 | |

### Tetrahexes

### Pentahexes

| 5 | |

| 1 | |

| 1 | |

| √3 | |

| 1 | |

| 1 | |

| 2√3 | |

| 1 | |

| 1 | |

| 1 | |

| 1 | |

| 1 | |

| 1 | |

| 1 | |

| √3 | |

| 1 | |

| 5√3 | |

| 1 | |

| 1 | |

| 1 | |

| 5 | |

| 2√3 | |

Back to Polyform Curiosities.

Col. George Sicherman
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