# Polyomino Bireptiles

## Introduction

In combinatorial geometry a *reptile* is a geometric figure,
equal copies of which can be joined to form an enlarged form of the figure.
For example, four copies of the P-pentomino can form a P-pentomino at
double scale, or four times as large:

Reptiles are known for polyominoes, polyiamonds, polyaboloes,
and other polyforms.

Few polyforms of any kind form reptiles.
A *bireptile* is a figure of which copies can be joined to
form two joined, equally enlarged copies of the original figure.

Any figure with a reptiling trivially has a bireptiling, but not every
figure with a bireptiling has a reptiling.
That is, bireptiles are more common than reptiles.

Below I show minimal known bireptilings for various polyominoes.

Number of Cells | Number of Reptiles | Number
of Bireptiles |

1 | 1 | 1 |

2 | 1 | 1 |

3 | 2 | 2 |

4 | 4 | 4 |

5 | 4 | 4 |

6 | 10 | 11 |

7 | 6 | 6 |

8 | 12 | 16 |

9 | 41 | 41 |

10 | 28 | 35 |

## Pentominoes

## Hexominoes

## Heptominoes

## Octominoes

## Enneominoes

## Decominoes

*Last revised 2015-12-10.*

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Polyform Curiosities

Col. George Sicherman
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