# Polyabolo 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-triabolo can form a P-triabolo 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 polyaboloes.

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

1 | 1 | 1 |

2 | 3 | 3 |

3 | 1 | 3 |

4 | 5 | 10 |

5 | 0 | 3 |

6 | 7 | 19 |

7 | 0 | 4 |

## Triaboloes

## Tetraboloes

## Pentaboloes

## Hexaboloes

## Heptaboloes

*Last revised 2015-12-10.*

Back to Bireptiles
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Polyform Tiling
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Polyform Curiosities

Col. George Sicherman
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