# Catalogue of Tetrakis Polyaboloes

A polyabolo is a figure made of equal isosceles right triangles
joined at equal edges.
The *tetrakis
grid* is a square grid whose cells are subdivided into diagonal halves,
using alternate diagonals.
A *tetrakis polyabolo* is a polyabolo whose cells conform to the
tetrakis grid.
It is equivalent to a polyform whose cells are triangular quadrants
of the cells in a square grid.
In particular, every polyomino is a tetrakis polyabolo.
Thanks to Mark Smith for drawing my attention to tetrakis polyaboloes.

## Enumeration

*Two-sided* tetrakis polyaboloes may be rotated and reflected.
*One-sided* tetrakis polyaboloes may be rotated but not reflected.
Thanks to Joseph S. Myers for clearing up a point about enumerating
tetrakis polyaboloes.

Order | Two-Sided | One-Sided |

1 | 1 | 1 |

2 | 2 | 2 |

3 | 2 | 3 |

4 | 6 | 8 |

5 | 8 | 14 |

6 | 21 | 34 |

7 | 42 | 80 |

8 | 110 | 202 |

9 | 252 | 494 |

10 | 642 | 1 242 |

11 | 1 584 | 3 144 |

12 | 4 066 | 8 035 |

13 | 10 369 | 20 676 |

14 | 26 842 | 53 439 |

15 | 69 651 | 139 144 |

16 | 181 784 | 362 963 |

17 | 476 272 | 952 148 |

18 | 1 251 826 | 2 502 128 |

19 | 3 302 187 | 6 603 367 |

20 | 8 729 026 | 17 454 225 |

The figures below show two-sided tetrakis polyaboloes.

## Monabolo

## Diaboloes

## Triaboloes

## Tetraboloes

## Pentaboloes

## Hexaboloes

## Heptaboloes

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Polyform Curiosities

Col. George Sicherman
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