# Catalogue of Polyenns

A polyenn is a figure made of regular enneagons (9-gons) joined
edge to edge.
Here I show all the polyenns with up to 5 cells.
*Two-sided* polyenns may be rotated and reflected.
*One-sided* polyenns may be rotated but not reflected.
Thus two distinct mirror images of a polyenn
are regarded as distinct one-sided polyenns.

## Enumeration

Cells | Two-Sided | One-Sided |

1 | 1 | 1 |

2 | 1 | 1 |

3 | 3 | 3 |

4 | 14 | 24 |

5 | 82 | 148 |

6 | 585 | 1 145 |

7 | 4 418 | 8 728 |

8 | 34 838 | 69 503 |

Matthias Koch and
Sascha Kurz have enumerated polyenns up through 13 cells.
See Matthias Koch and Sascha Kurz, Enumeration of Generalized
Polyominoes.

The enumeration for two-sided polyenns is A103467 in the On-Line
Encyclopedia of Integer Sequences.

The figures below show two-sided polyenns.

## Monenn

## Dienn

## Trienns

## Tetrenns

## Pentenns

Last revised 2024-03-27.

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Col. George Sicherman
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