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

CellsTwo-SidedOne-Sided
111
211
333
41424
582148
65851 145
74 4188 728
834 83869 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 [ HOME | MAIL ]