Counting Polyforms
The table below gives counts for the number of polyforms of the most common classes. Much of the data below comes from a set of enumeration programs written by Aaron Siegel, although many of the figures appear in puzzle literature as well. The counts for octotans and enneatans (order 8 and 9 polytans, also called polyaboloes) correct earlier published data, and have been confirmed by Nob Yoshigahara, citing computer analysis by his colleague Taro. Counts of polyedges were made by hand by Brian Barwell up through order 6, and confirmed by Siegel's program.

Class

1 2 3 4 5 6 7 8 9 10 11
Polyominoes 1 1 2 5 12 35 108 369 1285 4655 17073
Polyhexes 1 1 3 7 22 82 333 1448 6572 30490 143552
Polytans 1 3 4 14 30 107 318 1116 3743 13240 46476
Polyiamonds 1 1 1 3 4 12 24 66 160 448 1186
Polycubes 1 1 2 8 29 166 1023 6922 48311 346543 2522522
Polyominoids 1 2 11 80
Polyedges 1 2 5 16 55 222 950 4265

Hyperlinks show full-set constructions with various sets.

The best source for polyform puzzle sets is Kadon Enterprises, which makes wood and acrylic versions of most of the standard polyomino, polycube, polytan, polyhex, and polyiamond sets (these are shaded (grey background) in the table above); see their website for other sets.

This article is copyright 2001, 2007 by Michael Keller.  All rights reserved.

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