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.