Polyomino

Polyominoes are shapes made from a finite number(side-to-side connected) unit squares on the standard plane. The following pairs of squares are not side-side connected:

The following pair is side-side connected:

Types of Polyomino

n	name	number of free polyominoes	number of free polyominoes with holes	number of one-sided polyominoes	$A_{n}$ = number of fixed polyominoes
1	monomino	1	0	1	1
2	domino	1	0	1	2
3	tromino/triomino	2	0	2	6
4	tetromino	5	0	7	19
5	pentomino	12	0	18	63
6	hexomino	35	0	60	216
7	heptomino	108	1	196	760
8	octomino	369	6	704	2,725
9	nonomino	1,285	37	2,500	9,910
10	decomino	4,655	195	9,189	36,446
11	undecomino	17,073	979	33,896	135,268
12	dodecomino	63,600	4,663	126,759	505,861

Trominoes (3-ominoes)

A polyomino made from three squares is a tromino. There are only two possible trominoes:

Tetrominoes (4-ominoes)

Pentominoes (5-ominoes)

  

Hexominoes (6-ominoes)

The 35 free hexominoes	The 11 cubic nets

Heptominoes (7-ominoes)

90° reflection

45° reflection

Rotation

Both

Octominoes (8-ominoes)

90° reflection

45° reflection

C2 rotation

C4 rotation

Both

Permutominoes

Ferrer partitioning diagrams