Polyomino
polyform whose cells are squares
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 edit
n | name | number of free polyominoes | number of free polyominoes with holes | number of one-sided polyominoes | = 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) edit
A polyomino made from three squares is a tromino. There are only two possible trominoes:
Tetrominoes (4-ominoes) edit
Pentominoes (5-ominoes) edit
Hexominoes (6-ominoes) edit
The 35 free hexominoes | The 11 cubic nets |
---|---|
Heptominoes (7-ominoes) edit
90° reflection |
45° reflection |
Rotation |
Both |
Octominoes (8-ominoes) edit
90° reflection |
45° reflection |
C2 rotation |
C4 rotation |
Both |