Polyomino

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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:

Cornerconnectedsquares.jpg Cornersideconnectedsquares.jpg Disconnectedsquares.jpg Overlapping squares.jpg Part side connected squares.jpg

The following pair is side-side connected:

Side side connected.jpg

Types of Polyomino[edit]

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)[edit]

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

TrominoI.jpg TrominoV.jpg

Tetrominoes (4-ominoes)[edit]

Tetromino Tiling 5x8.svg Tetromino Tiling 4x10.svg

Pentominoes (5-ominoes)[edit]

All 18 Pentominoes.svg

L-pentomino Symmetry.svgF-pentomino Symmetry.svg  N-pentomino Symmetry.svgY-pentomino Symmetry.svg

Pentomino Naming Conventions.svg
Pentomino Puzzle Solutions.svg
Pentomino Cube Solutions.svg

Hexominoes (6-ominoes)[edit]

The 35 free hexominoes The 11 cubic nets
All 35 free hexominoes.svg
The 11 cubic nets.svg

Heptominoes (7-ominoes)[edit]

Heptominoes.svg
Reflection Symmetrical Heptominoes-90-deg.svg
90° reflection
Reflection Symmetrical Heptominoes-45-deg.svg
45° reflection
Rotation Symmetrical Heptominoes.svg
Rotation
Rotation and Reflection Symmetrical Heptominoes.svg
Both

Octominoes (8-ominoes)[edit]

All 369 free octominoes.svg
Reflection symmetrical octominoes 90 deg.svg
90° reflection
Reflection symmetric octominoes 45 deg v.svg
45° reflection
Rotation symmetric octominoes C2 v.svg
C2 rotation
Rotation symmetrical octomino (C4).svg
C4 rotation
Rotation and reflection symmetric octominoes v.svg
Both

Permutominoes[edit]

Permutominoes 2x2.svg
Permutominoes 3x3.svg

Ferrer partitioning diagrams[edit]

Ferrer partitioning diagrams.svg