POLYOMINO TILINGS

Rectifiable Polyominoes

Here is list of known rectifiable polyominoes - polyominoes which tile rectangles.

Click on polyomino picture to view more information about it.

Click on underlined column headers to sort by values in clicked column.

Picture
Area
Order
Min. rect.
Min. rect. area
Prime rect.
Square order
Min. square
Min. sqr. area
Odd order
Min. odd rect.
Min. odd. area
Min. reptile
L1 20-omino
20
12
12x20
240
≥ 3
20
20x20
400
?
?
?
?
L2 15-omino
15
60
30x30
900
≥ 1
60
30x30
900
?
?
?
?
L1 12-omino
12
8
8x12
96
≥ 2
12
12x12
144
?
?
?
12
P1 11-omino
11
≤ 270
54x55
≤ 2970
≥ 1
?
?
?
≤ 423
47x99
≤ 4653
?
P2 9-omino
9
4
6x6
36
≥ 21
4
6x6
36
≤ 87
27x29
≤ 783
6
B1 9-omino
9
4
6x6
36
≥ 22
4
6x6
36
?
?
?
?
P3 9-omino
9
2
2x9
18
≥ 7
≤ 36
18x18
≤ 324
≤ 95
15x5719x45
≤ 855
?
P1 9-omino
9
2
2x93x6
18
≥ 4
4
6x6
36
15
5x279x15
135
2
L1 9-omino
9
2
2x9
18
≥ 7
36
18x18
324
33
11x27
297
8
A2 9-omino
9
2
3x6
18
≥ 16
4
6x6
36
≤ 247
19x117
≤ 2223
6
O 9-omino
9
1
3x3
9
1
1
3x3
9
1
3x3
9
2
I 9-omino
9
1
1x9
9
1
9
9x9
81
1
1x9
9
2
L2 octomino
8
≤ 180
36x40
≤ 1440
≥ 12
?
?
?
?
?
?
?
P3 octomino
8
2
4x4
16
≥ 4
2
4x4
16
?
?
?
4
P2 octomino
8
2
2x8
16
≥ 2
8
8x8
64
?
?
?
4
P1 octomino
8
2
2x8
16
≥ 5
8
8x8
64
?
?
?
4
L1 octomino
8
2
2x8
16
4
8
8x8
64
4
J1 octomino
8
2
4x4
16
≥ 1
2
4x4
16
?
?
?
?
G octomino
8
2
4x4
16
≥ 1
2
4x4
16
?
?
?
4
I2 octomino
8
1
2x4
8
1
2
4x4
16
1
2x4
8
2
I1 octomino
8
1
1x8
8
1
8
8x8
64
1
1x8
8
2
P2 heptomino
7
76
19x28
532
≥ 26
?
?
?
≤ 153
21x51
≤ 1071
?
P3 heptomino
7
28
14x14
196
≥ 37
28
14x14
196
45
15x21
315
?
P4 heptomino
7
2
2x7
14
3
28
14x14
196
33
11x21
231
4
P1 heptomino
7
2
2x7
14
≥ 3
28
14x14
196
≤ 57
19x21
≤ 399
?
L1 heptomino
7
2
2x7
14
2
28
14x14
196
27
9x21
189
6
I heptomino
7
1
1x7
7
1
7
7x7
49
1
1x7
7
2
Y1 hexomino
6
92
23x24
552
≥ 6
≤ 384
48x48
≤ 2304
?
?
?
?
B hexomino
6
18
9x12
108
≥ 26
96
24x24
576
9
D hexomino
6
4
4x6
24
2
24
12x12
144
6
P hexomino
6
2
2x63x4
12
5
6
6x6
36
11
6x11
66
2
L hexomino
6
2
2x6
12
8
6
6x6
36
21
9x14
126
6
J hexomino
6
2
3x4
12
1
24
12x12
144
6
F hexomino
6
2
3x4
12
≥ 1
24
12x12
144
?
?
?
8
A hexomino
6
2
3x4
12
≥ 1
24
12x12
144
?
?
?
?
O hexomino
6
1
2x3
6
1
6
6x6
36
1
2x3
6
2
I hexomino
6
1
1x6
6
1
6
6x6
36
1
1x6
6
2
Y pentomino
5
10
5x10
50
40
20
10x10
100
45
15x15
225
9
P pentomino
5
2
2x5
10
2
20
10x10
100
21
7x15
105
2
L pentomino
5
2
2x5
10
2
20
10x10
100
21
7x15
105
4
I pentomino
5
1
1x5
5
1
5
5x5
25
1
1x5
5
2
T tetromino
4
4
4x4
16
1
4
4x4
16
4
L tetromino
4
2
2x4
8
2
4
4x4
16
2
O tetromino
4
1
2x2
4
1
1
2x2
4
1
2x2
4
2
I tetromino
4
1
1x4
4
1
4
4x4
16
1
1x4
4
2
L triomino
3
2
2x3
6
2
12
6x6
36
15
5x9
45
2
I triomino
3
1
1x3
3
1
3
3x3
9
1
1x3
3
2
Dominoes
2
1
1x2
2
1
2
2x2
4
1
1x2
2
2
Monominoes
1
1
1x1
1
1
1
1x1
1
1
1x1
1
2