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.

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