POLYOMINO TILINGS

Polyomino Tilings

Select polyominoes for a set (currently 1 or 2), for which tilings should be shown.

Then click "Show" button.

You may also see list of all polyomino sets for which data is available here.


O tetromino and T tetromino

Prime rectangles: ≥ 8.

Smallest rectangle tilings

Smallest rectangle (4x6):

Smallest square (6x6):

Rectangle tilings' solutions count (including symmetric)

Blue number - strongly prime rectangle (which cannot be divided into two or more number of rectangles tileable by this set).

Green number - weakly prime rectangle (which cannot be divided into two rectangles tileable by this set, but which can be divided into three or more rectangles).

Purple number - prime rectangle (unknown if weakly or strongly prime).

Red number - composite rectangle (which can be divided into two rectangles tileable by this set).

Gray number - it is unknown whether rectangle is prime or composite.

Question mark (?) - solution count is unknown.

Click on underlined numbers to view picture with one solution.

w \ h
1-3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
N>0
1-3
0
4
0
0
5
0
0
0
6
0
4
0
8
7
0
0
0
0
0
8
0
6
5
37
21
292
9
0
0
0
0
0
327
0
10
0
24
0
94
0
1671
0
12318
11
0
0
0
0
0
1680
0
0
0
12
0
40
2
349
54
11760
6472
162595
≥1
≥1
13
0
0
0
0
0
16532
0
0
0
≥1
0
14
0
120
0
1046
0
70616
0
1618697
0
≥1
0
≥1
15
0
0
0
0
0
97718
0
0
0
≥1
0
0
0
16
0
218
41
3570
2289
471844
574782
19296382
≥1
≥1
≥1
≥1
≥1
≥1
17
0
0
0
0
0
789151
0
0
0
≥1
0
0
0
≥1
0
18
0
576
0
11370
0
2953858
0
215121681
0
≥1
0
≥1
0
≥1
0
≥1
19
0
0
0
0
0
5024039
0
0
0
≥1
0
0
0
≥1
0
0
0
20
0
1112
40
37504
23966
19366662
26076872
2.51503447×10¹⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
21
0
0
0
0
0
36942535
0
0
0
≥1
0
0
0
≥1
0
0
0
≥1
?
22
0
2732
0
121546
0
124602001
0
2.91879613×10¹¹
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
23
0
0
0
0
0
243590561
0
0
0
≥1
0
0
0
≥1
0
0
0
≥1
?
24
0
5494
381
396541
497127
815480016
1.81906529×10¹⁰
3.42299952×10¹²
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
25
0
0
0
0
0
1.71225795×10¹⁰
0
0
0
≥1
0
0
0
≥1
0
0
0
≥1
?
26
0
12904
0
1290738
0
5.33461446×10¹⁰
0
4.03003273×10¹³
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
27
0
0
0
0
0
1.14632901×10¹¹
0
0
0
≥1
0
0
0
≥1
0
0
0
≥1
?
28
0
26656
624
4200683
7032464
3.50890306×10¹¹
1.08127359×10¹²
4.75367099×10¹⁴
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
29
0
0
0
0
0
7.88650979×10¹¹
0
0
0
≥1
0
0
0
≥1
0
0
0
≥1
?
30
0
60848
0
13683346
0
2.31900641×10¹²
0
5.62867250×10¹⁵
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
31
0
0
0
0
0
5.31192220×10¹²
0
0
0
≥1
0
0
0
≥1
0
0
0
≥1
?
32
0
127914
4009
44525830
123180871
1.53526938×10¹³
7.23365063×10¹³
6.66717070×10¹⁶
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
33
0
0
0
0
0
3.61784681×10¹³
0
0
0
≥1
0
0
0
≥1
0
0
0
≥1
?
34
0
286720
0
145023030
0
1.02144295×10¹⁴
0
7.91505337×10¹⁷
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
35
0
0
0
0
0
2.44212603×10¹⁴
0
0
0
≥1
0
0
0
≥1
0
0
0
≥1
?
36
0
609616
9042
472012210
1.90562336×10¹⁰
6.80161565×10¹⁴
4.65227526×10¹⁵
9.39837409×10¹⁸
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
37
0
0
0
0
0
1.65567320×10¹⁵
0
0
0
≥1
0
0
0
≥1
0
0
0
≥1
?
38
0
1350612
0
1.53707105×10¹⁰
0
4.54630790×10¹⁵
0
1.11724458×10²⁰
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
39
0
0
0
0
0
1.11844318×10¹⁶
0
0
0
≥1
0
0
0
≥1
0
0
0
≥1
?
40
0
2892742
46451
5.00360517×10¹⁰
3.16772055×10¹¹
3.04110611×10¹⁶
3.08662273×10¹⁷
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
41
0
0
0
0
0
7.56775906×10¹⁶
0
0
0
≥1
0
0
0
≥1
0
0
0
≥1
?
42
0
6361208
0
1.62918725×10¹¹
0
2.03959304×10¹⁷
0
≥1.84467440×10²⁰
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
43
0
0
0
0
0
5.11366168×10¹⁷
0
0
0
≥1
0
0
0
≥1
0
0
0
≥1
?
44
0
13688824
127342
5.30392158×10¹¹
5.04968942×10¹²
1.36893278×10¹⁸
2.02783618×10¹⁹
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
45
0
0
0
0
0
3.45756573×10¹⁸
0
0
0
≥1
0
0
0
≥1
0
0
0
≥1
?
46
0
29958440
0
1.72687322×10¹²
0
9.20407059×10¹⁸
0
≥1.84467440×10²⁰
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
47
0
0
0
0
0
2.33680534×10¹⁹
0
0
0
≥1
0
0
0
≥1
0
0
0
≥1
?
48
0
64663706
573569
5.62214722×10¹²
8.25043460×10¹³
6.19273193×10¹⁹
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
49
0
0
0
0
0
1.57977744×10²⁰
0
0
0
≥1
0
0
0
≥1
0
0
0
≥1
?
50
0
141086400
0
1.83044210×10¹³
0
≥1.84467440×10²⁰
0
≥1.84467440×10²⁰
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
?
N>0
x
?
4k
2k
4k
all
4k
2k
?
?
?
?
?
?
?
?
?
?

Smallest common multiples

Smallest known common multiple (area 16):

Common multiples' solutions count (excluding symmetric)

area
4
8
12
16
solutions
0
?
?
≥1

See Also

L tetromino and Z pentominoO tetromino and I pentomino