POLYOMINO TILINGS

Polyomino Tilings

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Then click "Show" button.

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


Tetrominoes

Prime rectangles: 11.

Smallest rectangle tilings

Smallest rectangles (3x8, 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
1-2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
1-2
0
3
0
0
4
0
0
0
5
0
0
0
0
6
0
0
16
0
26272
7
0
0
240
0
0
0
8
0
16
2320
151740
6820196
≥1
≥1
9
0
0
16970
0
0
0
≥1
0
10
0
0
113902
0
≥1
0
≥1
0
≥1
11
0
0
674488
0
0
0
≥1
0
0
0
12
0
5812
3791414
779579633
≥1
≥1
≥1
≥1
≥1
≥1
≥1
13
0
0
20417678
0
0
0
≥1
0
0
0
≥1
0
14
0
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
15
0
0
≥1
0
0
0
≥1
0
0
0
≥1
0
0
0
16
0
616284
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
17
0
0
≥1
0
0
0
≥1
0
0
0
≥1
0
0
0
≥1
0
18
0
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
0
≥1
19
0
0
≥1
0
0
0
≥1
0
0
0
≥1
0
0
0
≥1
0
0
0
20
0
43095302
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
N>0
x
4k
all
4k
2k
4k
all
4k
2k
4k
all
4k
2k
4k
all
4k
2k
4k
all

Smallest prime reptiles

Smallest prime reptiles (4Ix3, 4Ox3, 4Lx3, 4Tx3, 4Zx3):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
I tetromino
0
0
5812
L tetromino
0
0
4386
O tetromino
0
0
26272
T tetromino
0
0
6730
Z tetromino
0
0
2812

Smallest common multiples

Smallest common multiple (area 32):

Common multiples' solutions count (excluding symmetric)

area
4
8
12
16
20
24
28
32
solutions
0
?
?
?
?
?
?
≥1

Attributions

  1. Smallest known common multiple found by Livio Zucca (http://www.iread.it/lz/4chall.html)

See Also

L triominoI tetromino