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 hexomino

Area: 6.

Perimeter: 10.

Size: 2x3.

Is rectangular: yes.

Is convex: yes.

Holes: 0.

Order: 1.

Square order: 6.

Odd order: 1.

Prime rectangles: 1.

Smallest rectangle tilings

Smallest rectangle and smallest odd rectangle (2x3):

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
N>0
1
0
2
0
0
3
0
1
0
4
0
0
1
0
5
0
0
0
0
0
6
0
1
1
1
2
2
7
0
0
0
0
0
3
0
8
0
0
1
0
0
4
0
0
9
0
1
0
1
0
5
0
11
0
10
0
0
1
0
0
7
0
0
19
0
11
0
0
0
0
0
9
0
0
0
0
0
12
0
1
1
1
4
12
9
33
45
76
171
316
13
0
0
0
0
0
16
0
0
0
0
0
504
0
14
0
0
1
0
0
21
0
0
105
0
0
1110
0
0
15
0
1
0
1
0
28
0
96
0
253
0
1816
0
≥1
0
16
0
0
1
0
0
37
0
0
219
0
0
3390
0
0
≥1
0
17
0
0
0
0
0
49
0
0
0
0
0
6549
0
0
0
0
0
18
0
1
1
1
8
65
27
281
475
913
3229
11728
≥1
≥1
≥1
≥1
≥1
≥1
19
0
0
0
0
0
86
0
0
0
0
0
21465
0
0
0
0
0
≥1
0
20
0
0
1
0
0
114
0
0
1061
0
0
41083
0
0
≥1
0
0
≥1
0
0
21
0
1
0
1
0
151
0
821
0
3175
0
73049
0
≥1
0
≥1
0
≥1
0
≥1
2k
22
0
0
1
0
0
200
0
0
2313
0
0
136710
0
0
≥1
0
0
≥1
0
0
3k
23
0
0
0
0
0
265
0
0
0
0
0
253812
0
0
0
0
0
≥1
0
0
6k
24
0
1
1
1
16
351
81
2400
5027
11227
60619
463017
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
N>0
x
3k
2k
3k
6k
all
6k
3k
2k
3k
6k
all
6k
3k
2k
3k
6k
all
6k
3k

Smallest prime reptiles

Smallest prime reptile (6Ox2):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
O hexomino
1
1
5
33
253
11728

See Also

L hexominoP hexomino