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.


U pentomino and V pentomino

Prime rectangles: ≥ 92.

Smallest rectangle tilings

Smallest known rectangle and smallest square (20x20):

Rectangle tilings' solutions count (including symmetric)

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

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

Red number (C) - 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 \ h1234567891011121314151617181920
100
2??00
3????00
4??????00
5????????00
6??????????00
7????????????00
8??????????????00
9????????????????00
10??????????????????00
11????????????????????00
12??????????????????????00
13????????????????????????00
14??????????????????????????00
15????????????????????????????00
16??????????????????????????????00
17????????????????????????????????00
18??????????????????????????????????00
19????????????????????????????????????00
20??????????????????????????????????????1212P
21??????????????????????????????????????44P
22??????????????????????????????????????≥1≥1
23??????????????????????????????????????≥1≥1
24????????????????????????????????????????
25??????????????????????????????????????≥1≥1
26??????????????????????????????????????≥1≥1
27??????????????????????????????????????≥1≥1
28????????????????????????????≥2≥2P????????≥1≥1
29??????????????????????????????????????≥1≥1
30??????????????????????????????≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1
31??????????????????????????????????????≥1≥1
32????????????????????????????≥1≥1????????≥1≥1
33??????????????????????????????????????≥1≥1
34??????????????????????????????????????≥1≥1
35??????????????????????????????≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1
36????????????????????????????≥1≥1????????≥1≥1
37????????????????????????????≥1≥1????????≥1≥1
38????????????????????????????≥1≥1????????≥1≥1
39??????????????????????????????????????≥1≥1
40??????????????????????????≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥144≥144
41????????????????????????????≥1≥1????????≥48≥48
42????????????????????????????≥1≥1????????≥16≥16
43????????????????????????????≥1≥1??????????
44????????????????????????????≥1≥1??????????
45??????????????????????????≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1??
46????????????????????????????≥1≥1??????????
47????????????????????????????≥1≥1??????????
48????????????????????????????≥1≥1??????????
49????????????????????????????≥1≥1??????????
50??????????????????????????≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1??
51????????????????????????????≥1≥1??????????
52????????????????????????????≥1≥1??????????
53????????????????????????????≥1≥1??????????
54????????????????????????????≥1≥1??????????
55??????????????????????????≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1??
56????????????????????????????≥1≥1??????????
57????????????????????????????≥1≥1??????????
58????????????????????????????≥1≥1??????????
59????????????????????????????≥1≥1??????????
60??????????????????????????≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1??
61????????????????????????????≥1≥1??????????
62????????????????????????????≥1≥1??????????
63????????????????????????????≥1≥1??????????
64????????????????????????????≥1≥1??????????
65??????????????????????????≥1≥1≥1≥1??????????
66????????????????????????????≥1≥1??????????
67????????????????????????????≥1≥1??????????
68????????????????????????????≥1≥1??????????
69????????????????????????????????????????
70??????????????????????????≥1≥1????????????
71????????????????????????????????????????
72????????????????????????????????????????
73????????????????????????????????????????
74????????????????????????????????????????
75??????????????????????????≥1≥1????????????

Attributions

  1. Prime rectangle list taken from http://www.recmath.com/PolyPages/PolyPages/index.htm?5pairs.htm

See Also

T pentomino and Y2 hexominoU pentomino and X pentomino