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.


Z tetromino and U pentomino

Prime rectangles: ≥ 98.

Smallest rectangle tilings

Smallest rectangle (3x6):

Smallest square (6x6):

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 \ h123456789101112131415
100
20000
3000000
400000000
50000000000
6000022000088
700000000000000
80000000000000000
900000000002424000000
10000000002200121200885656
1100000000000000224040808010001000
120000440000808000565673673628322832760876083066830668
13000000000000003232332332338833881318813188129782129782≥21000≥21000
1400000000000000145614561162116212780127806058860588≥80000≥80000≥1000≥1000≥200≥200
1500000000002602600075275211961196≥1≥1≥53000≥53000??≥1000≥1000≥1≥1≥1≥1
1600000000006060484832632673867386??≥1≥1??≥1≥1????
17000000000018180067626762??????????????
18000088002285685619619642004200??????????????
190000000000290290001678816788??????????????
20000000008872723683685863258632??????????????
21000000000029342934007137671376??????????????
22000000002216721672208208≥1≥1??????????????
230000000000470470196196????????????????
2400001616000098409840392392????????????????
25000000000072707270224224????????????????
260000000022??71307130????????????????
270000000000??652652????????????????
28000000001616??2002420024????????????????
290000000000??20722072????????????????
3000003232003636??2686426864????????????????
310000000000??1356413564????????????????
32000000001616??5830058300????????????????
330000000000??4086840868????????????????
340000000044??286104286104????????????????
350000000000??≥1≥1????????????????
3600006464002424????????????????????
370000000000????????????????????
3800000000102102????????????????????
390000000000????????????????????
4000000000176176????????????????????
410000000000????????????????????
42000012812800104104????????????????????
430000000000????????????????????
44000000005656????????????????????
450000000000????????????????????
4600000000202202????????????????????
470000000000????????????????????
48000025625600608608????????????????????
490000000000????????????????????
5000000000910910????????????????????

See Also

Z tetromino and T pentominoZ tetromino and V pentomino