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.


T1 hexomino and I 9-omino

Prime rectangles: ≥ 8.

Smallest rectangle tilings

Smallest known rectangle (13x45):

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 \ h1-12131415161718192021222324252627N>0
1-120
13000
1400000
150000000
16000000000
1700000000000
180000000000000
19000000000000000
2000000000000000000
210000000000000000000
220000000000000000000??
230000000000000000000????
240000000000000000000??????
250000000000000000000????????
2600000000000000000????????????
2700000000000000000??????????????
28000000000???????????????????????
29000000000???????????????????????
30000000000???????????????????????
31000000000???????????????????????
32000000000???????????????????????
33000000000???????????????????????
34000000000???????????????????????
35000000000????????????????????≥4≥4P?
36000000000????????????????????≥1≥1?
37000000000????????????????????≥1≥1?
38000000000????????????????????≥1≥1?
39000000000????????????????????≥1≥1?
40000000000????????????????????≥1≥1?
41000000000????????????????????≥1≥1?
42000000000????????????????????≥1≥1?
43000000000????????????????????≥1≥1?
440000000??????????????????????≥1≥1?
45044P88P1212P≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥16≥16C≥1≥1C?
460000000?????????????????????????
470000000?????????????????????????
480000000?????????????????????????
490000000?????????????????????????
500000000?????????????????????????
510000000?????????????????????????
520000000?????????????????????????
530000000?????????????????????????
54015201520P3056305646084608?????????????????????????
550000000?????????????????????????
560000000?????????????????????????
570000000?????????????????????????
580000000?????????????????????????
590000000?????????????????????????
600000000?????????????????????????
610000000?????????????????????????
620000000?????????????????????????
630184700184700P375728375728573156573156?????????????????????????
640000000?????????????????????????
650000000?????????????????????????
660000000?????????????????????????
670000000?????????????????????????
680000000?????????????????????????
690000000?????????????????????????
700000000?????????????????????????
710000000?????????????????????????
7201182196011821960P24480224244802243800445638004456?????????????????????????
730000000?????????????????????????
740000000?????????????????????????
750000000?????????????????????????
760000000?????????????????????????
770000000?????????????????????????
780000000?????????????????????????
790000000?????????????????????????
800000000?????????????????????????
810493142276493142276P1.04630700×10¹⁰10463070001.66374438×10¹⁰1663744380?????????????????????????
820000000?????????????????????????
830000000?????????????????????????
840000000?????????????????????????
850000000?????????????????????????
860000000?????????????????????????
870000000?????????????????????????
880000000?????????????????????????
890000000?????????????????????????
9001.51310990×10¹¹15131099048C3.31353050×10¹¹331353050565.43517753×10¹¹54351775368?????????????????????????
910000000?????????????????????????
920000000?????????????????????????
930000000?????????????????????????
940000000?????????????????????????
950000000?????????????????????????
960000000?????????????????????????
970000000?????????????????????????
980000000?????????????????????????
9903.69857597×10¹²369857597976C8.42663098×10¹²8426630986481.43678948×10¹³1436789485272?????????????????????????
1000000000?????????????????????????
1010000000?????????????????????????
1020000000?????????????????????????
1030000000?????????????????????????
1040000000?????????????????????????
1050000000?????????????????????????
1060000000?????????????????????????
1070000000?????????????????????????
10807.63056091×10¹³7630560919784C1.82367816×10¹⁴182367816383683.25730894×10¹⁴32573089442328?????????????????????????
1090000000?????????????????????????
1100000000?????????????????????????
1110000000?????????????????????????
1120000000?????????????????????????
1130000000?????????????????????????
1140000000?????????????????????????
1150000000?????????????????????????
1160000000?????????????????????????
11701.38915216×10¹⁵138915216680628C3.50965099×10¹⁵3509650993124646.61346618×10¹⁵661346618476476?????????????????????????
1180000000?????????????????????????
1190000000?????????????????????????
1200000000?????????????????????????
1210000000?????????????????????????
1220000000?????????????????????????
1230000000?????????????????????????
1240000000?????????????????????????
1250000000?????????????????????????
12602.31272334×10¹⁶2312723342780640C6.21471043×10¹⁶62147104355394081.24247964×10¹⁷12424796462211264?????????????????????????
1270000000?????????????????????????
1280000000?????????????????????????
1290000000?????????????????????????
1300000000?????????????????????????
1310000000?????????????????????????
1320000000?????????????????????????
1330000000?????????????????????????
1340000000?????????????????????????
13503.62905390×10¹⁷36290539063607132C1.04044025×10¹⁸1040440258039070802.21413948×10¹⁸221413948228153812?????????????????????????
1360000000?????????????????????????
1370000000?????????????????????????
1380000000?????????????????????????
1390000000?????????????????????????
1400000000?????????????????????????
1410000000?????????????????????????
1420000000?????????????????????????
1430000000?????????????????????????
14405.51913384×10¹⁸551913384942311712C1.68490536×10¹⁹16849053635442625123.81585887×10¹⁹3815858872276428096?????????????????????????
145000?????????????????????????????
146000?????????????????????????????
147000?????????????????????????????
148000?????????????????????????????
149000?????????????????????????????
150000?????????????????????????????
151000?????????????????????????????
152000?????????????????????????????
15308.36340901×10¹⁹8363409012746397792C?????????????????????????????
N>0x???????????????

Attributions

  1. 13x45 rectangle have been found by Florian Fischer

See Also

T1 hexomino and I1 octominoMonominoes, Dominoes and I triomino