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.


T pentomino and U pentomino

Prime rectangles: ≥ 18.

Smallest rectangle tilings

Smallest rectangle (13x25):

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 \ h1-111213141516171819202122N>0
1-110
1200
13000
140000
15000000000
160000000
1700000000
18000000000
190000000000
2000000000000≥1≥1≥1≥100≥1≥1
210000000000≥1≥10
220000000000≥1≥100
230000000000≥1≥1005k
240000≥1≥10000≥1≥1005k
2500022P000000≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1all
260000000000≥1≥100?
270000000000≥1≥100?
280000≥1≥10000≥1≥100?
290000≥1≥10000≥1≥100?
30022P3434P0000≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1?
310000≥1≥10000≥1≥100?
320000≥1≥10000≥1≥100?
330000≥1≥10000≥1≥100?
340000≥1≥10000??00?
350006868P88P≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1??≥1≥1???
360000≥1≥10000??00?
370000≥1≥10000??00?
380000≥1≥10000??00?
390000≥1≥10000??00?
4001010P656656P4040P≥1≥1≥1≥1????≥1≥1???????
410000≥1≥10000??00?
420000≥1≥10000??00?
430000≥1≥10000??00?
440000≥1≥10000??00?
4501414P33543354P568568P≥1≥1≥1≥1????≥1≥1???????
460000≥1≥10000??00?
470000≥1≥10000??00?
480000≥1≥10000??00?
490000≥1≥10000??00?
500104104P2613426134C41304130P≥1≥1≥1≥1?????????????
510000≥1≥10000??00?
520000??0000??00?
530000??0000??00?
540000??0000??00?
550344344P170644170644C4181241812P??≥1≥1?????????????
560000??0000??00?
570000??0000??00?
580000??0000??00?
590000??0000??00?
60016321632C12152381215238C352476352476P?????????????????
610000??0000??00?
620000??0000??00?
630000??0000??00?
640000??0000??00?
65060546054P82343128234312C33966503396650P?????????????????
660000??0000??00?
670000??0000??00?
680000??0000??00?
690000??0000??00?
7002786427864C5733923257339232C3116746431167464C?????????????????
710000??0000??00?
720000??0000??00?
730000??0000??00?
740000??0000??00?
750112518112518C392710870392710870C297022614297022614C?????????????????
760000??0000??00?
770000??0000??00?
780000??0000??00?
790000??0000??00?
800533096533096C2.71482101×10¹⁰2714821012C2.79638830×10¹⁰2796388304C?????????????????
810000??0000??00?
820000??0000??00?
830000??0000??00?
840000??0000??00?
85022466602246660C1.86615649×10¹¹18661564982C2.65830770×10¹¹26583077094C?????????????????
860000??0000??00?
870000??0000??00?
880000??0000??00?
890000??0000??00?
9001067340010673400C1.28691690×10¹²128691690324C2.52011047×10¹²252011047238C?????????????????
910000??0000??00?
920000??0000??00?
930000??0000??00?
940000??0000??00?
9504669916646699166C8.85776708×10¹²885776708574C2.39425986×10¹³2394259864478C?????????????????
960000??0000??00?
970000??0000??00?
980000??0000??00?
990000??0000??00?
1000219143978219143978C6.10363213×10¹³6103632130304C2.27377914×10¹⁴22737791418952C?????????????????
N>0x5k5k5kall5k5k5k5kall5k5k

See Also

R pentomino and Y2 hexominoT pentomino and W pentomino