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 O hexomino

Prime rectangles: ≥ 11.

Smallest rectangle tilings

Smallest rectangle (5x7):

Smallest square (8x8):

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 \ h1-34567891011121314N>0
1-30
4000
500000
60000000
700022P0000
800000000022
90000000000000
10000000066C00004040
1100000001212P1010002200
1200000000000000012125656
1300088P0000001818227227448448170170768768
1400044C0022P454500131131704704638638≥1000≥1000≥1000≥1000
1500000001616C8868689797880880≥1000≥1000≥1000≥1000≥1000≥1000?
1600000005656C161622≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000?
1700000005454P176176178178≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000?
18000000044P52528484≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000?
190002424P001616C110110632632≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000?
200002424C005656C685685468468≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000?
210??88C00216216C276276?????????????
220??0000346346C601601?????????????
230??0000232232C26062606?????????????
240??0000120120C13341334?????????????
250??6464P00264264C29182918?????????????
260??9696C00840840C97469746?????????????
270??6464C0017481748C60446044?????????????
280??1616C0018261826C1320613206?????????????
290??000013941394C3618036180?????????????
300??000015401540C2648926489?????????????
310??160160P0035563556C???????????????
320??320320C0081548154C???????????????
330??320320C001123611236C???????????????
340??160160C001060610606C???????????????
350??3232C001105611056C???????????????
360??00001739617396C???????????????
370??384384P003731837318C???????????????
380??960960C006165661656C???????????????
390??12801280C007008270082C???????????????
400??960960C007419874198C???????????????
410??384384C00?????????????????
420??6464C00?????????????????
430??896896P00?????????????????
440??26882688C00?????????????????
450??44804480C00?????????????????
460??44804480C00?????????????????
470??26882688C00?????????????????
480??896896C00?????????????????
490??21762176C00?????????????????
500??71687168C00?????????????????
N>0x?all?????????

See Also

T pentomino and N3 hexominoT pentomino and P hexomino