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.


O tetromino and T tetromino

Prime rectangles: ≥ 8.

Smallest rectangle tilings

Smallest rectangle (4x6):

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 \ h1-345678910N>0
1-30
4000
50000
6044P088P
7000000
8066P55P3737C2121P292292C
9000000327327C0
1002424P09494C016711671C01231812318C
1100000016801680C00?
1204040C22P349349C5454P1176011760C64726472C162595162595C?
130000001653216532C00?
140120120C010461046C07061670616C016186971618697C?
150000009771897718C00?
160218218C4141C35703570C22892289C471844471844C574782574782C1929638219296382C?
17000000789151789151C00?
180576576C01137011370C029538582953858C0215121681215121681C?
1900000050240395024039C00?
20011121112C4040C3750437504C2396623966C1936666219366662C2607687226076872C2.51503447×10¹⁰2515034470C?
210000003694253536942535C00?
22027322732C0121546121546C0124602001124602001C02.91879613×10¹¹29187961340C?
23000000243590561243590561C00?
24054945494C381381C396541396541C497127497127C815480016815480016C1.81906529×10¹⁰1819065294C3.42299952×10¹²342299952012C?
250000001.71225795×10¹⁰1712257950C00?
2601290412904C012907381290738C05.33461446×10¹⁰5334614460C04.03003273×10¹³4030032735218C?
270000001.14632901×10¹¹11463290124C00?
2802665626656C624624C42006834200683C70324647032464C3.50890306×10¹¹35089030692C1.08127359×10¹²108127359808C4.75367099×10¹⁴47536709938788C?
290000007.88650979×10¹¹78865097900C00?
3006084860848C01368334613683346C02.31900641×10¹²231900641306C05.62867250×10¹⁵562867250968196C?
310000005.31192220×10¹²531192220602C00?
320127914127914C40094009C4452583044525830C123180871123180871C1.53526938×10¹³1535269388624C7.23365063×10¹³7233650637340C6.66717070×10¹⁶6667170709145004C?
330000003.61784681×10¹³3617846819836C00?
340286720286720C0145023030145023030C01.02144295×10¹⁴10214429508673C07.91505337×10¹⁷79150533737093742C?
350000002.44212603×10¹⁴24421260341693C00?
360609616609616C90429042C472012210472012210C1.90562336×10¹⁰1905623362C6.80161565×10¹⁴68016156574407C4.65227526×10¹⁵465227526803712C9.39837409×10¹⁸939837409670719840C?
370000001.65567320×10¹⁵165567320006632C00?
38013506121350612C01.53707105×10¹⁰1537071056C04.54630790×10¹⁵454630790603571C01.11724458×10²⁰11172445836666643767C?
390000001.11844318×10¹⁶1118443184288301C00?
40028927422892742C4645146451C5.00360517×10¹⁰5003605175C3.16772055×10¹¹31677205581C3.04110611×10¹⁶3041106112768555C3.08662273×10¹⁷30866227378931820C≥1.84467440×10²⁰≥18446744073709551615C?
410000007.56775906×10¹⁶7567759066384073C00?
42063612086361208C01.62918725×10¹¹16291872516C02.03959304×10¹⁷20395930417269225C0≥1.84467440×10²⁰≥18446744073709551615C?
430000005.11366168×10¹⁷51136616822020719C00?
4401368882413688824C127342127342C5.30392158×10¹¹53039215871C5.04968942×10¹²504968942662C1.36893278×10¹⁸136893278700340473C2.02783618×10¹⁹2027836181315618472C≥1.84467440×10²⁰≥18446744073709551615C?
450000003.45756573×10¹⁸345756573587338680C00?
4602995844029958440C01.72687322×10¹²172687322490C09.20407059×10¹⁸920407059020331539C0≥1.84467440×10²⁰≥18446744073709551615C?
470000002.33680534×10¹⁹2336805342569671010C00?
4806466370664663706C573569573569C5.62214722×10¹²562214722532C8.25043460×10¹³8250434600625C6.19273193×10¹⁹6192731933598845579C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
490000001.57977744×10²⁰15797774440476778898C00?
500141086400141086400C01.83044210×10¹³1830442104422C0≥1.84467440×10²⁰≥18446744073709551615C0≥1.84467440×10²⁰≥18446744073709551615C?
N>0x?4k2k4kall4k2k

Smallest common multiples

Smallest known common multiple (area 16):

Common multiples' solutions count (excluding symmetric)

area481216
solutions0??≥1

See Also

L tetromino and Z pentominoO tetromino and I pentomino