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.


U pentomino and L1 octomino

Prime rectangles: ≥ 16.

Smallest rectangle tilings

Smallest rectangle (10x11):

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 \ h1-56789101112131415N>0
1-50
6000
70000
8000000
900000000
100000000000
1100000000≥1≥1P00
1200000000????00
1300000000??????00
1400000000????????00
1500000000??????????00
1600000000?????????????
1700000000?????????????
1800000000?????????????
1900000000?????????????
200000003232P?????????????
2100000000?????????????
2203232P00000?????????????
2300000000?????????????
2400000000?????????????
2500000000?????????????
2600000000?????????????
2700000000?????????????
2800000000?????????????
290000009331293312P?????????????
300512512P0001010P?????????????
3100000000?????????????
3200000000?????????????
3300000011521152?????????????
3400000000?????????????
3500000046084608?????????????
360000006425664256?????????????
3700000000?????????????
38061446144P0001900819008?????????????
3900000000?????????????
4000000010241024?????????????
4100000000?????????????
4200000067184646718464?????????????
43000000147456147456?????????????
44010241024C000512512?????????????
45000000306846720306846720?????????????
4606553665536P000196020196020?????????????
4700000000?????????????
48000000829440829440?????????????
4900000097600009760000?????????????
500000002726427264?????????????
510000001667520016675200?????????????
5202457624576C000152786432152786432?????????????
5300000074142727414272?????????????
540655360655360P0005016678450166784?????????????
55000000484040704484040704?????????????
560000002435993624359936?????????????
570000007504075040?????????????
580000003.53191610×10¹¹35319161088?????????????
59000000423942336423942336?????????????
600393216393216C00071967727196772?????????????
610000008.05155084×10¹²805155084288?????????????
62062914566291456P0001.28630739×10¹⁰1286307392?????????????
630000001981900819819008?????????????
640000003.89367500×10¹⁰3893675008?????????????
650000003.54165949×10¹¹35416594944?????????????
6603276832768C0002.23240064×10¹⁰2232400640?????????????
670000004.63714232×10¹¹46371423232?????????????
68052428805242880C0003.72136431×10¹²372136431936?????????????
690000003.82787799×10¹¹38278779904?????????????
7005872025658720256P0001.22678505×10¹²122678505728?????????????
710000003.49660997×10¹³3496609972224?????????????
720000001.25088343×10¹²125088343296?????????????
730000002.68515609×10¹⁰2685156096?????????????
74010485761048576C0001.24952549×10¹⁵124952549335040?????????????
750000001.14528367×10¹³1145283679744?????????????
7606291456062914560C0002.85671061×10¹¹28567106144?????????????
770000001.90039766×10¹⁶1900397666052096?????????????
780536870912536870912P0005.88200129×10¹³5882001299904?????????????
790000003.85905340×10¹²385905340416?????????????
800000001.36864765×10¹⁴13686476520832?????????????
810000001.08401241×10¹⁵108401241784320?????????????
8202097152020971520C0001.19559463×10¹⁴11955946337280?????????????
830000001.18005834×10¹⁵118005834477824?????????????
840704643072704643072C0001.03920088×10¹⁶1039200888114176?????????????
850000001.24832620×10¹⁵124832620093440?????????????
8604.83183820×10¹⁰4831838208P0002.78788886×10¹⁵278788886075392?????????????
870000001.56980082×10¹⁷15698008237569664?????????????
88010485761048576C04.29496729×10¹⁰4294967296P4.26577107×10¹⁵426577107068544?????????????
890000??1.32357393×10¹⁴13235739352608?????????????
900335544320335544320C0??3.70327092×10¹⁸370327092543742952?????????????
910000??3.08118885×10¹⁶3081188854825984?????????????
9207.51619276×10¹⁰7516192768C0??1.21000479×10¹⁵121000479433040?????????????
930000??4.22696430×10¹⁹4226964303660822016?????????????
9404.29496729×10¹¹42949672960P0??2.16439857×10¹⁷21643985733350912?????????????
950000??2.31409609×10¹⁶2314096095913984?????????????
9604194304041943040C0?????????????????
970000??3.11716495×10¹⁸311716495328392192?????????????
9804.69762048×10¹⁰4697620480C0??4.36230334×10¹⁷43623033444597760?????????????
990000??2.83282730×10¹⁸283282730268077056?????????????
10007.73094113×10¹¹77309411328C0??3.24133506×10¹⁹3241335060744899840?????????????
1010000?????????????????
10203.77957122×10¹²377957122048P0?????????????????
1030000?????????????????
10401.00663296×10¹⁰1006632960C0?????????????????
1050000?????????????????
10606.01295421×10¹¹60129542144C0?????????????????
1070000?????????????????
10807.73094113×10¹²773094113280C0?????????????????
1090000?????????????????
11003.29856843×10¹³3298568437760C0?????????????????
1110000?????????????????
11201.87904819×10¹¹18790481920C0?????????????????
1130000?????????????????
11407.21554505×10¹²721554505728C0?????????????????
1150000?????????????????
11607.55914244×10¹³7559142440960C0?????????????????
1170000?????????????????
11802.85889129×10¹⁴28588912934912C0?????????????????
1190000?????????????????
12003.00647710×10¹²300647710720C0?????????????????
1210000?????????????????
12208.24633720×10¹³8246337208320C0?????????????????
1230000?????????????????
12407.25677674×10¹⁴72567767433216C0?????????????????
1250000?????????????????
12602.46335701×10¹⁵246335701778432C0?????????????????
1270000?????????????????
12804.32932703×10¹³4329327034368C0?????????????????
1290000?????????????????
13009.07097092×10¹⁴90709709291520C0?????????????????
1310000?????????????????
13206.86096329×10¹⁵686096329474048C0?????????????????
1330000?????????????????
13402.11202439×10¹⁶2112024398004224C0?????????????????
1350000?????????????????
13605.77243604×10¹⁴57724360458240C0?????????????????
1370000?????????????????
13809.67570232×10¹⁵967570232442880C0?????????????????
1390000?????????????????
14006.40361584×10¹⁶6403615849709568C0?????????????????
1410000?????????????????
14201.80317158×10¹⁷18031715817619456C0?????????????????
1430000?????????????????
14407.25677674×10¹⁵725677674332160C0?????????????????
1450000?????????????????
14601.00627304×10¹⁷10062730417405952C0?????????????????
1470000?????????????????
14805.91116692×10¹⁷59111669254586368C0?????????????????
1490000?????????????????
15001.53399464×10¹⁸153399464260796416C0?????????????????
1510000?????????????????
15208.70813209×10¹⁶8708132091985920C0?????????????????
1530000?????????????????
15401.02456925×10¹⁸102456925882417152C0?????????????????
1550000?????????????????
15605.40478134×10¹⁸540478134772826112C0?????????????????
1570000?????????????????
15801.30110048×10¹⁹1301100487658962944C0?????????????????
1590000?????????????????
16001.00627304×10¹⁸100627304174059520C0?????????????????
1610000?????????????????
16201.02457111×10¹⁹1024571114250043392C0?????????????????
1630000?????????????????
16404.90083998×10¹⁹4900839984346431488C0?????????????????
1650000?????????????????
16601.10084863×10²⁰11008486339153756160C0?????????????????
1670000?????????????????
16801.12702580×10¹⁹1127025806749466624C0?????????????????
1690000?????????????????
17001.00881423×10²⁰10088142330147110912C0?????????????????
N>0x?x????????

See Also

U pentomino and L1 heptominoV pentomino and W pentomino