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.


V pentomino and V1 hexomino

Prime rectangles: ≥ 0.

Smallest rectangle tilings

Smallest rectangle and 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 \ h1-6789N>0
1-60
7000
800022
90000000
100000000?
110000000?
120002200?
130000000?
140000000?
150000000?
16000101000?
170000044?
18000626222?
190002200?
20022363688?
2100028283636?
220001041045454?
230001121126464?
24000706706570570?
25000768768212212?
2600022982298362362?
27000710710644644?
2800022022202732732?
290003294329427842784?
300009926992627982798?
3100023954239541122811228?
32000359663596694209420?
3300046744467441778017780?
3402273132731322596825968?
3500093404934045884058840?
36000231832231832122968122968?
37000460564460564193636193636?
38088839456839456439286439286?
3900014967701496770717144717144?
400441802718180271812606661260666?
410002964488296448820515282051528?
420005621642562164240176324017632?
43000106154201061542071540687154068?
4400021436624214366241340785213407852?
4500034922566349225662523870425238704?
4600054184218541842184568075845680758?
4700087300154873001548176360481763604?
4801010138526884138526884141437902141437902?
49000266968342266968342257719172257719172?
50000501720736501720736467095874467095874?
51000874685748874685748865301808865301808?
52024241.48875678×10¹⁰14887567821.55971905×10¹⁰1559719052?
530002.31191228×10¹⁰23119122822.84111941×10¹⁰2841119412?
540883.80904114×10¹⁰38090411405.09886293×10¹⁰5098862930?
550006.77056171×10¹⁰67705617149.10377409×10¹⁰9103774092?
56034341.21109326×10¹¹121109326741.65045462×10¹¹16504546216?
570002.21349011×10¹¹221349011582.99371957×10¹¹29937195704?
58032323.75700636×10¹¹375700636245.45355462×10¹¹54535546206?
590006.19432809×10¹¹619432809349.85229170×10¹¹98522917080?
600881.02940611×10¹²1029406110741.78200232×10¹²178200232168?
610001.73355055×10¹²1733550552443.21606553×10¹²321606553712?
62026263.07752530×10¹²3077525305345.80697136×10¹²580697136390?
630005.50270754×10¹²5502707546021.05124395×10¹³1051243955444?
640009.52079287×10¹²9520792875501.90312808×10¹³1903128087716?
650001.62529988×10¹³16252998825603.45019090×10¹³3450190906044?
6601121122.69406656×10¹³26940665674446.23745212×10¹³6237452128990?
670004.55082681×10¹³45508268137201.12761132×10¹⁴11276113218780?
68044447.89642354×10¹³78964235417522.03915972×10¹⁴20391597253376?
690001.38222962×10¹⁴138222962460003.68870080×10¹⁴36887008030072?
7001661662.42573918×10¹⁴242573918616346.67424509×10¹⁴66742450958540?
710004.16504495×10¹⁴416504495265541.20813957×10¹⁵120813957369820?
7201281287.02883522×10¹⁴702883522624362.18628851×10¹⁵218628851335012?
730001.19125780×10¹⁵1191257807589503.95444026×10¹⁵395444026190620?
7401681682.03297569×10¹⁵2032975698866087.15166388×10¹⁵715166388278032?
750003.53338481×10¹⁵3533384816317401.29356485×10¹⁶1293564858271608?
7602822826.16458805×10¹⁵6164588058261842.34047934×10¹⁶2340479344551020?
770001.06412421×10¹⁶10641242177419744.23519396×10¹⁶4235193969514256?
78096961.82090484×10¹⁶18209048442149467.66359693×10¹⁶7663596935223560?
790003.08987983×10¹⁶30898798384842021.38636144×10¹⁷13863614445357084?
8004164165.26832268×10¹⁶52683226861866942.50781360×10¹⁷25078136084179988?
810009.08256003×10¹⁶90825600307449304.53618363×10¹⁷45361836359450844?
8201441441.57253832×10¹⁷157253832694100888.20615678×10¹⁷82061567858423830?
830002.72373174×10¹⁷272373174888511821.48483027×10¹⁸148483027403996808?
8408928924.68083695×10¹⁷468083695379510462.68655017×10¹⁸268655017593571980?
850007.98901882×10¹⁷798901882837602004.86048789×10¹⁸486048789216257036?
8607047041.36445250×10¹⁸1364452501308182328.79260946×10¹⁸879260946969363484?
870002.33900462×10¹⁸2339004625284526761.59058411×10¹⁹1590584113900716724?
880112011204.03496283×10¹⁸4034962830820956442.87743242×10¹⁹2877432425218335898?
890006.97481140×10¹⁸6974811402740348185.20585007×10¹⁹5205850079611973512?
900142614261.20101337×10¹⁹12010133778377694749.41869922×10¹⁹9418699226652852506?
910002.06001771×10¹⁹20600177151363377601.70401080×10²⁰17040108077364005568?
920109010903.52302369×10¹⁹3523023691776709336≥1.84467440×10²⁰≥18446744073709551615?
930006.03421938×10¹⁹6034219386858082118≥1.84467440×10²⁰≥18446744073709551615?
940264826481.03787896×10²⁰10378789634078341474≥1.84467440×10²⁰≥18446744073709551615?
950001.78891500×10²⁰17889150048665540502≥1.84467440×10²⁰≥18446744073709551615?
96013241324≥1.84467440×10²⁰≥18446744073709551615≥1.84467440×10²⁰≥18446744073709551615?
97000≥1.84467440×10²⁰≥18446744073709551615≥1.84467440×10²⁰≥18446744073709551615?
98041644164≥1.84467440×10²⁰≥18446744073709551615≥1.84467440×10²⁰≥18446744073709551615?
99000≥1.84467440×10²⁰≥18446744073709551615≥1.84467440×10²⁰≥18446744073709551615?
100029762976≥1.84467440×10²⁰≥18446744073709551615≥1.84467440×10²⁰≥18446744073709551615?
101000?????
102066246624?????
103000?????
104080108010?????
105000?????
106082668266?????
107000?????
10801428014280?????
109000?????
110098969896?????
111000?????
11202386623866?????
113000?????
11401792017920?????
115000?????
11603604036040?????
117000?????
11803889038890?????
119000?????
12005173451734?????
121000?????
12208025680256?????
123000?????
12407111671116?????
125000?????
1260133122133122?????
127000?????
1280108706108706?????
129000?????
1300207208207208?????
131000?????
1320214218214218?????
133000?????
1340306478306478?????
135000?????
1360420720420720?????
137000?????
1380447240447240?????
139000?????
1400753812753812?????
141000?????
1420695854695854?????
143000?????
144011917441191744?????
145000?????
146012083381208338?????
147000?????
148018024281802428?????
149000?????
150022993362299336?????
151000?????
152027204362720436?????
153000?????
154041382484138248?????
155000?????
156042394484239448?????
157000?????
158068528646852864?????
159000?????
160071552427155242?????
161000?????
16201059868410598684?????
163000?????
16401277196212771962?????
165000?????
16601618775216187752?????
167000?????
16802294139422941394?????
169000?????
17002551191225511912?????
171000?????
17203880106438801064?????
173000?????
17404210940242109402?????
175000?????
17606185710861857108?????
177000?????
17807308099473080994?????
179000?????
18009601710096017100?????
181000?????
1820128186230128186230?????
183000?????
1840151240856151240856?????
185000?????
1860219160264219160264?????
187000?????
1880248058906248058906?????
189000?????
1900357397700357397700?????
191000?????
1920421051330421051330?????
193000?????
1940564787072564787072?????
195000?????
1960727192708727192708?????
197000?????
1980894302596894302596?????
199000?????
20001.23989929×10¹⁰1239899298?????
N>0x???

See Also

V pentomino and T3 hexominoV pentomino and W1 hexomino