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.


N pentomino and O1 12-omino

Prime rectangles: ≥ 0.

Smallest rectangle tilings

Smallest rectangle (14x16):

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 \ h1-10111213141516N>0
1-100
11000
120000
13000000
1400000000
150000000000
16000000440000
1700000000001212?
18000000000000?
19000000???????
20000000???????
21000000???????
22000000???????
23000000???????
24000000???????
25000000???????
26000088???????
27000000???????
28000022???????
29000000???????
30000000???????
31000000???????
32000022???????
33000000???????
34000022???????
35000044???????
3600001616???????
3700006060???????
380000138138???????
3900008888???????
4000002828???????
410000164164???????
420000234234???????
430000208208???????
440000370370???????
450880584584???????
460000352352???????
470000556556???????
48000018981898???????
49000035363536???????
50000052005200???????
51000079967996???????
52088088208820???????
5300001183611836???????
5400002471824718???????
5500002638826388???????
5600004172241722???????
570606006722467224???????
580000103314103314???????
590000148536148536???????
6002002000224316224316???????
61048480354520354520???????
62042420495464495464???????
63064640775764775764???????
640186186011422021142202???????
650152152015642841564284???????
6602424026150322615032???????
670144144038676403867640???????
680104104056678425667842???????
690456456085830328583032???????
700646401346658813466588???????
71027227201890486818904868???????
7201448144802840796028407960???????
73058458404453726044537260???????
74055855806504316465043164???????
75080080009617116896171168???????
760175417540154371836154371836???????
770223222320223895304223895304???????
780114811480325867074325867074???????
790224022400514171008514171008???????
800248424840765869662765869662???????
8107560756001.11046460×10¹⁰1110464600???????
8202556255601.72531801×10¹⁰1725318016???????
8305256525602.58137686×10¹⁰2581376868???????
840120001200003.76185533×10¹⁰3761855334???????
850103441034405.80840966×10¹⁰5808409660???????
8606230623008.85421590×10¹⁰8854215902???????
870140081400801.29058652×10¹¹12905865272???????
880175221752201.97988947×10¹¹19798894768???????
890301443014403.02919848×10¹¹30291984880???????
900172801728004.41088818×10¹¹44108881836???????
910313963139606.73306608×10¹¹67330660880???????
920366463664601.03146871×10¹²103146871578???????
930751287512801.50866966×10¹²150866966500???????
940431244312402.27066958×10¹²227066958760???????
950586565865603.49926197×10¹²349926197124???????
96011563011563005.20497915×10¹²520497915936???????
97012236012236007.71274730×10¹²771274730344???????
98011273011273001.19607755×10¹³1196077554400???????
99015416015416001.79575272×10¹³1795752727528???????
100023626023626002.64192768×10¹³2641927683668???????
N>0xallxall???

See Also

L pentomino and Z2 hexominoN pentomino and O1 15-omino