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.


L tetromino and N pentomino

Prime rectangles: 23.

Smallest rectangle tilings

Smallest rectangles (2x9, 3x6):

Smallest square (5x5):

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 \ h12345678910N>0
10
2000
300000
40000000
500000003232P
600022P007676P1616C
700044P22P116116P≥1000≥1000C≥1000≥1000C
80000044P180180P≥1000≥1000C≥1000≥1000C≥1000≥1000C
9022P44P1414C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C
1000088P4040P≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C
110001616P190190P≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
120001212C386386P≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
13088P3232C15681568C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
14022P8282C37463746C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
150007272C1214212142C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
160009696C2804228042C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
1702424P296296C8312483124C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
1801212C328328C190068190068C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
19022P496496C529070529070C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
2000010701070C11988101198810C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
2106464P14961496C31988963198896C?????????????
2204848C22842284C72373207237320C?????????????
2301616C39563956C1875079418750794C?????????????
24022P60646064C4245822042458220C?????????????
250160160P1006410064C107819860107819860C?????????????
260160160C1533015330C244743300244743300C?????????????
2708080C2511225112C612179586612179586C?????????????
2802020C4288442884C1.39449804×10¹⁰1394498042C?????????????
290386386P6267262672C3.44705964×10¹⁰3447059648C?????????????
300480480C101880101880C7.87995357×10¹⁰7879953576C?????????????
310320320C176272176272C1.92927185×10¹¹19292718586C?????????????
320120120C259934259934C4.42454733×10¹¹44245473390C?????????????
330920920C418088418088C1.07475578×10¹²107475578558C?????????????
34013461346C711764711764C2.47177170×10¹²247177170080C?????????????
35011201120C10862521086252C5.96470546×10¹²596470546742C?????????????
360560560C17346481734648C1.37515459×10¹³1375154598260C?????????????
37022162216C28680002868000C3.30027347×10¹³3300273476050C?????????????
38036123612C44938984493898C7.62491493×10¹³7624914932888C?????????????
39035863586C72116887211688C1.82163009×10¹⁴18216300992062C?????????????
40022402240C1161795611617956C4.21646793×10¹⁴42164679390372C?????????????
N>0xallallallallallallallallall

See Also

L tetromino and L pentominoL tetromino and P pentomino