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 C hexomino

Prime rectangles: ≥ 154.

Smallest rectangle tilings

Smallest rectangle (6x9):

Smallest square (13x13):

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 \ h123456789101112131415161718
100
20000
3000000
400000000
50000000000
6000000000000
700000000000000
80000000000000000
9000000000022000000
1000000000000000000000
110000000000000000000000
12000000000000000044220000
13000000000000000000444466304304
14000000000000008822441010116116≥30≥30≥1≥1
15000000000000000012128844100100≥1≥1≥1≥1≥1≥1
160000002200000088664418188282≥1≥1≥1≥1≥1≥1≥1≥1
1700000000000000004426267272≥165≥165≥1≥1??≥1≥1????
18000000000044001212181856564646≥1≥1≥1≥1??≥1≥1??????
190000000000000042421616102102208208≥1≥1≥1≥1??????????
2000000000000000141418185858546546≥1≥1≥1≥1??????????
210000006600000060606868188188≥1≥1≥1≥1????????????
22000000000000004444110110328328≥1≥1≥1≥1????????????
23000000000000001761767272556556≥1≥1≥1≥1????????????
2400000000000000120120204204892892≥1≥1≥1≥1????????????
2500000000000000138138356356≥200≥200≥1≥1≥1≥1????????????
260000001212000000382382420420??≥1≥1≥1≥1????????????
2700000000008800392392820820??????????????????
28000000000000001224122411601160??????????????????
290000000000000070070016961696??????????????????
300000000000000013081308????????????????????
31000000202000000022962296????????????????????
3200000044C00000032783278????????????????????
330000000000000069346934????????????????????
340000000000000063186318????????????????????
3500000000000000??????????????????????
36000000303000161600??????????????????????
370000002424000000??????????????????????
3800000000000000??????????????????????
3900000000000000??????????????????????
4000000000000000??????????????????????
410000004242000000??????????????????????
420000008484000000??????????????????????
4300000000000000??????????????????????
4400000000000000??????????????????????
450000000000323200??????????????????????
460000005656000000??????????????????????
47000000224224000000??????????????????????
4800000088000000??????????????????????
4900000000000000??????????????????????
5000000000000000??????????????????????
510000007272002200??????????????????????
52000000504504000000??????????????????????
530000007272000000??????????????????????
540000000000646400??????????????????????
5500000000000000??????????????????????
56000000909000161600??????????????????????
5700000010081008000000??????????????????????
58000000360360000000??????????????????????
5900000000000000??????????????????????
600000000000101000??????????????????????
6100000011011000727200??????????????????????
6200000018481848000000??????????????????????
63000000132013200012812800??????????????????????
640000001616000000??????????????????????
650000000000989800??????????????????????
660000001321320024024000??????????????????????
6700000031683168000000??????????????????????
6800000039603960008800??????????????????????
6900000019219200323200??????????????????????
70000000000056656600??????????????????????
710000001561560066066000??????????????????????
72000000514851480026426400??????????????????????
73000000102961029600888800??????????????????????
74000000124812480034634600??????????????????????
7500000000002496249600??????????????????????
76000000182182001584158400??????????????????????
77000000800880080014814800??????????????????????
7800000024024240240063263200??????????????????????
7900000058245824002230223000??????????????????????
800000003232009218921800??????????????????????

See Also

N pentomino and B hexominoN pentomino and D hexomino