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.


T pentomino and W pentomino

Prime rectangles: ≥ 23.

Smallest rectangle tilings

Smallest known rectangle (8x10):

Smallest known square (10x10):

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 \ h123456789101112131415
1??
2????
3??????
4????????
5??????????
6????????????
7????????00????
8????????????????
9??????????????????
10????????????0022P44P66P
11??????????????????44??
12??????????????????44????
13??????????????????66??????
14??????????????????66????????
15????????????002200181844262640408282376376
16??????????????????2424????????668668
17????????????????????????????20962096
18??????????????????????????????
19??????????????????????????????
20????????????00885252??192192574574??????
21??????????????????????????????
22??????????????????????????????
23??????????????????????????????
24??????????????????????????????
25??????????????1818110110????????????

Smallest prime reptiles

Smallest prime reptiles (5Tx8, 5Wx8):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
T pentomino000000060P≥1P
W pentomino000000016P≥11000P

Smallest common multiples

Smallest common multiple (area 70):

Smallest common multiple without holes (area 80):

Common multiples' solutions count (excluding symmetric)

area5101520253035404550556065707580
solutions?????????????≥1?≥1

See Also

T pentomino and U pentominoT pentomino and Y pentomino