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.


O tetromino and L pentomino

Prime rectangles: ≥ 1.

Smallest rectangle tilings

Smallest rectangle (2x7):

Smallest square (6x6):

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 \ h12345678
100
20000
3000000
400000000
50000000000
600002200442222
70044P00161600787800
800000055181820220243843813901390
900660036360037237229629659065906
1000000018186464952952319231922176221762
110088006464161624102410506850689186691866
1200121244185185300300658265823111631116353954353954
13001010001721721921921721417214633206332013039701303970
140024240068268210101010??????
150012120064864810401040??????
16004040001868186832903290??????
17004646002972297243124312??????
1800606088495149511395013950??????

See Also

O tetromino and I pentominoO tetromino and N pentomino