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 triomino and O tetromino

Prime rectangles: ≥ 10.

Smallest rectangle tilings

Smallest rectangle (2x5):

Smallest square (4x4):

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 \ h123456789N>0
10
2000
30000
4000055P
5044P01616C00
600001818P6464C382382P
7066P09292C0018561856C55045504P
801212P0244244C11281128C90199019C7124871248C652035652035C
9088P0472472C004251242512C231296231296C49372244937224C≥1≥1C
1002424C014251425C81208120C199683199683C≥1≥1C≥1≥1C≥1≥1Call
1104242P037203720C69126912P922464922464C≥1≥1C≥1≥1C≥1≥1Call
1204040C086008600C5236052360C42563624256362C≥1≥1C≥1≥1C≥1≥1Call
1309292C02280822808C7513675136C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
140140140C05817658176C491960491960C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
150174174C0142988142988C643840643840C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
N>0xallxallallallallallall

See Also

L triomino and L tetrominoL triomino and T tetromino