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.


Z tetromino and Y pentomino

Prime rectangles: ≥ 42.

Smallest rectangle tilings

Smallest known rectangle (4x7):

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 \ h123456789
100
20000
3000000
400000000
50000000000
600000000001414
7000000220016163232
8000000008814144040164164
900000022161612412425225276476436723672
1000000000545417217259659636263626??
11000000228871271218961896????
120000002223023016601660??????
130000002217217241484148??????
140000001212468468????????
150000002218801880????????
16000000323236043604????????
17000000161639523952????????
1800000076761811218112????????
1900000078782178421784????????
200000001461464202042020????????

See Also

Z tetromino and V pentominoZ tetromino and A hexomino