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 pentomino and G hexomino

Prime rectangles: ≥ 1.

Smallest rectangle tilings

Smallest known rectangle (25x39):

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 \ h1-232425N>0
1-230
240??
250????
260?????
270?????
280?????
290?????
300?????
310?????
320?????
330?????
340?????
350?????
360?????
370?????
380?????
390??≥1≥1P?
N>0x??

Attributions

  1. Smallest rectangle taken from here http://www2.stetson.edu/~efriedma/mathmagic/0810.html

See Also

Z pentomino and F hexominoZ pentomino and I hexomino