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.


Monominoes, Dominoes and I triomino

Prime rectangles: 10.

Smallest rectangle tilings

Smallest rectangles (1x6, 2x3):

Smallest square (3x3):

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 \ h1234N>0
100
20000
30044P100100P
4002828P12141214C2710027100C
500166166P1218212182C552079552079Call
666P812812C113956113956C1070464410704644Call
71212P36303630C10202541020254C201350498201350498Call
83232P1553215532C89265068926506C3.72839620×10¹⁰3728396208Call
97272P6452064520C7695280476952804C6.83571751×10¹¹68357175135Call
10152152P262750262750C656821346656821346C1.24524100×10¹³1245241000103Call
11311311P10555291055529C5.56791685×10¹⁰5567916857C2.25910053×10¹⁴22591005322182Call
12625625C41980674198067C4.69703041×10¹¹46970304161C4.08731379×10¹⁵408731379044798Call
N>0allallallall

See Also

T1 hexomino and I 9-ominoI triomino, T tetromino and X pentomino