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.


I triomino and T1 hexomino

Prime rectangles: ≥ 4.

Smallest rectangle tilings

Smallest rectangle (3x4):

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 \ h1-23456N>0
1-20
3000
4022P0
5044P00
6066P4040C100100C402402C
701212P00≥1≥1C3k
802626C00≥1≥1C3k
904848C440440C16481648C≥1≥1Call
1008484C00≥1≥1C3k
110152152C00≥1≥1C3k
120278278C44164416C≥1≥1C≥1≥1Call
130496496C00≥1≥1C3k
140872872C00≥1≥1C3k
15015361536C4283042830C≥1≥1C≥1≥1Call
16027082708C00≥1≥1C3k
17047484748C00≥1≥1C3k
18082868286C408452408452C≥1≥1C≥1≥1Call
N>0xall3k3kall

Smallest common multiples

Smallest common multiple (area 6):

Common multiples' solutions count (excluding symmetric)

area6
solutions1P

See Also

I triomino and Z pentominoL triomino and I tetromino