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 and O tetromino

Prime rectangles: 4.

Smallest rectangle tilings

Smallest rectangle (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
10
2000
3022P44P
4033P1010C3333C
5077P2020C9292Call
601111C4242C267267Call
702020C8484C746746Call
803232C170170C21132113Call
905454C340340C59325932Call
1008787C682682C1671516715Call
110143143C13641364C4700247002Call
120231231C27302730C132289132289Call
130376376C54605460C372156372156Call
140608608C1092210922C≥1≥1Call
150986986C2184421844C≥1≥1Call
16015951595C4369043690C≥1≥1Call
N>0xallallall

Smallest prime reptiles

Smallest prime reptiles (1Ox3, 4Ox2):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
O monomino???P?P
O tetromino??P?P?P

Smallest common multiples

Smallest common multiple (area 4):

Common multiples' solutions count (excluding symmetric)

area4
solutions1P

See Also

Monominoes and L tetrominoMonominoes and T tetromino