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 Y pentomino

Prime rectangles: ≥ 27.

Smallest rectangle tilings

Smallest rectangle (4x8):

Smallest square (7x7):

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 \ h1-3456789N>0
1-30
4000
500000
60000000
7000004848P6868P
8088P2424P9696P16041604P1235212352C
902828P7070P256256P1422814228P9819498194C441692441692C
10000124124P24182418P1984819848P≥1≥1C≥1≥1Call
110112112P834834P91529152P196986196986P≥1≥1C≥1≥1Call
120538538P40664066P2616626166P15844841584484C≥1≥1C≥1≥1Call
1309898P98889888P106414106414P36859523685952C≥1≥1C≥1≥1Call
140952952P1767217672P461580461580C1848914418489144C≥1≥1C≥1≥1Call
15057725772P132238132238P≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
16034583458C326806326806C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
17090029002C300548300548C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
1804905049050C26442462644246C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
1905144451444C69471306947130C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
200106090106090C56650625665062C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
N>0xallallallallallall

See Also

I triomino and X pentominoI triomino and Z pentomino