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.


Tetrominoes

Prime rectangles: 11.

Smallest rectangle tilings

Smallest rectangles (3x8, 4x6):

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 \ h1-2345678N>0
1-20
300
400000
500000
6001616P02627226272P
700240240P000
801616P23202320P151740151740P68201966820196C≥1≥1C≥1≥1C
9001697016970P000≥1≥1C4k
1000113902113902P0≥1≥1C0≥1≥1C2k
1100674488674488P000≥1≥1C4k
12058125812P37914143791414C779579633779579633P≥1≥1C≥1≥1C≥1≥1Call
13002041767820417678C000≥1≥1C4k
1400≥1≥1C0≥1≥1C0≥1≥1C2k
1500≥1≥1C000≥1≥1C4k
160616284616284C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
1700≥1≥1C000≥1≥1C4k
1800≥1≥1C0≥1≥1C0≥1≥1C2k
1900≥1≥1C000≥1≥1C4k
2004309530243095302C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
N>0x4kall4k2k4kall

Smallest prime reptiles

Smallest prime reptiles (4Ix3, 4Ox3, 4Lx3, 4Tx3, 4Zx3):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
I tetromino005812P
L tetromino004386P
O tetromino0026272P
T tetromino006730P
Z tetromino002812P

Smallest common multiples

Smallest common multiple (area 32):

Common multiples' solutions count (excluding symmetric)

area48121620242832
solutions0??????≥1

Attributions

  1. Smallest known common multiple found by Livio Zucca (http://www.iread.it/lz/4chall.html)

See Also

L triominoI tetromino