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 O tetromino

Prime rectangles: ≥ 14.

Smallest rectangle tilings

Smallest rectangle (2x5):

Smallest square (4x4):

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 \ h12345678N>0
10
2000
300000
40000022P
5022P0088C2828P
600022P77P4343C202202C
7033P44P3131C170170C649649C27442744C
8033P66P6969C456456C22082208C1234312343C6665266652C
9044P1616P108108C10561056C86248624C5279652796C≥1≥1Call
10066C3030P285285C30683068C2798727987C≥1≥1C≥1≥1Call
11099P4848P615615C80168016C9229792297C≥1≥1C≥1≥1Call
1201010C9494C11011101C2036420364C≥1≥1C≥1≥1C≥1≥1Call
1301616C168168C25482548C5469654696C≥1≥1C≥1≥1C≥1≥1Call
1402020C276276C53525352C142908142908C≥1≥1C≥1≥1C≥1≥1Call
1502727C492492C1025610256C370884370884C≥1≥1C≥1≥1C≥1≥1Call
1603636C854854C2231922319C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
1704949C14161416C4634946349C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
1806363C24302430C9177091770C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
1908686C41404140C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
200113113C68786878C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
210150150C1159211592C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
220199199C1951219512C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
230265265C3239232392C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
240349349C5408054080C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
250465465C9032090320C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
260615615C149706149706C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
270815815C248624248624C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
28010801080C413134413134C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
N>0xallallallallallallall

Smallest prime reptiles

Smallest prime reptiles (3Ix3, 4Ox2):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
I triomino???P?P?P
O tetromino??P?P?C?P

Smallest common multiples

Smallest common multiple (area 12):

Common multiples' solutions count (excluding symmetric)

area12
solutions≥1P

See Also

I triomino and L tetrominoI triomino and T tetromino