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 tetromino and N pentomino

Prime rectangles: 40.

Smallest rectangle tilings

Smallest rectangle (5x11):

Smallest square (8x8):

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 \ h1-456789101112N>0
1-40
5000
600000
70000000
80000044P1616P
90000044P5252P2424P
100001212P44P120120P452452P31663166P
11088P88P2424P420420P21522152P≥1000≥1000C≥1≥1C
1201010P2828P240240P15121512P98049804P≥1000≥1000C≥1≥1C≥1≥1C
130001616P260260P50005000P2152021520P≥1000≥1000C≥1≥1C≥1≥1Call
14044P205205P652652P≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1≥1C≥1≥1Call
1509292P288288P24722472P≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1≥1C≥1≥1Call
160150150P919919P≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1≥1C≥1≥1Call
1702020P10661066P≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1≥1C≥1≥1Call
1808686P41284128P≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1≥1C≥1≥1Call
190852852P88568856P≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1≥1C≥1≥1Call
20015221522P≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1≥1C≥1≥1Call
210460460P≥1≥1C????????????all
22013461346C≥1≥1C????????????all
23079007900C≥1≥1C????????????all
2401461214612C≥1≥1C????????????all
25085608560C≥1≥1C????????????all
2602147221472C≥1≥1C????????????all
2708210082100C≥1≥1C????????????all
280157994157994C≥1≥1C????????????all
290168084168084C≥1≥1C????????????all
300380054380054C≥1≥1C????????????all
N>0xallallallallallallallall

See Also

I tetromino and L pentominoI tetromino and P pentomino