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 pentomino and U pentomino

Prime rectangles: ≥ 72.

Smallest rectangle tilings

Smallest rectangle (12x20):

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 \ h1-9101112131415N>0
1-90
10000
110000
1200000
13000000
140000000
150000000000000
16000000000?
17000000000?
180000000≥1≥1P?
190000000≥1≥1P?
20000004040P≥1≥1P≥1≥1P≥1≥1P?
210000000≥1≥1P?
220000000≥1≥1P?
230000000≥1≥1P?
240000000≥1≥1P?
25000192192P≥586≥586P≥1≥1P≥1≥1P≥1≥1P?
260000000≥1≥1P?
270000000≥1≥1P?
280000000≥1≥1P?
290000000≥1≥1P?
30000≥192≥192P≥586≥586P≥1≥1P≥1≥1P≥1≥1P?
310000000≥1≥1P?
320000000≥1≥1P?
330000000≥1≥1P?
340000000≥1≥1P?
35000≥192≥192P≥586≥586P≥1≥1P≥1≥1P≥1≥1P?
360000000≥1≥1C?
37088P0000≥1≥1C?
3801616P0000≥1≥1C?
3902424P0000≥1≥1C?
4003232P≥192≥192P≥1600≥1600C≥1≥1C≥1≥1C≥1≥1C?
4105252P0000≥1≥1C?
420408408P0000≥1≥1C?
430928928P0000≥1≥1C?
44016441644P0000≥1≥1C?
45025882588P≥192≥192P≥23440≥23440C≥1≥1C≥1≥1C≥1≥1C?
46043164316P0000≥1≥1C?
4701469214692P0000≥1≥1C?
4803403234032P0000≥1≥1C?
4906646066460P0000≥1≥1C?
500117136117136P≥36864≥36864C≥23440≥23440C≥1≥1C≥1≥1C≥1≥1C?
510205384205384P0000???
520488032488032P0000???
53010723601072360P0000???
54021686342168634P0000???
55040828644082864P???????????
56074899107489910P0000???
5701545923215459232P0000???
5803199169031991690P0000???
5906447072064470720P0000???
600124953018124953018P???????????
610236219772236219772P0000???
620464575494464575494P0000???
630924549484924549484P0000???
6401.83377779×10¹⁰1833777790P0000???
6503.57753104×10¹⁰3577531048P???????????
6606.86571115×10¹⁰6865711152P0000???
6701.33078071×10¹¹13307807128P0000???
6802.59641574×10¹¹25964157402P0000???
6905.07670953×10¹¹50767095322P0000???
7009.87386156×10¹¹98738615632P???????????
7101.90397962×10¹²190397962128P0000???
7203.67406800×10¹²367406800670P0000???
730≥1≥1P0000???
740≥1≥1C0000???
N>0xall5k5k5k5kall

See Also

I pentomino and T pentominoI pentomino and V pentomino