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.


Pentominoes

Prime rectangles: 27.

Smallest rectangle tilings

Smallest rectangles (3x20, 4x15, 5x12, 6x10):

Smallest square (10x10):

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 \ h1-234567891011N>0
1-20
300
4000
50000000
6000000
70000000
800000000
9000000000
10000000093569356P≥1≥1P≥1≥1P≥1≥1P≥1≥1P
11000000000≥1≥1P0
1200040404040P0000≥1≥1C0?
13000271280271280P0000≥1≥1C0?
1400082983208298320P0000≥1≥1C0?
1500014721472P183598324183598324P2.05208039×10¹³2052080390212P≥1≥1P≥1≥1C≥1≥1C≥1≥1C≥1≥1C?
160003.33641767×10¹⁰3336417676P0000??0?
170005.25204609×10¹¹52520460964P0000??0?
180007.44245624×10¹²744245624704P0000??0?
190009.71582726×10¹³9715827268240P0000??0?
20088P540749904540749904P1.18879305×10¹⁵118879305163376P6.65070500×10¹⁹6650705002998048620C≥1≥1C≥1≥1C≥1≥1C?????
210001.37948944×10¹⁶1379489444796438P0000??0?
220001.53193736×10¹⁷15319373652432356P0000??0?
230001.63956824×10¹⁸163956824441893188P0000??0?
240001.70043388×10¹⁹1700433881284861974C0000??0?
250229344229344P9.39808083×10¹³9398080836248P1.71652106×10²⁰17165210687688711858C≥1.84467440×10²⁰≥18446744073709551615C≥1≥1C≥1≥1C≥1≥1C?????
26000≥1.84467440×10²⁰≥18446744073709551615C0000??0?
27000≥1.84467440×10²⁰≥18446744073709551615C0000??0?
28000≥1.84467440×10²⁰≥18446744073709551615C0000??0?
29000≥1.84467440×10²⁰≥18446744073709551615C0000??0?
300385887080385887080P6.81049507×10¹⁷68104950784133972C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1≥1C≥1≥1C≥1≥1C?????
31000≥1.84467440×10²⁰≥18446744073709551615C0000??0?
32000≥1.84467440×10²⁰≥18446744073709551615C0000??0?
33000≥1.84467440×10²⁰≥18446744073709551615C0000??0?
34000≥1.84467440×10²⁰≥18446744073709551615C0000??0?
3502.60555919×10¹²260555919792P≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1≥1C≥1≥1C≥1≥1C?????
36000≥1.84467440×10²⁰≥18446744073709551615C0000??0?
37000≥1.84467440×10²⁰≥18446744073709551615C0000??0?
38000≥1.84467440×10²⁰≥18446744073709551615C0000??0?
39000≥1.84467440×10²⁰≥18446744073709551615C0000??0?
4001.10821096×10¹⁵110821096859460C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1≥1C≥1≥1C≥1≥1C?????
N>0x5k5kall5k5k5k5kall5k

Smallest prime reptiles

Smallest prime reptiles (5Ix4, 5Lx4, 5Nx4, 5Px4, 5Rx4, 5Tx4, 5Ux4, 5Vx4, 5Wx4, 5Xx4, 5Yx4, 5Zx4):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
I pentomino000540749904P17165210687688711858P≥18446744073709551615P≥1P≥1P≥1P
L pentomino000≥1P≥1P≥1P≥1P≥1P≥1P
N pentomino000≥1P≥1P≥1P≥1P≥1P≥1P
P pentomino000≥1P≥1P≥1P≥1P≥1P≥1P
R pentomino000≥1P≥1P≥1P≥1P≥1P≥1P
T pentomino000≥1P≥1P≥1P≥1P≥1P≥1P
U pentomino000≥1P≥1P≥1P≥1P≥1P≥1P
V pentomino000≥1P≥1P≥1P≥1P≥1P≥1P
W pentomino000≥1P≥1P≥1P≥1P≥1P≥1P
X pentomino000≥1P≥1P≥1P≥1P≥1P≥1P
Y pentomino000≥1P≥1P≥1P≥1P≥1P≥1P
Z pentomino000≥1P≥1P≥1P≥1P≥1P≥1P

See Also

Z tetrominoI pentomino