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

Area: 5.

Perimeter: 12.

Size: 1x5.

Is rectangular: yes.

Is convex: yes.

Holes: 0.

Order: 1.

Square order: 5.

Odd order: 1.

Prime rectangles: 1.

Smallest rectangle tilings

Smallest rectangle and smallest odd rectangle (1x5):

Smallest square (5x5):

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 \ h12345N>0
10
200
3000
40000
511P11C11C11C22C
6000033C5k
7000044C5k
8000055C5k
9000066C5k
1011C11C11C11C88Call
N>05k5k5k5kall

Smallest prime reptiles

Smallest prime reptile (5Ix2):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
I pentomino11P≥1P≥1C≥1P≥1C

Smallest tori tilings

Smallest torus and smallest odd torus (1x5):

Smallest square torus (5x5):

Tori tilings' solutions count (including translations)

w \ h12345678910
100
20000
3000000
400000000
555252512512562562562506250
600000000156551565500
70000000078300783000000
800000000391625391625000000
900000000≥500000≥50000000000000
10552525125125625625≥500000≥50000016105161058054080540404145404145≥500000≥500000≥500000≥500000

Smallest Baiocchi figures

Smallest Baiocchi figure (area 20):

Smallest Baiocchi figure without holes (area 25):

See Also

PentominoesL pentomino