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

Area: 3.

Perimeter: 8.

Size: 1x3.

Is rectangular: yes.

Is convex: yes.

Holes: 0.

Order: 1.

Square order: 3.

Odd order: 1.

Prime rectangles: 1.

Smallest rectangle tilings

Smallest rectangle and smallest odd rectangle (1x3):

Smallest square (3x3):

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 \ h123456789N>0
10
200
311P11C22C
40033C0
50044C00
611C11C66C1313C2222C6464C
70099C00155155C0
8001313C00321321C00
911C11C1919C5757C121121C783783C28612861C81338133C3716037160C
10002828C0018881888C00143419143419C3k
11004141C0042334233C00468816468816C3k
1211C11C6060C249249C664664C99129912C5281752817C204975204975C18768551876855Call
13008888C002349423494C00≥1≥1C3k
1400129129C005417754177C00≥1≥1C3k
1511C11C189189C10871087C36433643C126019126019C972557972557C51582235158223C≥1≥1Call
1600277277C00295681295681C00≥1≥1C3k
1700406406C00687690687690C00≥1≥1C3k
1811C11C595595C47454745C1998719987C16001851600185C1789228117892281C≥1≥1C≥1≥1Call
1900872872C0037383323738332C00≥1≥1C3k
200012781278C0087129928712992C00≥1≥1C3k
2111C11C18731873C2071320713C109657109657C2029376120293761C≥151109437≥151109437C≥1≥1C≥1≥1Call
220027452745C004733740547337405C00≥1≥1C3k
230040234023C00110368563110368563C00≥1≥1C3k
2411C11C58965896C9041790417C601624601624C257206012257206012C≥2.78963548×10¹⁰≥2789635489C≥1≥1C≥1≥1Call
N>03k3kall3k3kall3k3kall

Smallest prime reptiles

Smallest prime reptile (3Ix2):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
I triomino11P19P249C3643P1600185C

Smallest tori tilings

Smallest torus and smallest odd torus (1x3):

Smallest square torus (3x3):

Tori tilings' solutions count (including translations)

w \ h123456789
100
20000
333995454
40000939300
500002882880000
6339991891820120167867846924692
700002775277500009369936900
8000086138613000034449344490000
933992675726757921921321332131384111384119853598535478017478017≥500000≥500000

Smallest Baiocchi figures

Smallest Baiocchi figure (area 9):

See Also

TriominoesL triomino