Pentomino Oddities

A polyomino oddity is a symmetrical figure formed by an odd number of copies of a polyomino. Here are the minimal known oddities and extended oddities for the 12 pentominoes, as found mostly by Mike Reid and me. Click on the gray figures to expand them.

Holeless variants and nontrivial variants are at the end of the page. Figures with green backgrounds have holeless variants with the same number of tiles.

Torsten Sillke was the first to investigate oddities.

For one-sided pentominoes, see One-Sided Pentomino Oddities. For hexominoes, see Hexomino Oddities.

LateralDiagonalRotaryDouble
Lateral
Double
Diagonal
Double
Rotary
Full
3
5

Mike Reid
7

George Sicherman
9

George Sicherman
15

George Sicherman
17

Mike Reid
21

Mike Reid
1
5
1
1
5
5
5
7

Mike Reid
5

Mike Reid
7

George Sicherman
11

George Sicherman
13

George Sicherman
13

Mike Reid
21

Mike Reid
7

Mike Reid
5

Mike Reid
9

Mike Reid
15

George Sicherman
15

Mike Reid
21

George Sicherman
29

Mike Reid
3
3

Torsten Sillke
5

Torsten Sillke
9

Mike Reid
7

Torsten Sillke
9

Torsten Sillke
13

Mike Reid
1
19

George Sicherman
23

Mike Reid
31

George Sicherman
     
1
13

George Sicherman
19

George Sicherman
19

George Sicherman
     
11

George Sicherman
1
15

George Sicherman
  35

George Sicherman
37

George Sicherman
 
7

George Sicherman
1
9

George Sicherman
21

Mike Reid
11

George Sicherman
25

George Sicherman
29

George Sicherman
1
1
1
1
1
1
1
5

George Sicherman
7

George Sicherman
7

Mike Reid
13

George Sicherman
17

Mike Reid
17

Mike Reid
29

Mike Reid
9

George Sicherman
13

George Sicherman
1
9

George Sicherman
13

George Sicherman
13

George Sicherman
73

George Sicherman

Holeless Variants

Lateral

Diagonal

Birotary

Double Lateral

Double Diagonal

Double Rotary

Full

Nontrivial Variants

These solutions have irreducible multiple tilings.

Lateral

Diagonal

Rotary

Last revised 2014-10-11.


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Col. George Sicherman [ HOME | MAIL ]