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.
Nontrivial variants
and holeless 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 hexominoes, see
Hexomino
Oddities.
| Lateral | Diagonal | Rotary | Double
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
|
These solutions have irreducible multiple tilings.
Lateral
Diagonal
Rotary
Lateral
Diagonal
Birotary
Double Lateral
Double Diagonal
Double Rotary
Full
Last revised 2012-10-27.
Back to Polyform Curiosities.
Col. George Sicherman
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