Polyhex Oddities
A polyhex oddity is a plane figure with binary
symmetry formed by joining an odd number of copies of a polyhex.
Here are the minimal known oddities for the trihexes,
tetrahexes, and pentahexes.
Please write if you find a smaller solution or solve an unsolved case.
[ Trihexes
| Tetrahexes
| Pentahexes
]
For hexahexes, see
Hexahex Oddities.
For heptahexes, see
Heptahex Oddities.
Rowwise Bilateral
| Columnwise Bilateral
| Birotary | Double Bilateral
| Ternary on Cell Rowwise Bilateral
| Ternary on Cell Columnwise Bilateral
| Ternary on Vertex Rowwise Bilateral
|
1
| 9
| 11
| 11
| 3
| 9
| 1
|
1
| 1
| 1
| 1
| 3
| 9
| 3
|
3
| 1
| 5
| 5
| 9
| 3
| 3
|
Holeless Variants
Ternary on Vertex, Rowwise Bilateral
Mike Reid
proved that the O and S tetrahexes have no sexirotary oddities.
Rowwise Bilateral
| Columnwise Bilateral
| Birotary | Double Bilateral | Sextuple Rotary | Full |
1
| 1
| 1
| 1
| 9
| 9
|
3
| 3
| 3
| 3
| 3
| 3
|
1
| 1
| 1
| 1
| None
| None
|
3
| 3
| 3
| 3
| 3
| 3
|
3
| 3
| 1
| 3
| None
| None
|
1
| 3
| 3
| 3
| 3
| 3
|
| None
| 1
| None
| None
| None
| None
|
Holeless Variants
Columnwise Bilateral
Double Bilateral
Pentahexes are tricky, so I got help from
Mike Reid.
Click on the gray figures to expand them.
| Rowwise Bilateral
| Columnwise Bilateral
| Birotary | Double Bilateral | Sextuple Rotary | Full |
1
| 9
| 11
 George Sicherman
| 11
 George Sicherman
|
| |
1
| 9
 George Sicherman
|
|
|
| |
1
| 3
| 5
 Mike Reid
| 5
 Mike Reid
| 11
 Mike Reid
| 11
 Mike Reid
|
1
| 9
 George Sicherman
| 9
 George Sicherman
| 9
 George Sicherman
|
|
|
3
| 5
 George Sicherman
| 7
 George Sicherman
| 11
 George Sicherman
(after Mike Reid)
| 29
 George Sicherman
| 29
 George Sicherman
|
3
| 3
| 7
 George Sicherman
| 11
 George Sicherman
| 23
 George Sicherman
| 29
 George Sicherman
|
1
| 1
| 1
| 1
| 59
 George Sicherman
|
|
3
| 3
| 5
 George Sicherman
| 7
 Mike Reid
| 29
 George Sicherman
|
|
3
| 3
| 5
 Mike Reid
| 9
 George Sicherman
| 17
 George Sicherman
| 35
 George Sicherman
|
3
| 3
| 5
 Mike Reid
| 9
 Mike Reid
| 17
 George Sicherman
| 23
 George Sicherman
|
3
| 3
| 3
| 5
 Mike Reid
| 17
 George Sicherman
| 29
 George Sicherman
|
3
| 3
| 5
 George Sicherman
| 7
 George Sicherman
| 11
 Mike Reid
| 11
 Mike Reid
|
5
| 1
| 11
 George Sicherman
| 15
 George Sicherman
| 77
George Sicherman
|
|
3
| 5
| 7
 George Sicherman
| 11
 George Sicherman
| 23
 George Sicherman
| 35
 George Sicherman
|
7
 George Sicherman
| 3
| 1
| 7
 George Sicherman
|
|
|
9
 George Sicherman
| 1
|
|
|
|
|
3
| 1
| 23
 George Sicherman
| 23
 George Sicherman
|
|
|
3
| 1
| 7
 George Sicherman
| 7
 George Sicherman
| 35
 George Sicherman
| 47
 George Sicherman
|
7
 George Sicherman
(squashed by Mike Reid)
| 1
| 9
 George Sicherman
| 9
 George Sicherman
| 65
 George Sicherman
| 65
 George Sicherman
|
1
| 1
| 1
| 1
| 101
 George Sicherman
|
|
3
| 5
| 7
 George Sicherman
| 9
 George Sicherman
| 17
 George Sicherman
| 17
 George Sicherman
|
5
| 5
| 7
 George Sicherman
| 15
 George Sicherman
| 17
 George Sicherman
| 17
 George Sicherman
|
Holeless Variants
Rowwise Bilateral
Columnwise Bilateral
Birotary
Double Bilateral
Sextuple Rotary
Full
Last revised 2012-07-27.
Back to Polyform Curiosities.
Col. George Sicherman
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