Polyhex Oddities

A polyhex oddity is a figure with binary symmetry formed by 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 my Hexahex Oddities Page.

For heptahexes, see my Heptahex Oddities Page.

Trihexes

Rowwise
Bilateral
Columnwise
Bilateral
BirotaryDouble
Bilateral
1
9
11
11
1
1
1
1
3
1
5
5

Tetrahexes

Mike Reid proved that the O and S tetrahexes have no sexirotary oddities.

Rowwise
Bilateral
Columnwise
Bilateral
BirotaryDouble
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

Pentahexes

Pentahexes are tricky, so I got help from Mike Reid. Click on the blue figures to expand them.

Rowwise Bilateral Columnwise Bilateral BirotaryDouble
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
47

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
   
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
41

George Sicherman
41

George Sicherman
1
1
1
1
   
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


Back to Polyform Curiosities.
Col. George Sicherman [ HOME | MAIL ]