# Polyhex Tri-Oddities

A polyhex *tri-oddity*
is a figure with ternary symmetry formed by some number of copies of
a polyhex that is not a multiple of three.
Torsten Sillke first studied them in 1996.
Here are the minimal known tri-oddities for the dihex, trihexes,
tetrahexes, and pentahexes.
Please write if you find a smaller solution or solve an unsolved case.

Mike
Reid proved that the straight trihex has no solution.

For hexahexes, see Hexahex Tri-Oddities.

[ Dihex
| Trihexes
| Tetrahexes
| Pentahexes
| Mirror Symmetry
]

## Holeless Variants

These figures have mirror symmetry as well as ternary symmetry.
### Horizontal

#### Holeless Variants

### Vertical

#### Holeless Variants

*Last revised 2024-06-30.*

Back to Polyform Oddities
< Polyform Curiosities

Col. George Sicherman
[ HOME
| MAIL
]