# Polyiamond Tri-Oddities

A polyiamond *tri-oddity*
is a figure with ternary symmetry formed by some number of copies of
a polyiamond that is not a multiple of three.
Torsten Sillke first studied them in 1996.
Here are the minimal known tri-oddities for polyiamonds of order
up to 6.
Impossible polyiamonds are shown in black.
Please write if you find a smaller solution or solve an unsolved case.

For heptiamonds (7-iamonds), see Heptiamond
Tri-Oddities.
For polyhexes, see Polyhex Tri-Oddities.

[ Moniamond
| Diamond
| Triamond
| Tetriamonds
| Pentiamonds
| Hexiamonds
]

### Mirror Variants

#### Holeless Variant

### Convex Variants

Some hexiamonds with no known tri-oddities can form tri-oddities
in pairs.
See Hexiamond Pair Tri-Oddities.

### Horizontal Mirror Variants

#### Holeless Variant

#### Convex Variant

### Vertical Mirror Variants

#### Holeless Variant

### Full Symmetry Variants

#### Convex Variant

*Last revised 2024-06-10.*

Back to Polyform Oddities
<
Polyform Curiosities

Col. George Sicherman
[ HOME
| MAIL
]