# Polygem Oddities

A *polygem*
is a plane polyform whose cells are gems—figures formed by
dividing a regular hexagon into thirds using lines from the center to
the midpoints of the sides.
A gem is one of the two dikites.
You can see more about polygems at
Abaroth's Polygem Page.
An *oddity*
is a figure with binary symmetry formed by an odd number of copies of
a polyform.
Here are the minimal known oddities for polygems
of orders 1–4.
The black trigem has no solution; the gray trigems and most of
the tetragems are unsolved.
Please write if you find a smaller solution or solve an unsolved case.

## Monogem

## Digems

## Trigems

## Tetragems

### Unsolved or Impossible

Last revised 2014-10-21.

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Polyform Curiosities

Col. George Sicherman
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