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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Col. George Sicherman [ HOME | MAIL ]