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

Vertical Mirror Variants

Holeless Variant

Full Symmetry Variants

Holeless Variant

Convex Variant

Last revised 2023-05-06.

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Col. George Sicherman [ HOME | MAIL ]