Polyiamond Tilings With Few Sides

A polyiamond is a plane figure formed by joining one or more congruent equilateral triangles edge to edge. Copies of a polyiamond can be arranged to form various larger polyiamonds.

Here I present polyiamonds with the fewest sides that a polyiamond can form. A polyiamond must have at least 3 sides, the number of sides of an equilateral triangle. Some polyiamonds can tile an equilateral triangle. See Tiling a Triangle with a Polyiamond.

Here are minimal known polyiamonds with fewest edges for polyiamonds of orders 1 through 8. Not all these solutions are uniquely minimal. The numbers below the figures tell how many sides they have.

Moniamond

Diamond

Triamond

Tetriamonds

Pentiamonds

Hexiamonds

Heptiamonds

The straight heptiamond can tile a triangle. See Tiling a Triangle with a Polyiamond. The smallest known such tiling has 45,927 tiles. This is too many to show here.

Octiamonds

Last revised 2024-07-30.

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Col. George Sicherman [ HOME | MAIL ]