Introduction to Heptiamonds


Heptiamonds (pronounced hept-eye-monds) are a member of the Polyforms puzzle family, which comprises sets of puzzle pieces based on squares (Polyominoes), triangles (Polyiamonds) or hexagons (Polyhexes). The Heptiamonds are a set of twenty-four puzzle pieces (called animals among Polyform enthousiasts), each representing one of the twenty-four possible ways to combine seven equilateral triangles by laying them side-to-side on a plane (picture below). The term Polyiamonds was coined in 1961 by T.H. O'Beirne who suggested that if a diamond (rhombus) has two such triangles, a polyiamond can have any amount of them. Consequently, a heptiamond is an animal with seven triangles. A full set of Heptiamonds has 24 x 7 = 168 equilateral triangles, which I call Basic Triangles.

A grid of equilateral triangles (known as an isometric grid) showing the twenty-four
Heptiamonds (left) and the same puzzle pieces together as a solution (right)

The aim of the game is to fit the pieces, without overlaps, into a configuration, which I call a Shape (cf. solved image in picture). The procedure is much like a classical jig saw puzzle but with these essential differences:

  • There are many possible Shapes to be solved;
  • For each Shape, there are usually more than one possible solution (sometimes running into the millions);
  • The pieces may be flipped and rotated in order to fit into the Shape.

Each Shape contains 168 Basic Triangles, unless one chooses to solve modified puzzles with, for instance, One-Sided Heptiamonds (described in some of the outside links). This site contains only solutions of the standard set of twenty-four.