Sets of Colored Polyiamonds


2025/03/08
Polyiamonds are polyforms based on equal sized equilateral triangles joined by complete edges. You can construct nice figures with these pieces as shown at The PolyPages, Mathematische Basteleien, Polyform Puzzler or Pentoma.

I bought a board game with four different colored sets of polyiamonds. The pieces have one up to six triangles and each set consists of 22 two-sided pieces. Instead of playing the game I tried to make symmetric constructions with these sets so that same colored pieces don't touch at their edges. This way the shapes of the pieces are separated and it's easier to spot them in a construction.

Furthermore I looked at sets of polyiamonds with more than six triangles for each piece. If pieces with less than five triangles are missing in a set or if only three colors are given, the construction are more difficult and a computer program is useful. Sometimes a solution for a third or fourth of a construction is possible and can be extended by a colorshift for the remaining parts. This also applies for hand solving as the following picture shows.

The following table shows some sets of pieces with a fixed number of triangles. They can be used for constructions like parallelograms, hexagons, hexagonal rings or stars with some kind of symmetry. Click the numbers of pieces to see one or more figures.

Basic Sets Number of squares Property One Set Three Sets Four Sets
Number of Pieces Total Area Number of Pieces Total Area Number of Pieces Total Area
Tetriamonds 4 Two-sided 3 12 9 36 12 48
One-sided 4 16 12 48 16 64
Pentiamonds 5 Two-sided 4 20 12 60 16 80
One-sided 6 30 18 90 24 120
Hexiamonds 6 Two-sided 12 72 36 216 48 288
One-sided 19 114 57 342 76 456
Heptiamonds 7 Two-sided 24 168 72 504 96 672
One-sided 43 301 129 903 172 1204
Octiamonds 8 Two-sided 66 528 198 1584 264 2112
One-sided 120 960 360 2880 480 3840

In the pictures you can see pieces with different numbers of triangles. This avoids problems with an odd number of unbalanced pieces and gives the chance to keep back smaller pieces for the end of a construction. Only one or few examples for combined sets are shown. Click the numbers of pieces to see the figures.

Basic Sets Number of squares Property One Set Three Sets Four Sets
Number of Pieces Total Area Number of Pieces Total Area Number of Pieces Total Area
Polyiamonds of Order 1 to 6 1..6 Two-sided 22 110 66 330 88 440
One-sided 30 166 90 498 120 664
Tetriamonds ∪ Pentiamodns ∪ Hexiamonds 4..6 Two-sided 19 104 57 312 76 416
One-sided 27 160 81 480 108 640
Pentiamonds ∪ Hexiamonds 5 or 6 Two-sided 16 92 48 276 64 368
One-sided 23 144 69 432 92 576
Hexiamonds ∪ Heptiamonds 6 or 7 Two-sided 36 240 108 720 144 960
One-sided 62 415 186 1245 248 1660


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