If you join equilateral triangles together edge-to-edge you make what, in 1961, recreational mathematician Thomas H. O’Beirne dubbed polyiamonds. If you use six triangles, you get a hexiamond. There are 12 distinct hexiamonds. A complete set of hexiamonds covers an area of 6 x 12 = 72 triangles,
As you’d guess, there are lots of pleasing shapes you can make with 72 triangles. Interestingly, it’s possible, but not at all easy, to cover many of those shapes with a set of hexiamonds. Since “possible but not easy” means “puzzle” to me, I decided to make a hexiamond-based puzzle.
I chose seven shapes, each of which can be covered in many different ways by the hexiamonds. Here are the shapes and an example showing each of them really has a solution:
and built them into a compact self contained box:
The box is composed of layers of 3mm BB held together in the corners by 4mm diameter, 2mm-thick neodymium magnets. If you remove the lid, this is what you see:
The hexiamonds themselves are cut from 6mm BB.
If you pull the layers all apart you get this:
To use the puzzle choose one of the shape layers, place it on the solid layer, stack the others under it, and snap on the bottom layer.
I put a solution to one of the shapes on the cover, both to hint at what’s inside, and to make the puzzle easy to reassemble for storage.
Here are the .svg files for it:
Hexiamonds.zip (47.4 KB)
I hope you enjoy playing with it as well as making it.
