This page shows all 131 ways to arrange the 12 hexiamonds to form three congruent polyiamonds. The problem was suggested by Andris Cibulis.
Abaroth has pointed out that some of these triplets can be joined to form 72-iamonds with compound symmetry:
Exactly 80 triplets have this property. Here is a more picturesque one:
You can buy sets of acrylic hexiamonds from Kadon Enterprises under the name Iamond Hex.
Last revised 2015-08-20.