Hexiamonds are 2D-puzzles in which you have all 12 possible pieces made of 6 triangles. Pieces may be rotated in every direction, even flipped upside down, to get the mirrorred piece. An Hexiamond is as nice as a pentomino and about the same level of difficulty.

The pieces can fit in a number of symmetrical trays:
Beat the Computer No. 6
beat the computer #6 puzzle

Onion-shape puzzle - 5.885 solutions.
Tenyo No. 6

4968 solutions
3x4 hexagon with hole

710 solutions
Irregular hexagon

6100 solutions exactly
Flag/ Harmonica shape

(Origami version) 974 solutions
6 x 6 diamond

156 solutions

Special challenges

Beat the computer-6 with enclosed hexagon:
Tenyo-6 in equal halfs resp. with enclosed hexagon:
Irregular hexagon in equal halfs or with enclosed hexagon is possible too:

You can download my Hexiamond solver (written in Delphi 6 for Windows) here.
The solver can show all solutions of the puzzles above.
Free Hexiamond solver

David Goodger's Hexiamond page