Puzzles of poly-forms are jigsaw puzzles with pieces that are created of the same basic elements, most often equal sided triangles, squares and hexagrams.
Regular puzzles of poly-forms exist of all unique combinations of the same number of such an element. De pieces can be gerotated and even put upside down, giving you the mirror image if it is asymmetric.

The 5 pieces of 4 squares (Tetrominos) are most famous, they are key parts in the original version of the computer game Tetris.

Pieces built of triangles
Polyamond #Triangles #Pieces Remarks Examples
Diamond 2 1 Icosaeder

triamond 3 1
Tetriamond 4 3
Pentiamond 5 4 You can create an Icosahedron
Hexiamond 6 12 more...
Septiamond 7 24 bekijk
Octiamond 8 ? One piece has enclosed an empty triangle
Andrew Clarke's Poly Pages

Pieces built of squares
Polyomino #Squares #Pieces Remarks Irregular polyominos
Domino 2 1
tromino 3 2
Tetromino 4 5 double set pieces...
Pentomino 5 12 more...
Hexomino 6 35 bekijk
Septomino 7 108 One piece has an empty square enclosed
Octomino 8 369 Several pieces have an empty square enclosed
Nonomino 9 1285

3D polyomino's
Examples of 3D-polyomino puzzles:
Pieces built of hexagrams
Polyhex #Hexagrams #Pieces Remarks Example
Diahex 2 1
Triahex 3 3
Tetrahex 4 7 maybe?
Pentahex 5 22 Beat the computer no. 22
Hexahex 6 ? One piece has an empty hexagram enclosed

Free Download
I've written a few solver programs in Delphi for Windows:

Site van Kadon Enterprises
Andrew Clarke's Poly Pages