Uwe Mèffert invented this puzzle before Rubik invented the cube.  Visit his excellent site where you can still purchase various puzzles.

Pyraminx

Pyraminx in mid-twist

Shown here is the way the Pyraminx turns.  It has a delightful click due to its ratcheting mechanism.  Another nice ray-traced image can be seen here.

The small corners are essentially ornamental since they easily twist into their proper position.  Also available is a version with the corners removed.

Tetraminx

Pyramorphix