The  original  puzzle has 9 triangles per face (size = 3) and
has period 3 turning (i.e. the face or points turn in 120 degree
intervals).  The  puzzle  was designed by Uwe Meffert and called
the Pyraminx.  This  has  2^5*3^8*6!/2  or  75,582,720 different 
combinations.
   Another puzzle Senior Pyraminx 3x3x3 exists only on paper, it
has period 2 turning (i.e. edges turn with 180 degree intervals)
but   the   corners  would  fall  off  unless it had some tricky
mechanism.  (This  may  be the same as the Master Pyraminx which 
has 446,965,972,992,000 different combinations).
   Another puzzle (which was not widely distributed), the Junior
Pyraminx  (and similarly  the Junior Pyraminx Star, a octahedron
formed by two tetrahedra, this has 7!*3^6 or 3,674,160 different
combinations), has  4  triangles  (size = 2) per face and at the
time  I  designed  this computer puzzle thought that it had only
period 2 turning (i.e the edges rotate). It turns out the puzzle
has a period  4  turning  (edges  turn with 90 degree intervals)
which makes it analogous to the 2x2x2 Rubik's cube.  This puzzle
makes various non-tetrahedral shapes.  The puzzle contained here
has no period 4 turning flexability.

WWW: http://www.tux.org/~bagleyd/puzzles.html