The  original  puzzle has 9 triangles per face (size = 3)
and has period  4 turning (i.e. the face or points turn with
90 degree intervals). The puzzle was designed by Uwe Meffert
and  called  the  Magic  Octahedron  (or Star Puzzler).  The
puzzle was not widely distributed but not exactly rare. This
puzzle  has  some  analogies  to  the  Rubik's  Cube and the
solving  techniques  are  the  same to that of the Pyraminx.
Christoph's  Magic  Jewel  is  similar  except  there are no
trivial    corners   to   solve.  This   has   2^22*12!   or
2,009,078,326,886,400 different combinations.
   Uwe Meffert also noticed that there could be an alternate
twisting  for  the  octahedron where it has period 3 turning
(i.e. faces turn with 120 degree intervals).
   One is able  to simulate a Trajber's Octahedron (period 3
turning and sticky  mode).  Also one is able to simulate one
with variant turning (period 4 turning and sticky mode).

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