Let the following notation exist:
the faces:
T=Top B=Bottom
F=Front P=Posterior (Rear, Back, but those letters are taken)
R=Right L=Left
The rotations:
+ Clockwise
- Clockwise
++ 180 Rotation (Two moves)
Note that the following algorithm exchanges corners diagonally on
top and bottom: (Parens for major functional components)
(+F+P)(++T++B)(-F-P)(-R-L)(++T++B)(+R+L)(++T++B)
This is now a tool. To do the Christman Cross, we do
-P [(+F+P)(++T++B)(-F-P)(-R-L)(++T++B)(+R+L)(++T++B)] +P
but since transforms associate, and F and P commute, and -P+P = I, we get
(+F)(++T++B)(-F-P)(-R-L)(++T++B)(+R+L)(++T++B) +P
Which is 20 quarter twists.
David Christman thinks he read in Singmaster, Edition 5 that this
cross can be done in less than 20 quarter twists. Can somebody
confirm or deny this recolection.