[next] [prev] [up] Date: Tue, 04 Nov 80 00:23:00 -0500 (EST)
[next] [prev] [up] From: David C. Plummer <DCP@MIT-MC >
[next] ~~~ [up] Subject: Christman Cross algorithm described

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)


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.

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