I believe the following is symmetric in the sense that any QTW
will bring you closer to home:
All corners are rotate, and letting + indicate clockwise
and - counterclockwise, each face has the following
corner configuration
+-
-+
(and all the edges are intact)
a total map of the cube corners might look like
+-
-+
+- -+ +- -+
-+ +- -+ +-
+-
-+
Each face is essentially the same: edges OK and all corners
rotated so that opposite corners are rotated in the same
direction. It is rather intuitive to me that rotating a face
clockwise is the same as rotating the face counterclockwise. This
fulfills the condition needed for maximality, but what flavor of
symmetric is it (if the symmetry is easily describable). Also,
does anybody have a 28 QTW algorithm (OR LESS!!) to go between
solved and this position.