I gave my father a cube a year ago (for which my mother may never forgive
me), and he has been working with it ever since. He has developed his own
notation, based on Angevine: Basically, take a corner as an X-Y-Z
co-ordinate system, and call the planes (e.g.) X1, X2, and X3 (where
x2 is the slice). L is X1, R is X3, F is Y1, etc. + is a clockwise
rotation, looking at the -1 face (thus the X3,Y3, and Z3 faces rotate
backwards from bfudlr); - is CCW. Half twists are (on a typewriter) +/-
(he doesn't have a computer terminal).
Anyway, his feeling on Singmaster nomenclature (with wich I disagree)
are as follows:
"I do feel that Singmaster's limited cubist vocabulary impairs
communication of his knowledge and insights. His general use of only
six of the nine groups available for rotation is like using only twenty
of the twenty-six letters in our alphabet. With an unabridged dictionary
and a thesaurus practically anything could still be said, but not as
well as using the whole alphabet. ... Perhaps mathematicians just don't
care about communication with ordinary people."
My father is a lawyer.