Obviously the age of mechanical polyhedra is long past. I propose
that the center cubies (polyhedries?) of the electronic marvels
be equipped with fixed arrows so that those who are hacking the
higher-order problem can be happy. (I really like this idea because
it closely resembles one of my favorite ideas: a keyboard which has
small character displays in each keytop in lieu of engraving; when you
hit SHIFT the legends change from qwertyiop to QWERTYUIOP and when you
hit CONTROL+META they change to ETAIONSHRDLU, etc.)
The all-electronic cube has many other potential features: instant
resettability, a stack of saved states, subroutines.... Given
extensible, customizible, self-documenting editors, I don't see why
we should settle for polyhedra that are any less featureful.
Speaking of higher-order polyhedra, I hereby nominate the tetrahedron
as being appropriate to my own level of expertise.