Well, whoever doesn't like the Supergroup didn't send me
any messages, and several who do did, so here goes. This message
is part one of three, separated for the benefit of MIT's
notoriously fragile mailer.
In case anyone has managed to miss it, the Supergroup is
the group underlying the cube when face center orientation is taken
into account. By the "orientation" of a face center, we refer to
the number of 90o twists of that face center from the position
designated "solved." To visualize this, Singmaster suggests
replacing the solid colors on the sides of the cube by some
nine-piece pictures, so that the centers must be restored to their
initial (untwisted) state to solve the cube. He reports that this
was done (on two sides only) by a company in England, which printed
its logo on cubes for a promotion. The term "Supergroup" is also
due to Singmaster, and I adopt it in favor of the term "the
extended problem," which has appeared in Cube-lovers.
To make the face center orientation visible on my cube, I
first used magic marker, which rubbed off, then paint, which
attacked the colortabs and looked and felt awful. [Then I went to a
stationery store and got plastic tape and replaced my colortabs --
no orange, so my cube now has a tan face.] I marked the face center
orientation by cutting out circles from the plastic colortabs to
let the black plastic show through. I like it, though some people
think it looks like the cube has been used for target practice.
Each cutout circle has a diameter of about 3/8" (1/2 the side of a
cubie) and is centered at the corner of a face center, overlapping
two edge cubies and one corner cubie. The orientation is then
visible if either the corners or the edges are in the home
position. It doesn't particularly matter which corners of the face
centers are used; I chose the pattern which has the same symmetry
group as Plummer's cross (unique up to M-conjugacy).
There will be a short intermission while we change reels.