Date: 9 January 1981 0551-EST (Friday) From: Dan Hoey at CMU-10A To: Cube-lovers at MIT-MC Subject: The Supergroup -- Part 1: Physical reality Message-Id: <09Jan81 055144 DH51@CMU-10A> 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.