Date: 1 JAN 1981 1315-EST From: DCP at MIT-MC (David C. Plummer) Subject: several subjects To: CUBE-LOVERS at MIT-MC One last try!! What I meant was the 12 sided frob built out of pentagons. And after refering to better and better dictionaries I discovered this thing is called a pentagonal dodecahedron, and I meant the faces to be the points of rotation. Perhaps McKeeman thought I meant the rhombic dodecahedron, and subsequent messages got me confused and I jumped the gun without thinking very heavily. Woods: Could you please send the manipulations for "baseball," "snake," and "cube-in-cube" for the benifit of those who do not have Singmaster. Please use prime notation (R' instead of (lower case) r) for counterclockwise twists since that seems to be the notation currently in use in this list. In general, my opinion is that it would be nice if people would send along the short algorithms that are known. ZILCH's 50 and 70 qtw algotithms are a little too long, but anything under 36 should probably be sent. I know it may be a spoiler, but (1) there seem to be several configurations mentioned and perhaps some people don't have time to find nice fast ways to get there, (2) it reduces needless duplication of effort, (3) parts of the algorithm (or the algorithm itself) might serve as a subroutine for other algorithms under development. On the concept of the higher order "cubes:" N dimensions has a reasonable geometric interpretation (maybe it doesn't have to have this condition?) built out of some number of "cubies" of dimension N Each "cubie" is in turn a "cube," perhaps of a different order than the larger cube (eg, a 3x3x3 cube whose cubies are 5x5x5) Each "cubie" of the "cubie" is a "cube," ad infinitum as desired In addition to all this, each faclet is a "cube" of dimension N-1, ad infinitum (at least until the dimensions run out!!) The thing I am doing is trying to PHYSICALLY construct a higher order (flavor: dimension 3, cubical, order 5, cubies are "atomic" (ie, not cubes in themselves), faclets are atomic). Personally, I think half the fun is being able to hold one of the beasties and mung it by twisting. ACW: I think it would be instructive to have an short intro to Group Theory for Cubist. This would benefit newcomers to the mailing list, and people who hack the cube and want to know some of the theory behind the cube. (5-10K characters if you can keep it down to that. If not, send it when machines are generally lightly loaded.) I vote: plase do.