From:

~~~ Subject:

The Megaminx is now on sale in the San Francisco Bay Area. It is,

as pictured, a dodecahedron with each face twistable in fifths, and

containing 5 corners, 5 edges, and a center. Instead of 12 different

colors it seems to have 10, with the red and yellow duplicated; that

means you can have a parity problem at the end if you exchange the

duplicate edges. Solving seems to be pretty straightforward, except

new edge moves must be developed - the "slice" moves aren't very

effective.

I also found an octahedron much more analogous to the cube then the

one with the 9 triangular faces (and independent vertices). ON this

one there is a triangular center, 3 diamond shaped corners, and longish

edges on each face. The centers are equivalent to the corners of a cube,

but monochromatic; the corners of the octahedron are equivalent to the

centers of a cube, but have 4 colors. You can solve it with supergroup

cube moves, but it can be solved more efficiently, I think, by doing

the corners first (matching up the colors), then the edges, then the centers.

Needed are moves that move edges without twisting corners (do we

have any good corner moves that don't rotate centers on a cube?)

One final puzzle that has come out - it's called Inversion, and it's

a sliding block cube. There are 19 identical cubies, each colored half

red and half blue (3 faces each) and arranged around the edges of a cube

with one extra empty space. They are held in place by a Rubiks-like

mechanism through the centers of the big cube. Thus each edge of the big

cube has 3 of the little cubes, or 2 of them plus a space. The little

cubes are each in one of the 8 possible orientations; One orientation

is represented by one cubie, 3 orientations by 2 cubies each, and 4

orientations by 3 cubies each. The idea is to slide the cubies around

the edges of the big cube so that the outside is all red or all blue,

or some other regular pattern; Inverting from (say) red to blue means

sliding all cubies to more-or-less the diagonal opposite positions.

-- Stan

-------