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
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