Message #1002

From: "Galla, Matthew" <mgalla@trinity.edu>
Subject: Re: [MC4D] a 3d puzzle based on the small stellated dodecahedron
Date: Wed, 14 Jul 2010 18:51:30 -0500

And I can give some insights on solving it ;)
The puzzle you have described is equivalent to a subgroup of the gigaminx
puzzle, which many people worldwide already know how to solve ( a virtual
gigaminx can be found here:
http://users.skynet.be/gelatinbrain/Applets/Magic%20Polyhedra/dodeca_f8.htm)
Specifically, your puzzle only has the edge-face pieces. The attachment
shows the solved subset of your puzzle using the same color scheme you have.
You’ll notice this doesn’t look solved and that is because your coloring
scheme distributes colors a little strangely (by no means a bad thing!) This
makes the resulting puzzle not necessarily harder but undeniably more
disorienting as it is difficult to tell when a given piece is correct. You
have also used the same colors on the opposite sides of the puzzle which
again adds to the disorientation, but not necessarily difficulty of the
puzzle. Finally a little quirk I should point out. Your puzzle has the moves
labelled "pyramid" and "star". A third option (depending on how you look at
it) is doing a "pyramid" and "star" move on the same face. The gigaminx also
has 3 potential moves for a single face as well: outer layer, inner layer,
and both layers. Because your "star" move does not move the pyramid as well,
the moves correlate as follows:
pyramid = outer layer
star = inner layer
pyramid and star = both layers
This should seem obvious. The quirk is that on a physical Gigaminx people
typically use either outer layers or both layers. Inner layer moves are
quite rare because they are more difficult to perform (one would turn both
layers and then put the outer layer back) and in general not needed for many
solutions. However your puzzle makes the "star" move the easier move to
access. This could be confusing at first to anyone trying to see the
similarity between the Gigaminx and your puzzle. (On the virtual gigaminx
above, the inner layer actually is an option, so this entire argument really
only applies to the analysis and a physical gigaminx).

I won’t give details on solving but looking at the gigaminx subset, these
pieces are actually pretty easy to solve alone since no outer layer turns
(aka pyramid moves) have any pieces in common. Simple commutators can be
implemented to solve this puzzle, provided you can correctly determine where
each piece goes. The unusual placement for the colors is more than a little
disorienting. By the way the correct placement for any piece on this puzzle
is not unique. i.e. any red piece can go in any spot that eventually needs a
red piece. There is a parity restriction on the puzzle. If it seems that two
pieces need to swap places at the end, it actually means that you must also
swap to identical pieces.

Good luck on this project. It is a good idea that I don’t think has ever
been made,
Matt Galla