[next] [prev] [up] Date: Mon, 09 Sep 91 00:48:09 -0400 (EDT)
~~~ [prev] [up] From: phil servita <meister@gaak.lcs.mit.edu >
[next] ~~~ [up] Subject: Square One

"Square One" is also available at Games People Play in Cambridge, Mass.
I just purchased one a few days ago. It turned out to be more interesting
than i had expected. The puzzle is comprised (essentially) of two halves
of 8 pieces each, 4 corners, and 4 'edges'. All pieces radiate outward from
the center. The 'edge' pieces expand outward at a 30 degree angle, while
the corners expand outward at a 60 degree angle. The center layer is composed
of just 2 pieces. If you removed the top slice, the center slices would trace
out quadrilaterals ABIK and BDJL (or ACIJ and BDKL, etc) below.

The center slice serves no major function save as a "gate"
which allows or disallows rotation about one of the skewed axes formed by
the two slices. To rotate about some axis you must line up the "gate"
with the axis. While it is possible to swap the center pieces with respect
to the corners frame of reference, doing so is really of no importance
to the "meat" of the puzzle.

Top View: (in lousy ascii resolution)

 A             B             C             D
  |             *           *              |
  |              *         *               |
  |               *       *                |
E *                *     *                 * F
  |     *           *   *            *     |
  |            *     * *     *             |
  |                   * O                  |
  |            *     * *     *             |
  |     *           *   *            *     |
G *                *     *                 * H
  |               *       *                |
  |              *         *               |
  |             *           *              |
  I            J             K             L

Side View:

|      |     |      |
|______|_____|______|  top
|      |            |  
|______|____________|  center "gate" lined up for left axis 
|      |     |      |
|______|_____|______|  bottom

All meaningful moves either rotate the top or bottom face, line up the
center gate with some skew axis, or twist about a skew axis 180 degrees.
The neat thing about the puzzle is that moves do not necessarily preserve
the cube shape of the puzzle, or even the number of corner/edge pieces
that are on each side. It is possible, for instance, to have only 3 corners
on the top face, and 6 edges, while 5 corners and 2 edges are on the bottom

A notation for this beast is somewhat cumbersome. If anyone wants, I will try
to describe what i am using.

After playing with it for a few hours, i *thought* i had mapped out a complete
solution algorithm; however i was later playing with the wierd shapes you could
put the puzzle into, and eventually started putting it back to "Square One",
and was very surprised to end up in a position with just 2 of the edges
swapped! Since this puzzle acts much like the Skewb, each move essentially
cutting the puzzle in half (ignoring the gate layer), i did not expect this
to be possible. It took a bit of thought before the light hit, and i went
on to construct a crude "Parity Swap" transform. Currently the best one i have
found cycles around UF -> UL -> UB -> UR, and takes 28 'moves'. (a 'move'
being defined as any motion of some slice, regardless of degrees turned)
Anyone else found anything better?

Square One is one of the better variations on the cube theme i have seen
in a long time. Find one and have fun.


[next] [prev] [up] [top] [help]