   Date: Mon, 23 Oct 95 13:33:08 -0400   From: David A. Bagley <bagleyd@source.asset.com >
~~~ ~~~ Subject: pyraminx-like puzzles (yet again)

Hi
> Recently I asked the question:
> > I have a question, I hope this makes sence. ;) On a "nxnxn"
> > tetrahedron with period 2 or period 3 turning or a "nxnxn" octahedron with
> > period 3 or period 4 turning, can the orientation of any of the center
> > triangles change when the puzzle is solved? If so, where does this
> > start to happen. I know from "experience" that this is not true on
> > a pyraminx.

The reported to answer to * was incorrect
> Well, if you believe proof by example on a simulated puzzle, then
> Tetrahedron period 2 turning: never happens
> Tetrahedron period 3 turning: starts when n=4 with center triangle
> Octahedron period 3 turning: starts when n=4 with center triangle *
> Octahedron period 4 turning: starts with n=4 with center triangle

It should be:
Octahedron period 3 turning: starts when n=2 with center triangle

The case where n = 3 (here there is no one center triangle) was interesting
because there seemed to be no easy repetition of moves where the colors of
the puzzle would be solved but the orientation of the triangles would
be changed.

```     /\
/__\
/\C /\
/__\/__\
/\C /\C /\
/__\/__\/__\
```

After much experimentation, I found a way of rotating
3 center triangles on a face which involved 216 moves, (this can be bettered
by one noting that 2 clockwise rotations = 1 counterclockwise rotation):

Repeat 5 times
{
With reference to the top "C" in diagram, turn center to the right and
then rotate face clockwise for a total of 42 moves. One will then get
a pattern where only 3 center colors are out of place on 3 different faces.
rotate this face clockwise
}
rotate this face clockwise

New versions of my pyraminx and octahedron puzzles are now out.
Cheers,
clockwise

```New versions of my pyraminx and octahedron puzzles are now out.
Cheers,
--__---------------------------------------------------------------
/  \ \   /           David A. Bagley                                \
|    \ \ /            bagleyd@source.asset.com                        |
|     \//\            Some days are better than other days.           |
|     / \ \                -- A short lived character of Blake's 7    |
\   /   \_\puzzles   Available at: ftp.x.org/contrib/games/puzzles  /
-------------------------------------------------------------------
```     