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Date: Sun, 7 Feb 1999 19:04:01 -0800 (PST)
From: Han Wen
Subject: Moves for Solving the Pyramorphix puzzle
To: Cube Lovers
Hi
For those cube masters out there getting bored, you may want to play
with Meffert's latest puzzle, the Pyramorphix. It only takes about
1-2 hours to solve, but it provides some Square-1-like entertainment.
For those who may not be familiar, the Pyramorphix looks like the
Pyraminx's little brother with 4 pieces instead of 9 pieces for each
face. However, unlike its big brother, the Pyramorphix turns a lot
differently (90 deg rotations), morphing into different shapes as you
twist and turn. As you know, with the Pyraminx, you're always
rotating little pyramids about one of the 4 tips. However, with the
Pyramorphix, when starting out with the pyramid shape, you rotate an
edge and its two adjacent corners (i.e. the whole edge of a given
face). The rotation axes lie along the intersection of the 4 center
triangle pieces.
There appears to be 6 general shapes you can "morph" the Pyramorphix
into I'll affectionately call: the Pyramid, the Butterfly, the Crown,
the Rocket, the Airplane and the truncated Star of David. (There are
actually two truncated Star of Davids, mirror images of one another).
You'll know what I mean if you actually have the little creature in
your hands. The hardest part of this puzzle is figuring out how to
morph between all these different shapes.
I solve the Pyramorphix by first solving the 4 corner pieces and then
orienting the 4 center pieces.
First, a few notation definitions. Hold the Pyramorphix so that you
have one of the faces facing you. I'll call that face Front (F). The
face on the bottom will be called Down (D), and the faces left and
right of the F face will be called Left (L) and Right (R) respectively.
An edge will refer to a center piece and its two adjacent corner
pieces. I'll specify which edge by indicating the two faces the edge
intersects (e.g. R-D edge is the edge formed by the interesection of
the Right and Down faces).
Now, unfortunately, I can't just refer to rotations of edges, because
as you'll see, sometimes you need to rotate strange shapes that look
nothing like an edge. Instead, it's better to refer to slices.
Namely the plane about which one of the edges rotates on. So, if you
look at the F face, you'll see three slices: the R-D slice (60 deg),
the L-D slice (120 deg) and the horizontal F-slice (0 deg). When the
Pyramorphix is in its pyramid shape, you can rotate the two edges on
the R-D and L-D slices, but you cannot rotate the corner piece sitting
on the F-slice. Don't worry, when we morph the pyramid into the
Rocket, you'll see that you'll be able to rotate the tip of the rocket
about the F-slice.
Now, that I've thoroughly confused you, here are my notations for
actual moves:
R - 90 deg clockwise rotation about the R-D slice
L - 90 deg clockwise rotation about the L-D slice
F - 90 deg clockwise rotation about the F-slice
R2 - 180 degree rotation about the R-D slice
R' - 90 degree counterclockwise rotation about the R-D slice
Finally, hold the Pyramorphix in your hands, so the the F-face is
facing towards you with the tip of the triangle pointing up. If you
now rotate the puzzle so the the D-face is facing towards you, you
should see an upside-down triangle with the tip pointing down. I will
refer to the three corner pieces that you see as:
DL - left corner piece
DR - right corner piece
DM - middle corner piece
_______________________________________________________
To solve the four corner pieces, first get them in their proper
positions by performing 180 rotations of the edges. Now, you need to
orient the corners by making appropriate clockwise or counterclockwise
twists. Here are some moves to do this:
Name: Single corner twister
Move: (R L' R' L) ^2
Shapes: Butterfly - Star of David - Airplane - Airplane - Star of
David - Star of David - Butterfly - Pyramid
Action: Clockwise (CW) twist of DM corner
Name: Left-side double corner twister
Move: (R L R' L' ) ^2
Shapes: Butterfly - Star of David - Crown - Star of David - Crown -
Star of David - Butterfly - Pyramid
Action: CCW twist of DL corner, CW twist of the DM corner
Name: Right-side double corner twister
Move: (R' L' R L) ^2
Shapes: Butterfly - Star of David - Crown - Star of David - Crown -
Star of David - Butterfly - Pyramid
Action: CCW twist of DR corner, CW twist of the DM corner
Name: Triple corner twister
Move: (R' L R L') ^2
Shapes: Butterfly - Star of David - Star of David - Airplane -
Airplane - Star of David - Butterfly - Pyramid
Action: CW twist of DL corner, CW twist of DR corner, CCW twist of DM
corner
_______________________________________________________
Now, to orient the center pieces in place, here are some moves to do
this:
Name: Double edge swapper
Move: R' L2 F2 L2 R
Shapes: Butterfly - Rocket - Rocket - Butterfly - Pyramid
Action: Swap F <--> L and R<-->D center pieces
Name: Tricycle swap
Move: (L R2 F' R2 L') (R' L2 F L2 R)
Shapes: (Butterfly - Rocket - Rocket - Butterfly - Pyramid ) ^2
Action: Permute F --> R --> L --> F center pieces
Name: Edge swapper
Move: (R' L2 F L2 R) (L R2 F R2 L') (R' L2 F L2 R)
Shapes: (Butterfly - Rocket - Rocket - Butterfly - Pyramid ) ^3
Action: Swap F <--> D center pieces
With these short collection of moves, you should be able to readily
solve the Pyramorphix...
_______________________________________________________
Epilogue:
So, you've solved the Pyramorphix, bored silly and you want to know
what's next?! Check out Meffert's Puzzle Ball. It's actually a bit
more challenging. Happy puzzling.... :)
==
_________________________________________________________
Han Wen
Applied Materials
3050 Bowers Ave, MS 1145
Santa Clara, CA 95054
e-mail: Han_Wen@amat.com / hansker@yahoo.com