From cube-lovers-errors@mc.lcs.mit.edu Tue Feb 9 20:27:47 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id UAA06044 for ; Tue, 9 Feb 1999 20:27:47 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <19990208030401.14755.rocketmail@send1e.yahoomail.com> 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