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Date: Sun, 22 Nov 1998 23:19:31 -0800 (PST)
From: Han Wen
Subject: Method for Solving the Megaminx
To: Cube-Lovers@ai.mit.edu
Hi,
Well, it took me a 2-3 days, but I finally solved the Megaminx. Whew.
I know, big deal. It's been done.. many many times... over a decade
ago. But, I thought some of the moves I found may of interest to some
of the Megaminx aficionados out there. So, here it is, I apologize
for its length:
Solving the Megaminx faces 1-11 are fairly straightforward.
Ironically, the larger number of faces makes it easier to solve than
the Rubik's cube, because they provide a lot more "free lanes" to move
pieces around. There's actually just one move you need to remember to
solve these faces. It's the same move when solving the middle layer
of the Rubik's cube, when you want to move edge pieces from the bottom
layer to their respective position in the middle layer. Namely,
D'R'DRF'RFR'
Solving the last face, however, is another matter. The general
strategy I followed is the same as some of the standard methods for
solving the bottom layer of the Rubik's cube. Namely, I first solve
the 5 corners, then I solve the 5 edge pieces. To solve the corners,
I simply used Sune's move applied with slight modification to the
Megaminx. For the remaining edge pieces, I had to develop moves that
only moved the edge pieces around, while leaving the corners
unchanged. Noel Dillabough's Puzzler program was an invaluable tool
for helping me experiment with various edge moves. Anyways, the
following are my notes describing some of the more useful moves I've
found. I'm pretty sure they're not the most efficient method for
solving the Megaminx, but they're the best I could come up with.
___________________________________________
Notation for Solving the Last Face corner pieces:
F=Front Face, D=Lower Face, L=Left Face, R=Right Face
The F and D faces are adjacent
The last layer containing the corners you need to flip/permute should
be positioned at the D-face
____________________________________________
Move for Solving the Last Face corner pieces:
Name: Sune's Double-Swap
Description: Sune's Rubik's Cube move applied to the Megaminx
Number of pairs of corners swapped: 2
Number of corners twisted counterclockwise: 3
Move: R'D'RD'R'D'3R
____________________________________________
Strategy for Solving the Last Face corner pieces:
- Position the corners
- Twist the corners in place by applying Sune's Double-Swap
move twice
============================================
Notation for Solving the Last Face edge pieces:
F=Front Face, U=Upper Face, L=Left Face, R=Right Face
The F and U faces are adjacent
X= L'R U2 LR' F2
X'=L'R U'2 LR' F'2
X2= X X = (L'R U2 LR' F2) (L'R U2 LR' F2)
Xa= L'R U2 LR' F'2
Y= LR' F2 L'R U2
The last layer containing the edges you need to flip/permute should be
positioned as the F-face or the U-face depending on the move described
below:
_____________________________________________
Moves for Solving the Last Face edge pieces:
Name: F Tricycle 1
Description: Permutes 3 adjacent edges clockwise on the lower left of
the F-face
No. Edges permuted: 3
No. Edges flipped: 2
Move: (Xa3 X'2)^2
Name: F Tricycle 2
Description: Permutes 3 adjacent edges clockwise on the upper half of
the F-face
No. Edges permuted: 3
No. Edges flipped: 2
Move: (Xa3 X2)^2
Name: U Tricycle 1
Description: Permutes 3 edges clockwise on the U-face
No. Edges permuted: 3
No. Edges flipped: 2
Move: F' X2 Y'2 F
Name: U Tricycle 2
Description: Permutes 3 edges counterclockwise on the U-face
No. Edges permuted: 3
No. Edges flipped: 2
Move: F X'2 Y2 F'
Name: Cross-country Tricycle
Description: Permutes 3 edges across the U and F faces
No. Edges permuted: 3
No. Edges flipped: 1
Move: (X2 X'2)^4
Name: U Bi-Flip 1
Description: Flips two opposite edges on the U-face
No. Edges permuted: 0
No. Edges flipped: 2
Move: (Xa3 X'2)^3
Name: U Bi-Flip 2
Description: Flips two adjacent edges on the U-face
No. Edges permuted: 0
No. Edges flipped: 2
Move: (X2 X2 X'2)^5
Name: Cross-country Bi-Flip
Description: Flips two edges, one on the U-face, one on the F-face
No. Edges permuted: 0
No. Edges flipped: 2
Move: (Xa3 X2)^3
Name: "W"-Cycle
Description: Permutes all edges on the F-face in a "W" pattern
No. Edges permuted: 5
No. Edges flipped: 2
Move: (X2 X2 X'2)^2
Name: "Figure 8"-Cycle
Description: Permutes all edges on the F-face in a "Figure 8" pattern
No. Edges permuted: 5
No. Edges flipped: 4
Move: (X2 X2 X'2)^4
____________________________________________
Strategy for Solving the Last Face edge pieces:
- You should only need to use F Tricycle and the Bi-Flip moves to
completely solve the edges. The F Tricycle move usually needs
to be applied twice.
If anything is vague/unclear please feel free to request clarification.
-Han Wen-