How do you solve the Megaminx (the dodecahedral Rubik's-type puzzle with 12 faces of 10 moving pieces each)?

[ Editor: from the web page "Megaminx" in "The Simplest Solutions"
(http://www.victoria.tc.ca/~ue451/solves.html); the author is not named
in the collected copy. ]

Combinations: 1.0*10^68
Mechanism: 12 armed spider

This puzzle's one of the most intimidating looking of the lot, having 12 faces
with 10 moving pieces each, but this method is so simple it'll make you puke.
Well, not literally (I hope). Each side is a pentagon shape that looks roughly
like this:

                        _-_
                      _-   -_
                    _- -_ _- -_
                  _-\   _-_   /-_
                  \  \_-   -_/  /
                   \_-\     /-_/
                    \__\___/__/
                     \  \ /  /
                      \__V__/

Well... you get the idea. In order to solve the Megaminx, we'll first attack
the edge pieces, and then the corners.

NOTATION

Hold the Megaminx with the front face as shown above. Each corner, edge, and
face will be represented by a number. The front corners are numbered from 1-5
starting from the top and proceeding clockwise. The front edge pieces and the
other faces they're attached to are numbered from 1-5 clockwise starting with
the top right. The front face is always 0. When dealing with pieces on the
front face, only the piece number will be used. When dealing with pieces on
other faces, they'll be mentioned in the form (face number, piece number). The
pieces on adjacent faces will be designated as they would be if the adjacent
face was at the front and the present front was on the bottom, ie. the adjacent
colours for each edge piece is designated as position 3, and the corner pieces
are in positions 3 and 4. Each piece in the adjacent sides maintains the
clockwise naming system. Each rotation will be given as a face number and a
number of + or - signs. A + designates a clockwise turn, and a - designates a
counterclockwise turn. ++ and -- mean turn the face twice clockwise or
counterclockwise respectively. And now, on to the solution...

THE SOLUTION

STEP 1: The top edges

These are practically a no brainer. Merely pick a centre to work with. Find the
edge pieces in question and move them into the proper place on the top layer.
If the piece you need to move is in the second layer in such a way that it
affects a properly positioned top edge, make sure you move the piece in
question out of the way first, and then move the correct edge piece back. If
a top edge piece is correctly placed but incorrectly flipped, then orient the
Megaminx so the top side is either side 1 or side 5. If it's:

Side 1: 0-- 3+ 2+ 0--
Side 5: 0++ 3- 4- 0++

STEP 2: Layer 2 edges

This is slightly more difficult, but still no problem. Locate the edges which
belong just below the top layer, and move it as necessary to get the edge into
the third layer in such a way that one of the colours matches the face colour,
and then rotate the puzzle so that the edge is in position 3. If it needs to
move into:

Position 2: 3- 0+ 3+ 0-
Position 4: 3+ 0- 3- 0+

Be careful not to destroy the top layer as you work on the second. If a piece
belonging in the second layer is already in the second layer but in the wrong
position, position the edge in either position 2 or 4 and perform the relevant
pattern shown above.

STEP 3: Layer 3 edges

This layer is unique in that it has 10 edge pieces to deal with instead of the
usual 5. First of all, we need to get the piece in question on to the bottom
layer. Make sure the bottom layer is side 3. If the edge piece is in position:

1: 0++ 3+ 0--
2: 0+ 3+ 0-
4: 0- 3- 0+
5: 0-- 3- 0++

Then rotate side 3 until a colour of edge 3 matches the colour of side 0. If
it has to be moved to:

Position 1, colour flipped: 3+ 0+ 2+ 0- 2-
Position 1, colour matched: 3+ 0++ 3- 0--
Position 5, colour flipped: 3- 0- 4- 0+ 4+
Position 5, colour matched: 3- 0-- 3+ 0++

STEP 4: Layer 4 edges

First thing we need to do is, once again, get the any necessary edges from
layer 4 to the bottom. Once again, the bottom is side 3. We do this by moving:

Edge 2: 2- 3- 2+
Edge 4: 4+ 3+ 4-

Rotate side 3 until the necessary edge piece gives an exact match of one of the
centres. Then if it needs to move to:

Edge 2: 3+ 0+ 3- 0-
Edge 4: 3- 0- 3+ 0+

STEP 5: Positioning the bottom edges

Now the fun REALLY begins. Up until now, we've basically been able to kludge
the edge pieces together because we didn't have to worry about destroying any
layers below the one we were working on, but now our room's run out. Now it's
do or die time. First off, rotate the bottom layer to match up as many edges
as possible. 2 edges is quite common, but you may only be able to get 1. If
you can line up all 5, consider yourself lucky and go to step 6. If there's 3
lined up, sorry, you'll have to take the Minx apart again and reassemble it
properly this time. You'll need to do the same thing if you have 1 edge
flipped, 2 corners swapped, or 1 or 2 corners rotated the same way at the
end of each successive step later on. There are 2 basic patterns to deal with
here... the first for edges which are all adjacent to each other, and the
second for a gap between the edges. Each pattern will be mirrored, so just use
whichever you feel most comfortable with. Inside the brackets are the basic
patterns from which the more complex ones are derived.

Rotate (3,1), (3,2), (3,3): 0+ (4+ 3+ 4- 3-) 0- (CCW)
Rotate (3,3), (3,4), (3,5): 0- (2- 3- 2+ 3+) 0+ (CW)
Rotate (3,1), (3,2), (3,4): 2+ 0++ (4+ 3+ 4- 3-) 0-- 2- (CCW)
Rotate (3,2), (3,4), (3,5): 4- 0-- (2- 3- 2+ 3+) 0++ 4+ (CW)

STEP 6: Flipping the bottom edges

Again, there will be the same basic patterns: either the edge pieces will be
adjacent or there will be a gap, so there will be 2 basic patterns mirrored
once again.

Flip (3,1), (3,2): [4- 4+] 3+ 4- 3+ 0- 3- 0+ 3- 4+
Flip (3,4), (3,5): [2+ 2-] 3- 2+ 3- 0+ 3+ 0- 3+ 2-
Flip (3,1), (3,3): 0+ 4+ 3+ 4- 3+ 0- 3- 0+ 3- 0-
Flip (3,3), (3,5): 0- 2- 3- 2+ 3- 0+ 3+ 0- 3+ 0+

We're almost done! Now on to the corners...

STEP 7: Positioning the corners

For this step, there is only ONE pattern which you need to worry about. Pick
whichever one you feel most comfortable with. On second thought, learn both.
You'll need them soon.

P1: Rotate 2, 3, 5: 2- 3- 4+ 3+ 2+ 3- 4- 3+ (CW)
P2: Rotate 2, 4, 5: 4+ 3+ 2- 3- 4- 3+ 2+ 3- (CCW)

Every other rotation is just a derivative of these 2 patterns. For example:

Rotate 3, 4, 5: 2+ P1 2-
Rotate 2, 3, 4: 4- P2 4+

Just be sure that your prefixes are exact inverses of your postfixes, eg. the
inverse of 4+ 3- would be 3+ 4-, ie. reverse the move order and flip the signs.

STEP 8 [Editor: numbered "STEP 7" again in the original]: Rotating the
corners

We're in the home stretch now! This is the final step! If you've mastered step
6, this one will be a piece of cake. In each of these patterns, the colour on
the front of the Minx will be rotated UPWARDS, ie. whatever's on the right will
be rotated clockwise, and whatever's on the left will be rotated
counterclockwise. Once again (are you seeing a pattern here? [no pun
intended]), we have one basic pattern mirrored depending on your preference.

[ Editor: the patterns below are built from P1 and P2 of step 7, so
"step 6" above probably means step 7. ]

P3: Rotate 2 and 4: P2 0-- P1 0++
P4: Rotate 3 and 5: P1 0++ P2 0--

Every other rotation can be derived from these 2 basic patterns. For example:

Rotate 3 and 4: 2+ P3 2- OR 4- P4 4+

If they need to be turned in the opposite direction, then position them as 2
and 5, and then:

Rotate 2 and 5: 4+ P3 4- OR 2- P4 2+

For the 0--/0++ moves, you'll probably find it quicker and easier to simply
rotate the whole Minx.

                     C O N G R A T U L A T I O N S ! ! !

You have just completed one of the hardest puzzles ever made! Give yourself a
good, solid pat on the back. Better yet, go out and celebrate. It's party time!
Unfortunately, I haven't been able to devise any patterns to leave you with,
and all the patterns I've found elsewhere on the net work flawlessly... IF the
purpose of the patterns is to leave you with a big mess. If any of you know of
any patterns at all for the Minx which actually WORK, then PLEASE e-mail them
to me ASAP and I'll include it on this page. Most important of all, HAVE FUN!