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Observations on the Magic Dodecahedron (Megaminx) -------------------------------------------------

I've never seen anything on patterns for the megaminx, with the

sole exception of Kurt Endl's book "Megaminx". Unfortunately there are

no detailed examples, only vague references to "many possible dot

patterns" and "star patterns". A pattern similar to the 6 X order 3

of the cube is on the cover, but only part of the dodecahedron is

visible.

Using the solving skills I developed myself, I deliberately solved

the megaminx with the centres not matching the surrounding face.

Techniques like mono-twists and mono-flips carried over well from

the cube.

My conclusion: A 10-dot pattern is possible!

Here is a description....

One pair of opposite faces is completely solid. The 5 faces adjacent

to solid face A are spotted, also the 5 faces adjacent to solid face

B (opposite to A) are spotted. If we look at one set of 5 faces we

can observe that in this particular 10-spot that the 5 centres

appear rotated to the left, or (since the centres don't really move

in position) that the rest of the face is moved to the right.

Similarly, in the lower tier of 5 faces, we can observe that 5 centres

appear rotated to the left also.

Let's try a small thought experiment. Imagine a skeleton, a

disassembled megaminx. Grab the top and bottom with thumb and

forefinger. Now, while keeping the top and bottom centres immobile,

rotate the rest of the puzzle. What happens? The 10 other centres

rotate in the same direction! If we do this on a cube skeleton the

same thing happens, but on a fleshed out cube this would become a

4 cycle of centres, which is in the swap orbit and can't be reached by

face turns. On the megaminx we have 2 five cycles of centres, and this

is legal.

There are 6 opposite pairs of faces on the megaminx. There are 4 ways

to rotate the centres for each pair to generate a 10 spot. I'll

speculate that there are 6*4 = 24 possible 10-spots.

I suspect various 12-spots are possible. I have no idea how to

easily permute centre pieces on the megaminx.

-> Mark <-