This is a variant of the Rubik's cube, in the shape of a dodecahedron. It is a very
logical progression from the cube to the dodecahedron, as can be seen from the fact
that the mechanism is virtually the same, and that many people invented it
simultaneously. To quote from
Cubic Circular, Issue 3&4, (David Singmaster,
"The Magic Dodecahedron has been contemplated for some time. So far I have seen
photos or models from: Ben Halpern (USA), Boris Horvat (Yugoslavia), Barry Lockwood (UK)
and Miklós Kristóf (Hungary), while Kersten Meier (Germany) sent plans
in early 1981. I have heard that Christoph Bandelow and Doctor Moll (Germany) have
patents and that Mario Ouellette and Luc Robillard (Canada) have both found mechanisms.
The Hungarian version is notable as being in production ... and as having planes
closer to the centre so each face has a star pattern."
"Uwe Mèffert has bought the Halpern and Meier rights, which were both filed on
the same day about a month before Kristóf. However there is an unresolved dispute
over the extent of overlap in designs."
There are several versions that have been made.
The standard megaminx has either 6 colours or 12 colours. The face layers are
fairly thin, so the edge pieces have some width to them.
A version called the Supernova was made in Hungary, and it has 12 colours and
thicker face layers which meet exactly at the middle of an edge.
The Ball.B is a spherical of this puzzle. The version with flags on the faces has the
extra complication that the orientation of the centres are visible, making it more difficult.
The Holey Megaminx is a version without face centres, inspired by the Void Cube.
Related puzzles are Alexander's Star, which is
equivalent to a megaminx without corners or centres, and the
Impossiball, which is equivalent to a megaminx
without edges or centres.
The number of positions:
There are 30 edge pieces with 2 orientations each, and 20 corner pieces with
3 orientations, giving a maximum of 30!·20!·230·320 positions. This
limit is not reached because:
- only even permutations of edges are possible (2)
- only even permutations of corners are possible (2)
- only and even number of flipped edges are possible (2)
- the total twist of the corners is fixed (3)
This leaves 30!·20!·227·319 =
or 1.0·1068 positions.
If only 6 colours are used, giving 15 pairs of indistinguishable pieces,
then this number has to be divided by 214 (not 215 since only an even
number of swaps are possible) which gives
or 6.1·1063 positions. Despite these huge numbers, the puzzle is no harder than
the Rubik's cube.
If the face centres have visible orientations, then the number of positions is
multiplied by a factor 512 because each of the 12 centres can be twisted
independently. A super-megaminx with 12 colours therefore has
or about 2.5·1076 positions.
Let U, R, F be three adjacent faces (Up, Right and Front), in other
words, U, R, F are faces arranged clockwise around a vertex. Let D be the
other face adjacent to both F and R. Clockwise 1/5 twists of a face are
denoted by the appropriate letter, anti-clockwise 1/5 twists by U', R', F' or D'.
In the solution below, the D face is usually still unsolved. We can denote
the locations of the edge pieces by using two letters, for example UF is the
edge location that lies in both the U and F faces. Similarly, corner locations
are denoted by three letters as they lie in three faces.
If you can solve the top and middle layer of the Rubik's cube, then you
can use the same techniques on the megaminx to solve everything but the
Phase 1: Solve all but final face
- Solve the edge pieces of one face. This is easy to do and need not be
explained in detail. Let that face be the U face.
- Solve the corners of the U face as follows:
1. Find a corner that belongs on the U face.
2. Hold the puzzle so that the corner belongs at URF, and that face D
3. Use any turns that do not disturb already solved pieces to place
the corner at RDF.
4. Use one of the following sequences to place the corner:
DFR->URF: R'DR FD'D'F'
These sequences only disturb the FR edge piece and the D layer, but
nothing else except for the corner. The sequences differ only in the
orientation of the corner. If you use the wrong sequence for your situation,
the URF corner can be twisted in place by R'DR FDF'.
5. Repeat 1-4 till done. If necessary you can use to use this method
to displace a corner that you need somewhere else.
- Place all yet unsolved edges adjacent to the solved corners. This is
similar to placing the corners, except that you use the following
sequences to place them:
DR->FR: DFD'F' D' R'DR
FD->FR: D'R'DR D FD'F'
These sequences only disturb the D layer, but nothing else except
for the edge. If an edge is in position but flipped, then displace it
by placing any other edge piece there with one of the sequences, and then
insert the edge piece in the correct orientation.
- Repeat steps b-c to solve each adjacent face in turn, until only one unsolved face is left.
In the phases below, we need to have names for all the faces adjacent to the D face in order to
describe all the possible pieces on the D face. Lets call these faces in clockwise order: L, F, R, b, B.
Phase 2: Orient the edges of the final face.
The edges are flipped in pairs. It is impossible to have only one edge
- Hold the puzzle so that the unsolved face is D, one edge to be flipped
is at DR, and another is either at DL or DF.
- Do one of the following sequences to flips the edges:
To flip DF, DR, do R D F D' F' R'
To flip DL, DR, do R F D F' D' R'
- Repeat the above if necessary.
Phase 3: Position the edges of the final face.
- Rotate D to place as many edges as possible in their correct places.
If, like Alexander's Star, your megaminx has only 6 colours, you might
find that the edges are in an odd permutation. In this case you will
have to swap any two identical edges elsewhere on the puzzle and try
solving it again.
- Hold the puzzle so that you can use one of the following sequences to
1. DR->DF->DL->DR: R D R' D R D'D' R'
2. DR->DL->DF->DR: R DD R' D' R D' R'
3. DR->DF->DB->DR: R D R' DD R DD R'
4. DR->DB->DF->DR: R D'D' R' D'D' R D' R'
5. DR-DB, DF-DL: R D R' D R D' R' DD R DD R'
Phase 4: Position the final corners.
- Hold the puzzle so that you can use one of the following sequences to
1. DFR->DLF->DBL->DFR: RUR' D RU'R' D RUR' D'D'RU'R'
2. DFR->DBL->DLF->DFR: RUR' DD RU'R' D' RUR' D' RU'R'
3. DFR->DLF->DbB->DFR: RUR' D RU'R' DD RUR' DD RU'R'
4. DFR->DbB->DLF->DFR: RUR' D'D'RU'R' D'D'RUR' D' RU'R'
5. DFR-DbB, DLF-DBL: RUR' D RU'R' D RUR' D' RU'R' DD RUR' DD RU'R'
Note the similarity between these sequences and those of phase 3.
Phase 5: Orient the final corners.
- Hold the puzzle so that the DFR corner needs to be twisted
anti-clockwise. If there is no such corner, then put a different twisted
- To turn DFR anti-clockwise, and another clockwise, do one of these:
1. DFR->RDF, DLF->LFD: RU'R'F'U'F D F'UFRUR' D'
2. DFR->RDF, DBL->BLD: RU'R'F'U'F DD F'UFRUR' D'D'
3. DFR->RDF, DbB->bBD: RU'R'F'U'F D'D' F'UFRUR' DD
4. DFR->RDF, DRb->RbD: RU'R'F'U'F D' F'UFRUR' D
- Repeat the above until all corners are correct.
Phase 6: Orient the centres (for some types of megaminx only).
- Hold the puzzle so that the D face has a centre that needs to be twisted.
- The following sequences twist the centre by the amounts listed:
1. Once clockwise: F'F' RR FF D R'R' D performed three times
2. Once anti-clockwise: RR F'F' R'R' D' FF D' performed three times
3. Two steps clockwise: R' DD R D R' DD R F' DD F D F' DD F DD
4. Two steps anti-clockwise: F' D'D' F D' F' D'D' F R' D'D' R D' R' D'D' R D'D'
- Repeat the above until all centres are correct.