This is a puzzle consisting of two overlapping circular disks, reminiscent of other
circle puzzles such as Turnstile and Rashkey.
It actually most resembles the Cohan Circle but instead of 6fold
symmetry it has 3 fold symmetry, so it is as if you are playing on a Cohan Circle but restrict
yourself to only do 120 degree turns.
Each disk consists of 3 large diamond shaped pieces, and 9 small lozenge shaped pieces of
which 6 form the perimeter of the disk and 3 form spokes between the diamond pieces. The
two disks share a diamond and its four adjacent lozenges, so all together there are 5
diamonds and 14 lozenges.
The puzzle usually has three colours. In the solved state the overlapping area is one colour,
and the rest of the left disk a second colour, and the rest of the right disk a third colour.
The Triplex puzzle was invented by Douglas A. Engel, who also invented various other puzzles such as:
Mandorla is a neat version of the puzzle was produced in Hungary in 2013. It was invented by Ferenc Molnár, who also invented the Equator / Hungarian Globe puzzle.
If your browser supports JavaScript, then you can play the Mandorla/Triplex puzzle by clicking the link below:
There are 5 diamonds, and 14 lozenges. The lozenges however are split into two orbits
of 7 pieces which cannot intermingle.
Only even permutations are possible in each of the three orbits. If the pieces
were all unique this would give at most 7!^{2}·5!/2^{3} = 381,024,000
possibilities, and all of these positions are indeed attainable.
The standard version of the puzzle however has many identical pieces. The
set of 5 diamonds splits into 2+1+2 pieces of each colour, and the two sets of
7 diamonds each split as 4+2+1 into the three colours. This gives a total of
7!^{2}·5! / (2!^{4}·4!^{2}) = 330,750
possible positions.
I used a computer to calculate God's algorithm for the puzzle, and the results are shown in the tables below. The 3colour version needs at most 21 moves to solve (16.217 on average), and a version with unique pieces needs at most 33 moves (26.409 on average).
3colour version  Full version  




This solution assumes that you are using a version with 3 colours. If your puzzle has more colours, then this solution will not work. Further down this page I will give move sequences that cleanly swap some pieces, and those should suffice to solve any version of this puzzle.
Phase 1: Solve the five lozenge pieces in the left disk.
Phase 2: Solve the remaining lozenge pieces.
Phase 3: Solve the diamond pieces.
The sequences of phase 3 above move the diamonds without affecting the lozenges at all. Therefore I will list some sequences here that perform 3cycles of lozenges, with or without affecting diamonds. These are useful if you have a puzzle with a different colour design for which the solution above does not work.