Sunday, 26 January 2020

The Rua Required a Transformation of my Mind

The 12 Axis Dodecahedron aka the Rua
This might be my last ever post on the blog as I might be arrested and convicted of a murder within the next few days! I have passed on my very minor cold to Mrs S and she has incubated it and multiplied it until it is probably a mix of She-bola/SARs/Chinese coronavirus along with pneumonic plague (even the rats have been seen running in fear away from our house. The sound-effects have been truly grizzly here in PuzzleMad HQ and the incessant coughing has been impairing my beauty sleep. Those of you who have met me, know very well how much I need more beauty! I am on the verge of holding a pillow over the source of the coughing which my years of airway experience tells me is probably not a good idea and might end up with a visit to "Her Majesty's Hotel", Broadmoor. So on to the next/maybe last puzzle review...

I figured it was well past time that I wrote about a twisty puzzle. I've not really had much luck solving them recently and finally, after a change in my mindset, I finally solved one that I have been working on for 9 months on and off. Pictured above is the 12 axis dodecahedron by Lanlan which should really have been called the Rua, the original name given to it by Matt Shepit in 2008. Many people had wanted a copy of this puzzle but could not afford the massive prices that Shapeways had been charging to make one. This is a Dodecahedron like so many other puzzles I have reviewed before but unlike most of them, this is a rhombic dodecahedron which completely changes the approach. We were all very surprised and delighted when LanLan produced this although a little mystified why they had ignored the original name.

I bought my copy from the HKNowstore along with a bunch of other puzzles at the same time way back in May last year and immediately set to looking at the turning and wanting to see if there were any easy algorithms. It certainly is nice and smooth and quite quickly you can see one of the quirks of the rhombic geometry:

A single 180º face turn
A partial face turn allows it to be jumbled - 2 turns only
The rhombic face shape means that a 180º rotation of a face keeps the puzzle shaped like a rhombic dodecahedron, however, it is possible to turn a face a partial turn to align the edges of adjacent sides and then turn the next-door face which creates a very odd shape - effectively the puzzle becomes jumbled as pieces are taken out of their normal orbits.

This frightened me to death so I quickly undid it and made sure that it stayed in true shape for the majority of my puzzling. As is usual I did sequences of 2 face turns and three face turns (L, R, L, R or L, R, U, L, R, U etc) and discovered a nice feature that allowed me to swap about 2 pairs of the small inner triangles. I thought that this might come in handy later. I then tried a few turns of the faces to see what I could do with the corners and, as usual, got lost and scrambled it by accident:

"Just" a 180º scramble
This happened in June and I have been playing with it ever since! I think I have carried it with me everywhere since then and taken it out to play frequently. You guessed it...up until now, I have gotten nowhere with it! My main reason? I am seriously not very bright! Apart from that, I have been trying to solve it either layer by layer complete or layer by layer corners first and just could not work it out at all.

A week or so ago I tried again and for some reason decided that I should practice my counting (definitely not very bright) and a thought suddenly occurred to me (maybe not so sudden if it has taken 8 months!) - maybe I need to hold the puzzle a different way and think of it as a different shape? What made me think about this? There are 2 different types of corners to the puzzle. There are 4 colour corners (6 of them) and shallow 3 colour corners (8 of them). What does this remind you of? No? Well, it took me a long time as well! If you think of the 4 colour corners as centres of a cube and the 3 colour corners as true cube corners then suddenly a change of image might occur to you. This puzzle is a shape transformed cubic puzzle where the faces that turn are actually edge turns of the cube, like a helicopter cube or curvy copter. In particular, it seems this puzzle is a shape mod of the Curvy copter 3. Have a look at the pictures below to visualise the change of perspective:

Old face up perspective
Turned on its corner
In the right-hand picture, notice that the 4 colour corners are now in a centre position and we can see the top four 3 colour corners which are in the position where a cube's corners should be. The new centres each have 4 small triangles around them and when a face is turned 180º, the 2 corners and centres swap over. Think of this like the curvy copter 3 below:

Notice the centres with 4 triangles around them
The Rua is missing the petal-shaped pieces
Having finally had this wonderful epiphany, I set to attempting a solve. Starting with "corners" aka 3 colour corners first. This was now easy! Until I attempted to place the "centres"! It would appear that the moves of this puzzle MUST be done in a strict order to prevent ruining the orientation of the centres (after all it is effectively a "super-cube". After I ruined it a few times, a little experimentation revealed my error and I just needed to keep track of the order I turned the faces for each algorithm.

I also discovered that in my first attempt using this approach, there was a sort of parity. I managed to create it in such a way that I had either all centres correct and 2 corners needing to swap or vice versa. I spent a day trying to swap things around in multiple directions until I had another epiphany...I had placed the corners in such a way that I had placed a face in the space adjacent to where it was supposed to go. Thinking of the cube above, the centres are not fixed and I had inadvertently swapped the red and the blue colours which ensured the puzzle could not be solved.

I resolved the corners on the correct faces using the methods required for the Curvy copter and using all the same algorithms (but needing concentration to keep my head right) and I was left with only the triangles to place. Recalling my simple 4 or 6 move cycle that I had found initially 9 months previously, I tried to use it to move the triangles where they needed to go and...no bloody way was that going to work! Time to get my Curvy copter 3 out again and play. I had been very impressed with that puzzle all those years ago because it was one of the first puzzles where I had been able to design my own commutator for it.

Cycling triplets
Swap around the front 2 triangle
An L, R, L, R sequence cycles the three highlighted triplets as shown. If we do a B, F, B sequence it splits off the top front triangle from the triplet and replaces it with the one from below. Undoing the 4-move and then the three move sequences, in turn, creates a 3 cycle of triangles. This is exactly what I found in the Curvy copter 3 and worked perfectly for the Rua.

I have a "simple" 3-cycle!
This fun and surprisingly easy sequence can be used with various setup moves to finally solve the puzzle. Yessssss! At last! All it took was to transform my mind into a different orientation! It should have been easy as I have a very small mind and lots of space in my skull for twisting it about. I obviously need more practice.

If I had read the twisty puzzles museum post first then I would have had much less difficulty with this one - the description says the following:
"Rua is a face-turning rhombic dodecahedron and has therefore an axis system identical to an edge-turning hexahedron. Like all puzzle with this axis system it allows jumbling moves."
Knowing this would have made a HUGE difference!

Finally, it was time, under Derek's insistence that I perform a jumbling scramble. Oh boy, it gets very locked up very quickly! I suddenly wished that I hadn't done that:

Oh Crap! What have I done?
Movement becomes very difficult as the pointy triangles impinge on the movement of the edges. Luckily, it only takes a bit of fiddling about doing random movements to get it back to rhombic dodecahedron shape and then the solution to the puzzle is unchanged. It's worthwhile doing the full jumble just the once to say that you have done it but after that, it doesn't add anything to the process.

Overall it is a really fun puzzle and much less of a challenge once I had my perspective shift. What I now need to get is a copy of the Master Rua which SuperAntonioVivaldi showed off on his YouTube channel. Unfortunately, at nearly £300 that is not coming any time soon!

I can heartily recommend this wonderful head twister to all of you with an interest in twisty puzzles.

Now I am off to smother my wife with a pillow!!!! Aaaargh!


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