## Monday, 5 May 2014

### Six faces aren't tough enough? Try these, you minx!

 That's a lot of dodecahedra! (25 in all) Yes! The cubes really ARE dodecahedra.
I'm very late - because "She who MUST be obeyed" ordered me to spend the entire weekend and bank holiday doing DIY and gardening. Unfortunately I am quite good at DIY and so she keeps forcing me to do more. When I mentioned that I had a blogpost to write she gave me a really dirty look and I began to smell burning before suddenly realising that my forehead was on fire! She now can use the laser burning stare without me even being able to tell - no running and hiding until it's too late!

I think it might be time for another little attempt at encouraging you to have a go at twisty puzzles. I WILL keep trying you know! They are just so good that everyone should at least have a try and spend a while learning either the beginners solution or the Ultimate solution.

This is quite a long post (OK, it's a very long post) but I will show you lots of interesting possibilities with links to where you can get them. There is a whole new world out there for all puzzlers to try. In N America I would suggest using Puzzle Master, who have a really good stock of twisty puzzles and in Asia I have begun to use Cubezz.com - slightly more limited stock but amazing prices!

So having managed a cube (at least a 3x3 and maybe for the very adventurous the 4x4 too with all it's interesting little parities), what if you'd like to step it up a little? Add a little diversity of shape, give yourself some more movement, or even just vary the collection. After all, puzzlers are very interested in shapes and surely you cannot be satisfied until you have representatives of all the platonic solids!

 All 5 platonic solids - all are face turning
In my "advice to beginners post" I suggest that the next steps after a simple cube is to move to different turning mechanisms or to move to shape modifications to skew your vision. But an alternative approach would be to move to one or all of the different shapes shown above. BUT if you would rather keep your path narrow or you have already done the cube and alternative mechanisms then how about falling down the deep spiral of doom into the dodecahedra? It's not just one puzzle for you - it's a whole family of them!

 The Megaminx
Ah! This takes me back! It was amongst the first "different" twisties I bought several years ago. I still take it out to play even now. This is the very basic dodecahedral twisty and was designed many years ago by many people independently - Ben Halpern from USA, Boris Horvat from Yugoslavia, Barry Lockwood from UK and Miklós Kristóf  from Hungary, and Kersten Meier (Germany) sent plans in early 1981. I have heard that Dr Christoph Bandelow from Germany obtained  patents. The Hungarian version is notable as actually being in production. Shortly thereafter Uwe Meffert (one of the forefathers of twisty puzzling)  bought the rights to the Halpern and Meier design and marketed it as the Megaminx.

It has 12 face center pieces which are fixed, 20 corner pieces with 3 orientations, and 30 edge pieces with 2 orientations each! The theoretical maximum number of places is therefore 30! x 20! x 230 x 320 positions but not all can be reached because only even permutations of edges are possible (2), only even permutations of corners are possible (2), only an even number of flipped edges are possible (2) and the total twist of the corners is fixed (3)
This leaves:
$\frac{30!\cdot&space;20!\cdot&space;2^{30}\cdot&space;3^{20}}{2^{3}\cdot&space;3}=&space;30!\cdot&space;20!\cdot&space;2^{27}\cdot&space;3^{19}$ positions
or
100,669,616,553,523,347,122,516,032,313,645,505,168,688,116,411,019,768,627,200,000,000,000
or
1.01 x 1068 positions or 101 Unvigintillion/Undecillion.

Now hold on, hold on! Don't run away now! Thats all the maths I'll give! The numbers sound horrific but then they already do for the plain old Rubik cube and you know that the cube is easy. In fact the simple 3x3 face turning dodecahedron can be solved with EXACTLY the same method as the cube! Only a very minor alteration is needed for the megaminx. So it is really easy!! You can make it a bit tougher by giving the centre pieces an orientation - using Pochmann stickers for it from Oliver's stickers.

 Still a megaminx - but now a "super" version
So having decided that you love the idea of 12 faces, where could you go next? Well the sky is the limit! The first thing most puzzlers look for is to buy bigger (or smaller puzzles) and I was no exception. Having mastered the 3x3 equivalent, I went for a 2x2 version (called the flowerminx or Kilominx) and originally designed by David Litwin from Twisty Puzzles and manufactured by Uwe Meffert. I also went for a 4x4 version known as the Master Kilominx by David Gugl and produced by MF8 which, like the 4x4 cube has a rather fun parity but also has a very interesting method of solving which does not produce parities and involves 2x2 block building.

 2x2 - Flowerminx
 4x4 - Master Kilominx
How much pain do you want?

This series continues with Gigaminx (5 layers), Teraminx (7 layers) and even Petaminx (9 layers), all mass produced and available now (if you really want the biggest twisty puzzle there is then get this one and the price from cubezz.com is amazing). If you are loaded down with an excess of cash or have a huge urge to collect a series, then a six layer (Elite kilominx) was designed by Grégoire Pfennig and made by Shapeways and may someday be available at auction. I don't have any of these as yet because I keep getting sidetracked by other toys! and to be honest they don't really add much to the challenge (just as a 7x7 cube is not really harder than a 5x5 once you know the basic process).

Now if shear size is not terrifying enough then how else might you achieve 12 sided torture? My previous advice to beginner puzzlers who want to take the cube a bit further is to try different mechanisms and the exact same thing applies to these. How about an edge-turning version? One of my all time favourite twisty puzzles is the Curvy Copter - this is an edge turning cube with curved cuts thus giving some nice edge pieces - if you don't have one yet then buy one - NOW. It is a really fun puzzle because it jumbles and shapeshifts and ALL of this is possible in minx form as the Helicopter dodecahedron.

 Helicopter dodecahedron
 Scrambled, jumbled and shape-shifted
This little beauty is stunning to look at smooth as anything and enormous fun. The advantage is that right up to the last face you can solve it by intuition and then once left with just corners to position and orient, it's easy enough to flip it upside down and work out a few algorithms on the face you've done already. It takes your simple face turners in a new and unexpected direction.

 Dino
 Rex cube - deep cut corner turner
Next up I might suggest a corner turning puzzle or even 2! One of the easiest cubes for anyone to solve is the Dino cube with all 8 corners able to turn and that meet at the diagonals of the faces - According to Jaap this puzzle has "only" 19,958,400 possible positions and requires very little knowledge to solve (only L, R', L', R) - even an OLD man like me can solve it in under a minute! The Dino cube is perfect for a child. For a bit more of a challenge the Rex cube adds curved cuts which pass the centre and give us some extra bits to move around. This challenge is significantly harder but actually doesn't need any new techniques than the Dino.

Yet again, there are 12 sided equivalents - the equivalent to the Dino cube is the Starminx I which looks beautiful and very scary but requires no more skill than it's cubic version - it's truly easy peasy! The Rex cube equivalent is incredible - unfortunately they did not call it the Rex dodecahedron (many of us still refer to it that way) - it's the Bauhinia Dodecahedron and kept a lot of us on the Twisty puzzles forum busy for a very long time - this one is NOT for the faint-hearted as there are so many fiddly bits that need to be positioned and orientated. The Bauhinia is one of my all time favourites and solving that positions you very well to attempt the hardest twisty puzzle ever mass produced, Eitan's star.

 2 Corner turning dodecahedra - starminx I and Bauhinia -awesome puzzles.
Luckily, when scrambled they actually look really lovely because one of these (Bauhinia) might well stay scrambled for a rather long time!

 Corners thoroughly turned
 Erm! Just a bit harder
So far I've shown cube puzzles and their equivalents but you might ask "is there anything possible on the minx that cannot be done on the cube?" and the answer is a very emphatic YES! On a cube you cannot change the depth of a face cut because the cuts just divide the cube up but on a dodecahedron there are many more faces to play with and as a result it is possible to vary the depth of this cut.

The Starminx II is a straightforward deeper cut face turning puzzle in which the cut is a little beyond the centre of the adjacent faces and this introduces those star tips (they look very similar to the Bauhinia but this has a totally different mechanism). This one used to be very hard to find but has now been remade and apparently the new version is much more stable - it is tremendous! We were all very surprised and delighted when MF8 produced a curvy version of exactly the same puzzle - the Curvy starminx. Why bother? Because having curved cuts allowed for the same star pieces to be produced but the cuts did not reach the vertices and a new corner piece was introduced making the puzzle even harder. These 2 are really for the collector or hard core twisty puzzler. The most fascinating thing about them is that much of it can be solved almost by intuition using only very basic techniques that we all know from solving the cube - those star triangle pieces is where it gets tough as there are 60 of them to position and this requires you to develop a "commutator" - this is a sequence followed by another (usually smaller sequence) and then undoing each which leads to a means to cycle just 3 of these triangles without upsetting anything else. Designing these commutators is often hard (especially for me who is new to the technique) but very rewarding! Finally the 3rd in this series, the Pyraminx crystal, is a really good one for a beginner as it effectively splits the puzzle through the exact centre of each adjacent face. It is a wonderful puzzle which is solved as a mixture of a plain Kilominx (positioning corners) and a the edges are solved like the petals of a Rex cube. It is a wonderful idea and, whilst a challenge, it is not too tough for a relative newcomer to this group.

 3 scrambled face turners - all different
I can hear you all screaming into your blankets now! Surely this madness cannot continue!!! Oh how wrong you are! The puzzles so far have all really been the predictable variants that you would expect with a little knowledge of geometry! The Chinese designers and producers have taken the cube puzzles up a notch and allowed everything to go "CRAZY"!

I discussed the Crazy 3x3 planets and Crazy 4x4 series a very long time ago and encouraged you to buy them immediately because they were so so fantastic. I was proved correct in that they have pretty much sold out of most of these variants now. I would never have believed it possible but the same concept of a puzzle with separate centres which may (or may not) be bandaged to the outsides has been applied to the Megaminx. These puzzles are barely available now but the occasional one can be found on eBay or the odd twisty store. I was lucky enough to pick up a pair of them that, with the aid of a screwdriver, I can alter the position of all the centre pieces and thus allow me to make any of the series. So far I have only attempted the easiest of the series - the Jupiter crazy megaminx and had a thoroughly fun time solving it. Soon I will reconfigure and try the next in the series. If you find one or more available then go for it - they are a tremendous and hugely fun challenge!

 Crazy man!!!
 Hell no!!!
I won't begin to explain how to do these but if you decide to attempt them then good luck and do let me know how you get on!

Finally, there was a group of cubes that until recently I missed out on them completely - they were the Bermuda cubes. These are a series of cubes in which the centres are not necessarily square, meaning that the movement of the pieces around the centres are seriously inhibited. I managed to get the Bermuda cube Mars from my recent order from Cubezz.com because it looked great and a good challenge - I have suddenly realised that I may have bitten off more than I can chew and should have started on the easier ones. Luckily they have a few more in stock for me to try - my next order will almost certainly include them. Again the amazing designers have managed to produce 12 sided equivalents and taken the Twisty world by storm! So much so that the Mercury version (which I do not have) has completely sold out and the others are very much in short supply. I got the Saturn from Cubezz.com and they still have a few others available. If you want to start with an "easy" one then go with Venus or Saturn. I think that having 12 faces with only some bandaged and others with Fisher (rotated) orientation makes for an easier challenge but much more fun. I have 7 so far:

 Bermuda Megaminxes - Spot the challenge?
These require planning and thought but at no point do you need to learn any new algorithms - it's all just basic Megaminx - can you cope? Do give them a try - I am loving them!

Now what about those 2 cubes in the top photo??? They actually are Megaminxes in disguise! The plain old Megaminx was transformed into a cube by the great Tony Fisher initially and then Traiphum made a pillowed version. I bought mine from Traiphum and had great fun trying to get my head around the shape-shifting. Once you do work out what is happening then it is JUST a megaminx. Having spent a small fortune on mine, you can get the same puzzle for a very small amount of money as it has now been mass-produced by Calvin - this is a must have puzzle. It looks beautiful as a cube and very ferocious when scrambled but it's easy! Really it is.

 Hexaminx
 OMG!
Finally I end with one that you cannot have! Traiphum made just 3 of these - he took the nice "easy" Pyraminx crystal seen a little further up the page and turned it into a cube shape just like he did with the Hexaminx above. This time he called it the Hexaminx crystal. He made 3 - one for himself, one for me and another for Rline (of TP and the Twisty Puzzling YouTube channel) and declared that no more would be made due to the extreme difficulty and high failure rate. It is an incredible puzzle which again looks like one thing, scrambles horrifically and solves just like an easier puzzle but is made tough by the extreme shapeshifting!

 Hexaminx crystal
 Just one algorithm!

I hope that this little dive into the wonderful world of the dodecahedron has maybe enticed you to try something else! Leave the cube for a while and try a different shape. OR, if you are not into twisty puzzles (yet!) then maybe it will encourage you to look at them in the hope that there is more fun to be had. It is not all about solving in 5-15 seconds, it is not all about committing an enormous number of algorithms to memory. All but the very hardest of these can be seriously attempted with intuition and just knowledge of the basic cube. A little practice and learning and it suddenly clicks - hopefully you will give it a go and be attempting Eitan Cher's star sometime too!

Do let me know your thoughts below.

1. Awesome article Kevin. Beautifully written, very inspiring, and good luck with the ever-present Mrs S!

1. Thanks Rline! I made very sure to point people to your wonderful YouTube channel! As for Mrs S? I have bought a supply of Flamazine cream and a mirror!

2. Do you ever have trouble telling 12 colors apart on a 12-sided puzzle? I have a Felix cube where three of the six colors (pink, orange and red) are surprisingly hard to tell apart. I would think with 12 colors there would be several hard to tell apart.

1. Not really George! The standard MF8 colours are very easy to tell apart.

3. I have the 6 sided bermuda Saturn. It's ridiculously fun and challenging. I've got two layers solved but I need help moving around the pieces on the top face. Got any tips or recourses online that I could use to get this this solved?

1. Hi Austin,
I only have 1 Bermuda cube (Mars) and I cannot solve it as yet. Some quick reading tells me that the Saturn is also a very tough one. I would suggest you read through the thread on the Twisty Puzzles Solving forum. Also have a look on YouTube for solving strategies by Burgo and Andrea for these puzzles.