Sunday, December 15, 2013

It's the Small Stuff

It's coming up on 365 days that I got my very first Rubik's Cube. I've collected a number of puzzles since then (only about 21) and the time spent with this new hobby has been filled with insight and joy. At first I solved my puzzles with online methods but it didn't take long for me to want to tackle puzzles with my own intuition, using the tools from the methods I've already learned to solve each new challenge. Throughout this past year I find myself drawn to the same genre of puzzle time and time again - and that is the shape mod.

What's so fantastic about the shape mod? Well for me it really illustrates the diversity of the twisty puzzle universe. In the above picture I'm displaying all of my shape mods, roughly 35% of my total collection. Four of these puzzles are 3x3x3's that have been cut down, rebuilt and re-stickered - and they're all almost completely unique! The shape mod demonstrates how complex one single puzzle can be, with only minor and completely superficial changes to the puzzle itself.

For these 3x3x3 shape mods I have found that the absolute best way to tackle any of them is to use a layer by layer approach.When relying heavily on your skewed perspective to know you're placing the right cubie in the right place, it helps to see the final shape slowly forming as you go, and reducing the amount of puzzle real estate that is scrambled at any time. Rather than writing full tutorials for each (I will do so for each individual puzzle if requested) I'll just talk about how each puzzle solves differently than a regular 3x3x3

Mirror Blocks Cube
The Mirror Blocks Cube is one of my favorite shape mods. The pieces are all stickered the same color, but have unique dimensions, so the solving is dictated by shape more than color. With this puzzle, starting with the shortest side seems to be the best option, because the pieces look very distinct even when the puzzle is scrambled.
The cross is placed normally, but the with the corners I check each individually by rotating them into where they would go, and if the lengths are equal to the adjacent edge lengths then I place them. The other benefit of placing the shortest side first is knowing the opposite side is going to be the tallest. Therefore, when placing the middle edges, I know any edge that is as tall as the top center is not going to be in the second layer. I solve the second layer through orienting experimentation and then placing pieces once I figure them out (vague, yes, but blog length is important). I orient the last layer before permuting it, And I can tell which pieces are oriented by which are as tall as the center piece again, then corner 3-cycle until it's flush with the correct sides and edge 3-cycle home.

The Windmill Cube
The Windmill Cube is a fun and very visually appealing. The puzzle's axis system is rotated by (I think?) 30 degrees only through one axis. It's called the Windmill Cube because the shapes on the top and bottom look like the blades of a windmill! My puzzle was won in a contest held by YouTuber Twisty Puzzling and has beautiful glittering stickers that make it nice to look at, especially when shape shifted.
 I solve this puzzle white side first, but I strongly recommend starting with either the white or yellow, because they are the only "true" faces - meaning they rotate about their geometric centers. The cross is solved normally, but the second layer centers now have orientation so I put the cross pieces in the top layer and one turn either to the left or the right, and making sure the center and edge match up and F2 it into place. The corners solve normally, but only have two colors. The second color of the corner should always be on the left of its correct edge if you start with the white. The same is true  for the middle layer, but the orientation is a bit hard to visualize so I place a few incorrectly quite often. Just take it out and put it back in correctly with any edge placement method you personally have. Again I finish up this puzzle  with orientation first and follow up with permutation of the corners, and then the edges.

The Fisher Cube
The Fisher Cube is the first shape mod of a Rubik's Cube by Tony Fisher. One axis is rotated 45 degrees so that what look like edges are centers and what look like centers are actually edges! As we move through this list. many of my shape mod tactics are already explained so I'm going to pick up the pace a bit. The first layer solves like the windmill cube, with center orientation maintaining importance. The middle edges are to be placed between the two centers that share the color of that edge = in the picture you see the green edge. What's interesting is that these pieces are bilaterally symmetrical, so they have no orientation.
 This can cause what looks like a parity error in the last layer where an odd number of edges are flipped. If this occurs, once again take one middle layer edge out and re-insert correctly with any method you find apt. Alternatively you could request a walkthrough solve or tutorial and I'll explain all the quirks with this puzzle. The last layer I orient and then permute again. This puzzle is actually where I started 3-cycling the corners before the edges, because I realized the corners were more cogent with the rest of the puzzle when the last layer isn't permute-able (basically it's easier to tell if the corners are correct than the edges in the past three puzzles)

The Axis Cube
Ahh, the Axis Cube! The last of my 3x3x3 shape mods, and also the most unique! This puzzle is the reason I wrote this blog post - because it is challenging and different and made me realize just how fun shape mods can be. The Axis Cube has some interesting geometry; A normal 3x3x3 is truncated into a hexagonal dipyramid and then built back into a cube on the false sides. Doesn't make sense? That's okay, it doesn't have to!
I start this puzzle on the white/blue center, and start with the solid white and solid blue edge pieces. Orienting these edges and their centers takes some practice, but use the same tactics as described in the Windmill Cube. The other two edges are the  other blue and other white edges. The corners you can figure out using context clues. The middle layer is also found using context clues for which edge goes where. You can tell if the edge is oriented correctly by rotating them into place, and if they are flush with their adjacent centers then you can place them. It's important to have all of the middle layer centers correctly oriented here. 
The last layer is very challenging and not similar to all those preceding. I orient the edges by rotating them above the centers they belong to and checking of they're flipped, and then making a mental note of which edges are flipped and fixing it. I then 3-cycle the edges so  that they're properly oriented in relation to the top center. Then I 3-cycle the corners and finally I orient them. This is the last layer process that Pogobat teaches and Superantoniovivaldi uses on YouTube.

The 4x4x4 Octahedron 
The 4x4x4 Octahedron is precisely what it says it is - a 4x4x4 that's been shape modded into an octahedron. You can simulate solving one of these by stickering a 4x4x4 so that the 2x2 blocks that are around each corner are all one color, dividing the puzzle into 8 separate colors. What's interesting about this puzzle is that I solve it in a very different way as compared to the 4x4x4 cube, and it also doesn't shape shift, which most shape mods do.
To start this puzzle, I locate or make a center that has 4 different colors, and commutate the other two tips of each of these four triangles. I then use 3-cycles on the top four triangles to solve all of the centers. Next comes edge pairing. I pair these using normal 4x4x4 tactics, but based on which triangles are next to each other instead of based on the colors of the edges themselves. I like to solve the 4 bottom edges first so that there are fewer places to look for edges to pair. This stage is very difficult and I'm vastly over simplifying it.
Potentially one could solve all of the edges now and then 3-cycle the corners in since the corners have no orientation, but I usually solve layer by layer because it's less repetitive. The normal 4x4x4 parities may come up, and be dealt with using normal parity algorithms, but they will mess up the centers and you'll have to commutate them back into submission.

The Face Turning Octohedron
Some of you may be wondering why the Face Turning Octahedron is on this list - it's a stand alone puzzle isn't it!? Well I took it apart and it's actually got the same core and piece-type as a Rex Cube, And my solve is based on that somewhat.
I only just recently got this, and I'm having a very hard time with it still so I don't think I could succinctly talk about how to solve it, seeing as I CAN'T solve it succinctly! Instead I'll just list my solving order.
1) Place edges around one center
2)Place middle layer and then top layer edges
3)Place remaining corners
4) 2,2 swap the centers - extremely setup move heavy
5) Orient corners

A tutorial for how to solve this can be found here.

Wrap Up
You may be wondering why I took the time to write all this up. Well, it's because I wanted to demonstrate how puzzles with identical mechanisms can be turned into entirely new beasts with a few cuts and extensions, and the similarities that do float through between many of them. The pieces do the same thing they always have, but we treat them differently. Their cores are indiscernible from their classsic puzzles, but they take on new properties. It's these subtle details of the solve that really matter, the small stuff that we discover between the myriad of puzzles to be solved. That's what gets me going and keeps me collecting! I only own a few shape mods but I do plan on expanding my collection further. What shape mods would you suggest? Any discussion, criticisms, corrections or requests I encourage in the comments section below or in the comments of Reddit here and the Twisty Puzzles Forum topic here. Thanks so much for visiting and happy puzzling!

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