Hello all. This is my first post on the twistypuzzles forum, and I thought I'd begin by sharing an idea I've had when looking at the relation of different twisty puzzles to each other. The Dino series (Dino, DRD and DRT) have two axes that are different, which i have a personal distaste to. After looking at the Deltoidal series of shapes (which the Dino series of pieces are equivalent to), I've realized that they can be cut another way. I later discovered that the DRT when cut this way with added corners becomes a Dogic (of course, also allowing the Dino-type turning, resulting in two types of turning per axis.)

So here's my idea. The cuts are all slice cuts, shown in the pictures, once for each Dino puzzle. Unlike the Dogic, the Rhombic Triacontahedron and Rhombic Dodecahedron ones do not allow for a choice of the Dino-type or Dogic-specific type deeper cut. The mechanism, I later realized, can take in the form of the Crazy puzzles (Crazy Tetrahedron, 3x3x3 and Megaminx respectively). The indigo shaded pieces show the pieces that correspond to a slice layer of the Rhombic Dodecahedron idea. The same can be applied for: Crazy tetrahedron for the cube and crazy megaminx for the Rhombic Triacontahedron.

As this is my first post, I apologize if I have broken any rules. As I have no knowledge of CAD or how the mechanisms of twisty puzzles work and will probably not learn CAD anytime soon (This is my GCE A Level year in high school), this will remain an idea.

What do you think?

Hi, you are welcome and I am amazed that your first posting is about such a complicated topic.

The slices-only DRD you describe would be equivalent to a slices-only-faces-only-4x4x4. You can do something like this: http://www.twistypuzzles.com/cgi-bin/pu ... ?pkey=1564
with a 4x4x4 and peel of the stickers of all pieces except the faces.

I think the slices-only-Dino is a subset of Carl Hoffs Doctor Skewb:
http://www.twistypuzzles.com/cgi-bin/pu ... ?pkey=2304
Maybe Carl can say something usefull here?

Andreas

Those pieces of the crazy 3x3x3 show you the hidden side colors of the 3x3x3 edge pieces. That is assuming we aren't talking about a crazy plus 3x3x3. The pieces on your rhombic dodecahedron idea correspond to 4x4x4 face pieces. I'm not sure I see the point you are trying to make here. But you do have some very interesting puzzle ideas.Yes, welcome!!! And I agree this is one of those posts I've had to read a few times and I'm still not sure I've understood everything. Excellent first post.Since the corners remain fixed I'd design a core similar to my Doctor Cube which held in two slice layers on each axis. In the shape of a DRD you might even be able to hide the fixed corners inside the puzzle to make the puzzle look like your picture above.I think you are right. Just as you can vary the width of the slice layer on a Mixup Cube to make a normal 3x3x3. See Oskar's HandiCube. One could vary the width of the slice layer on my Doctor Skewb to make the edges much bigger. You should reach a point where the X-Centers, the corners, and the face centers, become hidden inside the puzzle. If you do this I believe you should have the puzzle you describe. Actually this puzzle should be much easier to make. Since you will break the possibility of making Mixup like moves you no longer need to use the S-curve cuts for the slice layer which make the Mixup moves possible and simple planar cuts should do.

Lots of great ideas and I think I know how to make two of them. The DRT idea I think could be made in a similar fashion but the geometry there is complex enough that I can't quite see it all in my head at the moment. If you don't mind I may try to make some of these down the road.

Carl

Your DRT is equal to the face pieces of a Master Kilominx. (If only the slice is turnable, then yes, those pieces correspond to the circle corners of a circle megaminx)

Also, welcome to the forum!

Great first post!

There is a notion of a "Complex" puzzle which is a puzzle that contains real pieces + imaginary pieces (where imaginary is a somewhat complicated to describe).

For background:
The Complex Tetrahedron
The Complex 3x3x3
How to visualize the pieces of a complex puzzle

The reason I mention complex puzzles is that building slice-only puzzles often creates completely new pieces types that correspond to pieces in the complex version of the puzzle.

For example, the The Multidodecahedron has all of the "simple" pieces from the Complex Dodecahedron but there are many other pieces types (if you count chiral piece types as the same piece then the complex dodecahedron has 82 different piece types and 4096 total pieces).

A puzzle that has several new pieces from the complex dodecahedron is the slice-only version of Eric Vergo's Master Starminx:

In general, the slice-only or circle version or slice+circle version of multi-layer puzzles can often create tons of new piece types. One of the more extreme examples is Gelatinbrain's 1.1.63 puzzle.

The thread to start with is this one:

Analysis of twistability and virtual pieces

In this thread Andreas start off explaining his way of analyzing twistability and we see how it can define new pieces not typically see in puzzles which we called virtual pieces. Matt Galla joined the conversation and he introduced his way of analyzing twistability which was a bit more general and introduced even more new pieces. We called those pieces imaginary pieces. I guess to be accurate it should be started that the virtual pieces are a subset of the imaginary pieces. However I typically think of there being three types of pieces:

(1) Real = pieces given real physical volume when 3-space is cut up with the N cut planes of an order N puzzle regardless of the spacing of the cut planes.
(2) Virtual = pieces defined by Andreas method of analyzing twistability but excluding the real pieces. The two cores of a skewb for example. Neither contains any volume as the cut planes pass through the origin.
(3) Imaginary = pieces which REQUIRE Matt Galla's method of analyzing twistability. I reserve this name for the subset which excludes the virtual and real pieces."Simple" isn't the correct word. These are the "Real" pieces.And using my definitions above, these new pieces are ALWAYS Virtual, and NEVER Imaginary. At least I'm 99% sure of that. You have to get even more extreme to bring the Imaginary pieces into play in a real physical puzzle and to date I don't think its been done. In this way, the Virtual pieces are much more like the Real pieces then Imaginary pieces.

To complete the terminology... the words Complex and Augmented do not apply to pieces but to puzzles.

(1) Complex = A puzzle containing both Real and Imaginary pieces (can also contain Virtual pieces).
(2) Augmented = A puzzle containing both Real and Virtual pieces.

And while we are on terminology the use of the word "slice" or "slice-only" in this thread isn't in agreement with what I typically think of with regard to those terms. I'm not sure if I'm the odd man out or not though in this case. Lets look at Eric Vergo's Master Starminx again.



This is what I'd call an order=4 puzzle as each axis is cut up with 4 cut surfaces. This divides the puzzle up into 5 layers per axis of rotation. I call the middle one the slice layer. Its about the equator of the puzzle. On each side of this you have 2 face layers, an inner and an outer. So what we are talking about here is actually what I'd call an inner face layer. Well except in the case of the Dino puzzle talked about in the first post. That is a slice layer. Am I alone in my use of these terms? Used the way I define this a "slice-only" puzzle always has pieces on opposite sides of the puzzle locked together.

I already know my use of the word "order" isn't in agreement with others here and we already seem stuck with a handful of different definitions for it. Does the word "slice" already fall in this catagory too? Or am I the only one using my definition? If so I can conform... but maybe we need a new term... how about "equatorial slice"?

Carl

I explored the idea of the crazy puzzles being a possible mechanism for these slice puzzles, as the inner corners also corresponds to the faces of the 4x4x4, which did not occur to me before. Of course, it is also possible to use the doctor skewb, slice-only 4x4x4 as mechanisms. I think they would make better mechanisms than the crazy puzzles as they are simpler. And yes, I was talking about the non-plus version. I apologize for the wrong image. The plus versions are just a marketing tactic.

I think a slice version of the master kilominx (with fixed corners) could be used, according to Coaster1235. It would be in the same fashion as the 4x4x4 idea, with corners and edges hidden. For the master kilominx, could I ask if there are any hidden pieces besides the face centres? I couldn't find any disassembly videos.

Sure! I don't mind.

Hmm. I think there may be many definitions for this. "Slice-only" for me means that all the possible turning moves are slices, where a slice layer is simply a layer that does not reach the nearest face perpendicular to the axis. For me the Master starminx has one face layer and one slice layer per axis, where in my analysis the Master Kilominx has two opposite axes in the picture, making a total of 12 axes (also the number of faces of the dodecahedron), hence I would not exactly consider the middle "layer" to be a layer at all. Just the part of the puzzle that is not being turned at that point in time.

As with all things twisty, as we explore more complicated puzzles our existing terminology starts to break down. I've generally called the equatorial slice the "middle slice layer" but "equatorial slice" seems more accurate so I'll try to switch to that.

In the past I haven't liked your "order-N" descriptions very much but they are starting to grow on me. I think my issue with your order-n description is similar to our different views on the Complex 2x2x2 versus Complex 3x3x3 and the complex 4x4x4 versus complex 5x5x5. My stance is basically that order-1 and order-2 are "essentially equivalent" and the same goes with order 3 and 4, 5 and 6, etc.

So talking about the Master Starminx here, what if we bandage the Megaminx corners to the core to create a "inner face layer"-only puzzle? Does that make it order-2? I'd say "yes" but I'm interested in hearing your reasoning on it.

Also, for what it's worth, you can view the "slice only" (sorry "inner-face-layer" is too cumbersome) as a circle-like puzzle. Imagine increasing the diameter of the circle so much that it's larger than a face. Here is an example of what starts to happen:

Now if instead of using circles you were using pentagons and you increased their diameter more than the diameter of a face you'd end up with exactly the slice-only Master Starminx.

I've started seeing the "slice-only" restriction and the circle technique as basically the same idea with a slightly different execution.

EDIT: very minor wording tweaks.

Ok it looks like my understanding of the word "slice" in this context was different from most others. I can change. In fact when you think about a loaf of bread getting cut up into slices, its not just the middle slice that is called a slice of bread. Though I guess in that context you could even call a face layer a slice. Hmmm...Yes, I understand your point of view. The 2x2x2 is a degenerate 3x3x3 where the 2 face cuts just happen to fall on top of one another. But I still view that as a different puzzle. A 3x3x3 has 2 independant layers per axis of rotation. A 2x2x2 only has 1.Yes. It becomes an order=2 puzzle. I define the order of a puzzle as the number of independant layers per axis of rotation. This assumes each axis has the same number of independant layers. I typically don't apply this term to cuboids but it could probably be generalized to state that the order of a puzzle is equal to the maximum number of independant layers any axis of rotation present in the puzzle has. In this light the Fuzed Cube is an order=1 puzzle. Each of the puzzles my Multi Gear Cube Kit can make (provided each face is geared to its opposite face) is an order=1 puzzle. Yes, you could leave some gears out and have 2 independant layes on some axes so I guess I would call those order=2.Agreed... and I still believe this technique can only pull virtual pieces into the physical puzzle. To pull imaginary pieces into a physical puzzle you need something like the picture we painted of the Complex 3x3x3 where the middle slice layer of a Multi-5x5x5 turns with BOTH the left and the right faces. Yet when I turn the right face the left face doesn't turn and vice-versa.

And yes, a Complex 3x3x3 which was made out out of a Multi-5x5x5 I'd consider an order=2 puzzle. You only have 2 independant layers for any axis of rotation.

Carl