All,

I figured the best way to thank everyone here on Thanksgiving is to share what I have on my new design. And to do that I'm working on some nice 3D animations. Not all of which are finished but I want to share what I have and put some place holders for the ones I'm still working on. I'll likely do this over several posts over the next few hours as I get things together. So where to start...

POST 1: Expectations

Let's start with what are the pieces one expects to find in a Real5x5x5©. Your typical 5x5x5 only has 6 but it should have ALL 10 of these:



Carl

The 3x3x3 edges are the same as the widgets, and the centers are the same too. To an extent, the corners are the same too, and the inner 1x1x1 is just the core. I don't see what this real 5x5x5 is but a circle cube. Would you mind guiding me in the right direction?

I don't think the 3x3x3 edges are the same as the widgets, they are on different layers. Nor are the corners the same, as they are also on different layers. Also, I BELIEVE (correct if I'm wrong) that the centers need to be individually oriented, so they're different, as well. The only non-important piece is the 1x1x1 core, which cannot change orientation nomatter what you do.

^all hypothesis, I'm no master on this subject. Please correct me, if I'm wrong

POST 2: History

The idea of finding a 3x3x3 inside a 5x5x5 has been around for probably as long as the idea of a 5x5x5 has been around. The first means of playing with this 3x3x3 inside a 5x5x5 that I'm aware of was the CubixPlayer2 program made by Per Kristen Fredlund that allowed you to Super Super solve NxNxN puzzles and that dates back to at least April 2004 as seen here. I assume there was a CubixPlayer1 program but I can't find its release date on line. If anyone can point me to it PLEASE post.

Our own Tony Fisher called this concept Hidden Cubes back in Nov. 2006. Seen here. He also mentions he small article he wrote for CFF (the newsletter for the Dutch Cube Club) several years ago so this may have been the inspiration for Per's program. I'm not sure. If Tony and Per want to post any more details PLEASE do so. I'd LOVE to see that article from CFF. Is it on-line in any format? If it can be found is it OK to post a scan of it in this thread?

Not liking the name Super Super Cubes, I struggled with what to call these puzzles here in Sept. 2009 and before that here in Oct. 2008. It wasn't till Jared came up with the name multi- here in Sept. 2009. that I was really happy what what to call this type of puzzle. I view these puzzles as Twisty Puzzles where you solve the volume of the puzzle... not JUST the surface.

And I've wanted a mechanism for the Multi-5x5x5 for a long time. My first shot at it wasn't really inteneded to be serious as I knew it wouldn't work well but it was posted here in January 2007. I even called it a new 3x3x3 wanting to keep the focus on the 3x3x3 on the INSIDE of a 5x5x5. Another issue with this idea is how to be able to see the 3x3x3 on the inside. Do you make the outer pieces clear? Personally I like Oskar's approach to the Multi-4x4x4 with his Framed Cube.

The other idea that I thought had potential with the Multicubes was the concept of the Circle Cubes. I started a discussion about that here, but at the time I didn't see a good way to carry that concept past the Multi-4x4x4's being sold as the Crazy 4x4x4's. It wasn't till bobthegiraffemonkey's post here last month that allowed me to see how this could be extended to the Multi-5x5x5 and beyond.

Carl

If you rotate the center slice layer this piece changes orientation. That and it IS a piece inside a 5x5x5 so it NEEDS to be represented.

Stay tuned and you may be... that topic will be covered here too.

Carl

POST 3: How to view a Circle Cube as a Multi-Cube

Previously I made these images to explain how the Crazy 4x4x4's were really Multi-4x4x4's that allowed you to see the 2x2x2 on the inside.

http://wwwmwww.com/Puzzle/Crazy1.png
http://wwwmwww.com/Puzzle/Crazy2.png
http://wwwmwww.com/Puzzle/Crazy3.png
http://wwwmwww.com/Puzzle/Crazy4.png

All 4 versions are really the same puzzle but they just differ on the exposed (stickered) faces of the cubies that make up the Multi-4x4x4. Here I want to take a different more visual approach that I hope will help others SEE at a glance what these pieces on a circle cube are.

So let's start with the typical 5x5x5...


Note here we can only see 6 types of pieces, each with its own color. We see nothing of the inner 3x3x3. So how do we fix that? Lets cut a hole in one of the faces to expose some of the interior pieces.



Here we now see some of the interior pieces. However this info comes at a price. We no longer see any info regarding the 5x5x5 Face Center on this side and the 5x5x5 T-Centers and X-Centers that we do see are different then the ones we were looking at originally. We are now looking at what was a hidden side of these cubies in the layer below. But we now have info on 8 of the pieces types seen on this side of the puzzle. Missing are just the 1x1x1 Core and the 5x5x5 Face Centers. So let's dig a little deeper.

Animation still rendering...but this gives you the idea.


We can now see ALL 10 piece types from this side of the cube. You just need to keep track of which face of each cubie you are looking at. Initially we were looking at the top of a single Face Center cubie before we made any cuts. Now we see the sides or the four adjacent 5x5x5 Face Centers inside the center circle.

With this type of analysis ii should be possible to look at any circle cube and easily match each exposed surface/sticker to a face of a cubie in the Multicube.

To finish this off we just need to project these circles to the surface of the cube.

(Animation showing how this projection is made will be posted here)

Without this projection, when you copy this menthod to the other faces you get this.



Clearly you've cut TOO much away. With this projection you have this...



However I've dropped the dark green piece in the outer circle as its just the side of the dark green piece you see below it. Actually I didn't drop it because its redundant, I dropped it because it makes the design just a bit more manageable.

Now can you tell what type of piece each of these surfaces belongs to?

Carl

POST 4: The Pieces

Here is the 1x1x1 Core:


This is a single 3x3x3 Face Center. Notice it is actually made up of 5 discontinuous parts:


The core with all the 3x3x3 Face Centers in place:


A 3x3x3 Edge is actually 3 discontinuous parts:


The puzzle with all the 3x3x3 Edges now put in place:


A 3x3x3 corner... just a single part:


The puzzle with all the 3x3x3 Corners now put in place:


This could be considered a shape mode of a 3x3x3 Circle Cube.

Moving on to the 5x5x5 pieces...

A 5x5x5 Face Center is 4 discontinuous parts:


The puzzle with all the 5x5x5 Face Centers now put in place:


A 5x5x5 T-Center is 3 discontinuous parts:


The puzzle with all the 5x5x5 T-Centers now put in place:


A 5x5x5 Midge is a single part:


The puzzle with all the 5x5x5 Midges now put in place:


A 5x5x5 X-Center is 2 discontinuous parts:


The puzzle with all the 5x5x5 X-Centers now put in place:


A 5x5x5 Wing is a single piece in this puzzle. The second discontinuous part has been left out.


The puzzle with all the 5x5x5 Wings now put in place:


A 5x5x5 Corner is a single piece.


And now the 5x5x5 Corners have been put in place to finish off the puzzle.


Carl

Bravo! Would these pieces be considered floating?

POST 5: How does the Real5x5x5© turn

The outer layers turn like this:


The next layer in turns like this:


And the center slice layer turns like this:


Any questions?
Carl

How does one define floating in the context of a twisty puzzle? I can't say I'm familiar with its use in this context.

Carl

Sorry if that was a bit vague, I'm referring to the corners and all of the other pieces that don't interact with the core.

I designed for a similar puzzle: Double-Zero Cube 5x5
viewtopic.php?p=208980#p208980

Still not certain I understand the question but I think the answer is yes... only the 3x3x3 Face Centers are attached to the core. The core is actually designed to come apart into 7 pieces so the 3x3x3 Face Center piece with the hole in it can be put in place.

Carl

Nice!

In the central circle you have:
1x1x1 Core
3x3x3 Face Centers
3x3x3 Edges

In the outer circle you have:
3x3x3 Edges
3x3x3 Corners
5x5x5 T-Centers
5x5x5 X-Centers

And outside the outer circle you have:
5x5x5 Midges
5x5x5 Wings
5x5x5 Corners

So you are only missing the 5x5x5 Face Centers or you too would have a 5x5x5 Multicube. As is, its another 5x5x5 Circlecube. However your puzzle does have something mine doesn't. Your puzzle allows 3 sides of each of the 3x3x3 Edges to be seen so each has a unique position and orientation. Mine only allows for two opposite sides of each 3x3x3 Edge to be seen so I have 3 sets of 4 identical parts that while having a unique orientation don't have a unique placement. This could be solved via a sticker variation and my 5x5x5 Multicube could be turned into a 5x5x5 Super Multicube.

Have you designed the full interior of your puzzle? If so, are you willing to share pics of the interior? I'd love to compare it to mine. Is your design ready to be printed? Mine is just a POV-Ray model at the moment so I have a ways to go yet before I can print it. Would you be interested in a collaboration? Maybe we could compare note, impove both puzzles, and ultimately get them up on Shapeways? PM me if you are interested.

Carl

Carl I'm very curious, what program are you using that has such beautiful renderings and animation capabilities? Very cool design by the way. I'd love to see it made reality.

Nice work! I'm glad I could play a little part in this puzzle. I'm more glad I left the mech design to someone else, some of that looks complicated! BTW Carl I sent you an email a few weeks back about bandaging this to a complex 3x3x3 with no reply yet, I was hoping for some feedback .

Matt

I'm using POV-Ray. You can get it for free here.

http://povray.org/

Carl

I got it. It may work but I haven't had enough free time to think it through yet. I confess that part of the reason I named this the Real5x5x5© is because if this can be turned into a Complex3x3x3 I was hoping to name that puzzle The Complex3x3x3© and play a bit on the Real+Imaginary=Complex part of this.

Carl

Fair enough. Brilliant idea with the names, the mathematician in me certainly approves

I was completely lost, and to be honest couldn't really see the point of overcomplicating a puzzle in this way, right up until I saw how the top, second and middle layers turn. WOW that is very nice.

Potentially shapeways mebe sometime soon?

That is amazing! Before seeing the pictures of each part I could not understand why this was both a 5x5x5, 3x3x3, and 1x1x1. Great work