Hi,

We all know the Fisher Cube: A 3x3x3 twisted by 45° inside its solid.
We all know the Axis Cube: A 3x3x3 twisted by 60° insided its solid around a different axis.
There is the Beveling Axis Cube, The Windmill Cube, the Greenhills Cube, ...

I tried to find all different 3x3x3-variants which result from reorienting a 3x3x3 inside its solid.
Obviously I had to ignore variants which have only slight difference.

What do you think?

EDIT: After this posting "XLL sym" was implemented under the name "Double Axis Cube"

Really nice overview.

It looks like you found a few good ones that haven't yet been made.

Thomas

Perfect overview about the angles and degrees.

Helpfull picture to complete the collection.

Hello Andreas,

Very interesting. Would you care to explain your classification? FEE, EXX, EXW, etc.

Also, if this classification is applicable to the 2x2x2, then it would be nice to see all the reoriented 2x2x2s. My first and only mod, Polyaxis Cube might get a different name...

Skarabajo.

Hey - you forgot mine!



I have been working on this shape mod for some time but have not had the time to do it due to work commitments.
I was going to make it with plastic sheet to fit an old Rubiks 3x3 I have lying around.
The interesting thing I found was that when you do the checker pattern, you get a cube for free.


...now the pictures work

It is there: Last row, second column. If I made a difference between rotating by 35° and 40° there would be an endless number.F, C, E, T, X, W, L are names for specific types of pieces in my classification scheme. They are all present in the 7x7x7.
The letters are given to the varaints depending on where the reoriented axis leave the surface of the solid. FEE means: One axes leaves the solid in the center of the side (like a Face piece). The other two axis leave the solid in the middle of the Edges. When the ObLique regions come into consideration it becomes ambiguous and I had to deal with symmetric and asymmetric variants.
I want to see that!

I personally prefer a classification scheme that involves the transformations done to the cube. For example, the Fisher cube is what happens when you rotate by 45˚ about an axis through opposite face centers. The axis cube is what you get when you rotate by 60˚ about an axis through opposite corners. The slice cube is another interesting transformation.

I think this would also help people understand how one might go about modding from a 3x3.

@oxymoronicuber: That is a cool way of showing a 3x3 mod. What did you use to create the graphic?

-Eitan

I would prefer that too but to explain all variants with only one single rotation the apropriate axes is not easily described.
If anyone is interested, I attached the Pov-Ray-Code (I changed the exension), so everyone with the appropriate knowledge (I had none until three weeks ago) can try to understand every rotation.

Eitan: I use Autodesk Maya to do all my (so far virtual) cubes. I also worte a Mel script that creates all the nets of the pieces so I can cut them out and fold the plastic sheet. This particular variant has 14 unique parts most of which are chiral mirrors of corners and edges. It might not be the best way to make them, but hey, each to their own!
I am hoping to output a puzzle for 3D printing soon, in Collada format, as Shapeways apparently support that, as I cannot get a decent STL exporter.