Hi Everyone,

I'm happy to introduce my latest puzzle, the OctoCube...
OctoCube is a shape modification of a fracture-sliced triakis octahedron, with additional corner and edge pieces added to make the shape fully cubic. The puzzle turns on six axes, much like a normal magic cube. However, when a face center displays eight-way symmetry, that axis can turn in 45 degree increments. This allows the puzzle to shape-shift as well as jumble.

You can see a video of OctoCube here.

You can also purchase OctoCube from my Shapeways shop.

Here are a few more pictures of OctoCube...
Enjoy!

Dave

Oh my goodness!

When shape shifted how do you even think about solving that?

Looks amazing!

Easily one of my favorites!

This looks absolutely incredible!
It is a shape mode of Please, can you give us a hint how the original "fracture-sliced triakis octahedron" looks like? Google did not find it.

What a fabulous looking puzzle! Wonderful work.

That does look insanely difficult to solve though.

Wow, this is really, really cool. And also very affordable. I will probably end up buying one some time in the future

Really, really good job. One of my favorites from you, David.

-Doug

The fracture-sliced triakis octahedron has actually never been made, but it would look like this:I considered making this into a puzzle (Fractured Octahedron), but did not like the proportions of the pieces, with the eight sided tips being so large relative to the edge and face parts. Plus I didn't want to make another puzzle requiring 24 colors. Still, the shape kept me intrigued because it is the only one of the archimedean solids that can be made in a fully symmetrical pattern when fracture-sliced. In other words, each vertex has two opposite edge pieces flipped, and each three-sided face (of the octahedron) displays the same pattern. So I decided to shape-mod it into a cube (since it has six axes), and changed the proportions of the slice pattern to be as close to a normal 3x3x3 as possible. Voila, OctoCube!

Wow.. absolutely gorgeous!!

David, I want to say that I am a huge fan of your inventions. Thank you for them. The question I ask myself each time you show us your new puzzle is when can I have it in plastic? Is there a chance that we will see them produced any time soon?

Unfortunately I dislike the material that Shapeways puzzles are made from, and so I don't consider investing into Shapeways puzzles.

Another wonderful puzzle, David. What would it take to fully unbandage this? Could it actually be done? (i.e. Is it truly jumbling?)

-Eitan

A very special design. I think it must be challenging. It's not so often to see David designing a cubie shape puzzle~

Thanks to everyone for the kind words, I really appreciate them!

I would love to have this happen too, but for now nothing is on the horizon. Keep asking though, and perhaps someone will hear you!

My reasoning for calling the puzzle jumbling is that the shape it was derived from (the triakis octahedron shown above) cannot be unbandaged. If additional slices were added to each face to form a five-pointed star, that star would not be regular (i.e., the center of the star is not a true pentagon). Therefore the vertex-turning triakis octahedron is a jumbling geometry.

The OctoCube is really little more than a shape-mod of the vertex-turning triakis octahedron. The edge parts of the triakis octahedron are the tiny triangles around the centers of the OctoCube, and the triangular face parts of the triakis octahedron are the small wedge-shaped edge pieces on OctoCube. I've added edge and corner pieces to make the puzzle fully cubic in shape, but that doesn't change the underlying geometry, so my conclusion is that the OctoCube jumbles too. Does that make sense?

I'm not sure if this is what Eitan meant, but is this possible?

This is also my interpretation of an unbandaged version. (Except that the 180 degree "Fisher style" moves would still not be allowed. An entirely different mechanism would be needed to accommodate the moving centers for those rotations to work.) Although it appears like the additional slices should work to unbandage the puzzle, I believe that it would not be possible because the tiny triangular pieces and the wedge-shaped edge pieces would exhibit the same jumbling properties as the edge and center parts of the vertex-turning triakis octahedron depicted above.

Yeah I think I was going crazy with those "fisher style" moves

I apologize for not being able to find the link, but I remember reading somewhere that Oskar believes his Mixup cube is bandaged, in the sense that the outer layers can not do the 45 degree turns which is why I had wondered