Hi everyone!

After some relatively complex puzzles, I'm back with a simpler concept. I found a cool symmetry between the dodecahedron and the octahedron, so I designed another FTO
The puzzle doesn't shape shift even if it's not in it's natural shape.

Here are the measurements: 55mm between two opposite faces, 24.7mm edge length, for a weight of 48g.

You can see the video here.
And find it in the marketplace.

Oh my god !

Nice work Mr. Mouflin! Although watching the video crashed this old PC... lol.

Really nice puzzle!

Made the code for this puzzle on PCubes. (View Here)

A dodecahedral Rex Cube! Nice one, I like the choice of using flat cuts .

It seems so simple and yet... Really beautiful. Love it. Congrats again.

Beautiful execution!

A subset of the Starminx III

I love dodecahedra and I love this puzzle

If there is a chance to get it at a reasonable price (fully assembled and stickered), I'm buying

Quite pretty!

Simple and clean, really like this one! Well.....especially a simple puzzle would be more solvable for me

Fantastic puzzle!
This deserves mass-production. Hope someone could mass-produce it!

Unless I'm mistaken, this is a higher order version of the Skewb Ultimate. Nice work!

Tyrgannus wrote:Unless I'm mistaken, this is a higher order version of the Skewb Ultimate. Nice work!

I was wondering what that face pattern reminded me of! It's a beautiful puzzle.

This is the third dodecahedron with this axis system and number of layers:
http://twistypuzzles.com/cgi-bin/puzzle.cgi?pkey=1907
http://twistypuzzles.com/cgi-bin/puzzle.cgi?pkey=1997
But yours beat them easily. Well done.
Thank you for the measurements.

hello
Another great puzzle from Raphael.
Like Konrad, I'm a big fan of dodec's. If price is right, I'll definitely buy one.
AMC

Clever name for a clever puzzle!

Great design, great name, great looks!!!



Pantazis

Wow, I'm really glad to read each of those nice comments and compliments, thank to everybody!

A special thank to Skallos who made the code for pCubes

Allagem wrote:Beautiful execution!
A subset of the Starminx III

I wasn't thinking that way when designing it, but yes, this is a valid description!

Andreas Nortmann wrote:This is the third dodecahedron with this axis system and number of layers:
http://twistypuzzles.com/cgi-bin/puzzle.cgi?pkey=1907
http://twistypuzzles.com/cgi-bin/puzzle.cgi?pkey=1997
But yours beat them easily. Well done.
Thank you for the measurements.

Oh... I wasn't aware of these puzzles. So, mine is extremely close to Your Rexahedron, the only difference is the flat cuts I used. I hope it doesn't bother you.

Nice looking puzzle. I just noticed that since most of the pieces just have a single color sticker, it looks like this puzzle should be able to be "solved" with the colors in a different configuration. Is that possible? If so, how many visually different solved states does it have?

Carl

wwwmwww wrote:I just noticed that since most of the pieces just have a single color sticker, it looks like this puzzle should be able to be "solved" with the colors in a different configuration. Is that possible? If so, how many visually different solved states does it have?

I believe it would only have two distinct solved states: this one, and the mirror image. That's because of the large rhombus pieces which act like Dino cube edges, having very distinct orbits, as well as the center pieces which must be between the same two colors. Might be wrong though.

benpuzzles wrote:

wwwmwww wrote:I just noticed that since most of the pieces just have a single color sticker, it looks like this puzzle should be able to be "solved" with the colors in a different configuration. Is that possible? If so, how many visually different solved states does it have?

I believe it would only have two distinct solved states: this one, and the mirror image. That's because of the large rhombus pieces which act like Dino cube edges, having very distinct orbits, as well as the center pieces which must be between the same two colors. Might be wrong though.

I rendered the puzzle in the same orientation on three different solids to help visualize the piece correspondence between this puzzle and more familiar cube variant: So we can see that the chiral triangles on the dodecahedron version correspond to the Master Skewb rectangles and the triangles on the faces of the octahedron version. These triangles come in two orbits of 12 pieces each. On the dodecahedron, each orbit has 12 unique colors. On the cube each orbit has two duplicates for each color. On the octahedron each orbit has triplicates of each color.

To solve the cube into a mirror color scheme you only have to swap two opposite faces. You can do this by drawing a mirror plane through the equator of the cube, bisecting 4 edges. The other 8 edges swap in 4 pairs which is an even number of swaps. This works nicely with the Dino Cube edges since no edge has to change orientation.

Edit 1: deleted mistakes. Hopefully noone read them yet

Edit 2: On a dodecahedron if you want to mirror about a plane, you're forced to slice through edges two different ways. One way leaves the edge in the some orientation and the other way forces the edge to be twisted 180 degrees. So two edges stay the same, two edges must be rotated 180, and two edges must swap position. We can flip edges 180 degrees on the docehaderon because they correspond to the square face pieces on the cube however the swapping of a single pair is an odd permutation which can't be done. Alternatively you could try to mirror the color scheme by point inversion through the origin but this is three swapped pairs which is also an odd permutation. For this reason I don't think you can solve the puzzle into its mirror color scheme.

Edit 3: I chatted with Matt Galla about this some. He pointed out that the puzzle has the same pieces as the Rex Cube (that is, no Skweb corners) and even the Rex Cube can't be solved into the mirror configuration because of the centers. Any way you try to mirror the puzzle you run into some limitation. Either you have to swap an odd number of center pairs or you have to swap an odd number of some other pieces or you need the Dino edges to twist 180 in place. All of these are no-goes. No mirror color scheme for this puzzle.

Wonderful puzzle, Raphael, as always! The idea seems so obvious and out-of-the-box at the same time.

To people talking about multiple solved states: on a FTO with hidden centers of rotation (like this one), you can technically solve the faces around "wrong" colors, but keep in mind that all colors belong to two "groups", two orbits, which can't be intermingled. I happen to have my FTO solved into this exact pattern right now to illustrate:



You can build the yellow face around the pink center and vice versa, but you can't build the yellow face around the green center, for example. In fact, no yellow sticker can end up on a green face, at all. The two groups of 4 faces each never mix together.

On a FTO with centers hidden (left), you can thus technically have many solved states, although they would all look the same.

Allagem wrote:Beautiful execution!

A subset of the Starminx III

This is a very interesting observation! I wonder if the "missing" cuts from Starminx III can be applied back to the octahedron shape, then? Would it produce a shapeshifting puzzle?

Doctor Hedron wrote:This is a very interesting observation! I wonder if the "missing" cuts from Starminx III can be applied back to the octahedron shape, then? Would it produce a shapeshifting puzzle?

The Starminx III cutdepth is particularly messy on the cube and octahedron. Here it is on a dodecahedron: And here is the same depth but with a cube: And here is the same cut depth on an octahedron: You would get shapeshifting if you were to somehow build these.

Brandon Enright wrote: And here is the same cut depth on an octahedron:

starminx_iii_octa.png

Oh snap! Yeah, that doesn't look good.

Btw, for the octahedron, "scaling down" the cuts (or, alternatively, "scaling up" the solid while keeping the cuts the same) determines whether or not the octahedron would have the center piece or it would be hidden. Since Raphael's puzzle has centers hidden, it would probably be more appropriate to compare it to the octahedron with centers hidden, too. Perhaps it would look slightly less messy, too, at least on the surface.

---

Edit: managed to do it with the renderer in your post signature.



Shape: octahedron, cut: icosahedron (= starminx 3). Left: depth 133, right: depth 100. Apex = depth in both cases.

It appears that either the mess on the edge can go away or the mess in the center of the face, but not two of them at the same time.

wwwmwww wrote:Nice looking puzzle. I just noticed that since most of the pieces just have a single color sticker, it looks like this puzzle should be able to be "solved" with the colors in a different configuration. Is that possible? If so, how many visually different solved states does it have?
Carl

I also had that intuition while I was stickering it. I don't know exactly how many different solved states exists. I just tried some and I found two different ways to permute face colors.

First one, invert 2 pairs of 2 adjacent faces, here White/Red and Grey/Orange.


Second one, permute 3 pairs of 2 adjacent faces, I turned around an axis between the white, blue and yellow faces (first pic). So, some initially opposite colors are now adjacent.



So it seems that there is A LOT of different solved states for this puzzle

leRAFs wrote:First one, invert 2 pairs of 2 adjacent faces, here White/Red and Grey/Orange.

Yeah this is an even permutation. There must be tons of alternate color schemes like this. You just can't reach the mirror color scheme.

There is 1 way to choose 0 pairs to swap from 6, 15 ways to choose 2 pairs to swap from 6, 15 ways to choose 4 pairs to swap from 6, and 1 way to choose 6 pairs to swap from 6.

The trick you've found leads to 32 different color schemes.

Also, I think you could permute the pairs so there should be 6! / 2 permutations and then each of these permutations has 32 variations. But you can always orient the dodecahedron so that one of the 6 is in a specific position and orientation which reduces this by 6 * 2 or 30 total even permutations of the edges. Put another way, there are 30 distinct ways to color a cube with 6 colors.

So there should be about 30 * 32 = 960 distinct color schemes for this puzzle that look solved. This could be off by a factor of two or so but the number is quite high, if not 960.

Absolutely superb shape and cuts. Really deserve a mass prod, I'd like to buy it.

hello
I have just received my copy of this puzzle. I must say how impressed I am with this quality of Raphael's work. It is a beautiful puzzle and turns very smoothly.
AMC