nice.... god i love the radiolarian..... but in retrospect... i cant decide which i like more, the corners look unnatural, but at the same time, i love them. awesome job!

I can: this looks great, and the corners make it so complete.

I love the corners and this puzzle as a whole.

Alex

Minor update? This is a whole different puzzle!

Looks (almost) as cool as the Radiolarian!

I agree. Can we see a video?

Carl

I like it better with the corners - nice job!

I definitely like the corners, but it still seems incomplete...
I sense many version of this puzzle existing in the future.
For now, a toast to my nomination for puzzle of the year!

hmmm... that could be very useful now for the Puzzle Ninja (as a puzzle *and* as a weapon!!!)




Pantazis

dont think about making a shuriken out of a ufo...

Hmm... Jason, do you think that this design could be adapted somehow into this, or would it be too fragile?

Wow I love this puzzle with or without corners. I feel like this version is better for completeness's sake.



That puzzle is nearly identical to this except the Radiolarian has centers exposed. If you unsticker the centers they would solve identically.

Wow, Jared, I hadn't seen that thread, but it looks like you all discussed some of the same issues.

I'm waiting for parts for these two to come in the mail. The one on the left is centerless, with straight cuts and more robust corners and star parts. The one on the right is a bit deeper, exposing moving centers, while keeping nice robust corner mechanisms. I can't wait for the parts to arrive!

... so am I. The one on the left, anyway. It will be interesting to compare the two. As long as the cat is out of the bag, this is what mine looks like (in Rhino):



So now you've already scooped me twice, icosahedron-wise, and it looks like the race is on for 2.1.1!

I also tried to do something like your Cornered Radiolarian, but I couldn't make it work. Congrats.

As for the one on the right above... what can I say, but wow!

I tried to do that. The closest I got was by merging the "star" pieces and the corners, and hollowing out the space behind the star pieces so they didn't interfere when rotating. However, I discovered that when you do this, there's nothing left to hold the corners in.



Jason succeeded in basically this goal, by using curved surfaces. I tried that too, but evidently I didn't get the curve right.

What if you took the left puzzle, sunk the little pieces underneath a little, beveled the kites so the outer part is triangular, and used the extra space for overhang? I dunno how little the little pieces are underneath the surface...

Wow! Again, it's funny how often these kind of things come to life at almost the same time.

I can't wait to compare the two!

Maybe when they're both revealed, we could compare mechanisms! Another reason for us to have a meetup in North California.

Jared, what you're suggesting can be done very easily, as long as there are no fixed centers of any real size. I was able to design stable corners as long as the center wasn't much bigger than 4mm but then it seemed pointless. But yes, after getting rid of the centers, angling the cuts downward in the correct way hides the star arms just fine. But after all my effort to minimize them, I'm starting to like the star arms.

Hehe, OK, I just wanted to know if it would work that way.

Much more handsome with corners!

With so many(20) cutting circles on a single sphere, nowhere can be neat enough though, even the deepest cut.

Also with this number of parts, i'd strongly suggest molding them coz printing resolution is just too low to provide a smooth rotation.

Leslie

OK, I couldn't help myself, and another member of the forum was asking me about this separately. This is what the radiolarian looks like with the star arms covered, and no center, which allows a nice beefy mech for the corners and star arms. I have to admit, I really love the curves and larger corners. I may need to make this one at some point.

We had
CD2[C1, E3, X9][E3]
and now we have
CD2[C1, F3, E3, X9][F3, E3]

The sketches are
CD2[F3, E3, X9, T12][F3, E3]
and
CD2[C4, F3, E3, X9, T12][C4, F3, E3]

Well made IO
and don't dare to make something like this with four cuts per axis!

Yes, I sort of had the feeling a few months ago that this was in the air. I tried to scramble to finish mine, but I got hung up trying to fillet in Rhino.


Yes, absolutely! Assuming mine works, that is. This is my first build since I made a Dino for practice. But I was confident enough to bite the bullet and order a complete print.

so, you can't have centers on that beefy FTI above? It seems like there'd be enough room...

If I had actually finished the 4x4x1 as planned, and everything could have turned out correctly, I could have had a FTI in my design stockpile as well.
Oh well, missed it, but you have done it better than I probably ever would have anyway!

Oh wow, I love that last design.

I agree. That last design is my favorite by far!

But the two that you have made so far are incredible, too! Keep it up!

-π (Eitan)

I love this puzzle so much

Although the left one is the true FTO analog (with extra bits ), I definitely believe the right version with the "floating centers" adds an extra challenge, similar to the Starminx versus the Pyraminx Crystal. The outer face pieces also seem well balanced in both designs, with the corner parts not being excessively small compared to the centers. The fact that the centers can transmute about the puzzle makes them one more part to solve. I'd imagine that the corners having five unique orientations apiece will make any variation of the FTI devilishly complex to solve.

The FTO is greatly simplified by the fact that the triangles meet four faces to a corner instead of two. That means that pieces starting on even-numbered faces stay on even faces, ditto with the odd. So meaning even though the pieces may be congruent so that they are physically interchangeable, logically, they are not, likewise edges have only one orientation and corners have two. I restickered my FTO with four colors (red, yellow, green, blue) to reflect this effect.

With the FTI, an edge must be transmuted between at least five different faces in order to flip it once. For the cube and Megaminx, this only requires the manipulation of three faces, respectively. That means A LOT MORE WORK would be required to perform even the most basic algorithms. Likewise, if each of twelve corners had five different possible orientations, the permutation would be 5^12/5 or 5^11. Multiply that by 12!/2 for the position parity, then divide by 60 to eliminate redundant whole-body rotations, and a corners-only FTI would have:

(5^11) * (12! /2) /60 = 194,906,250,000,000 or approximately 194 trillion (194*10^12) permutations.
That's actually much less than the Rubik's Cube or Kilominx, but the permutations for a full FTI will be astronomically higher than that!

By comparison, the corners-only Megaminx /Kilominx /Flowerminx is:
(3^19) * (20! /2) /60 = 23,563,902,142,421,896,679,424,000 or approximately 23.5 heptillion (23.5*10^24) permutations.

[/quote]

I have a question concerning these two FTIs. The rightmost FTI has deeper cuts than the leftmost, that's what causes the floating centers. What if the cuts were shallower ? imposing fixed centers ?? Is this version of the puzzle also possible ??

Unfortunately, if you do that then some pieces become disconnected during a turn, as would happen on a proportional 7x7x7 cube. At least that's what I found when I tried to do it. Maybe it could be done pillowed or with curved cuts.

And I'm still eager to see the right FTI!

That's the exact puzzle this thread is about.

No, that puzzle still has the tiny offset edges, which the Cornered Radiolarian doesn't. For some odd reason it doesn't occur on gelatinbrain, but to my way of thinking, it is the "most natural" icosahedron, the one most analogous to the Rubik's Cube. 2.1.1 -- the one on the left, which Jason and I built -- is I think the next best thing, similar in design to the Pyraminx or the FTI.

Yes, I understand that... However, the puzzle of this very thread is still missing
the very small pieces that the other two have at the junction between corners
and edges...

Oh. My brain failed at interpreting thoughts for a minute.

I found the same thing. Making a fixed center is possible, but it really makes the star arms fragile. There's a sweet spot where you can eek out about 2-3mm for the necks if you do it, but it's not a pretty puzzle in my opinion because the center face must be so small to make it work. I didn't find any angled or curved cuts that could get around the fact that the star arm necks will pass directly next to the face center on a turn (although I tried).

As I said earlier in the thread, I designed one with a 4mm center, but I wasn't willing to gamble on the strength of the star arms needed, and it was kind of an ugly puzzle. I got a few friends to give me the therapy I needed by telling me the fixed centers don't add much to the solving, and I moved on.

By the way, share my pain: The puzzle on the right was delayed because I forgot to add one of the parts to my order. I recieved the parts more than a week ago but didn't count them until last night. So I'm waiting for them yet again....

Man, this is soooooo unfortunate. I wish I had your design talent (I mean this to all the designers). It must be sooooooooo exciting to received a completed puzzle !!!

To be honest, I learned alibre in about two months by teaching myself. Experiment and find out what each button does.

I include above my classification of centerless and centered Rubik's like puzzles. Do you agree that these are the regular polyedra equivalent of each other ? The centered version of the icosahedra is the new creation by Io but is missing the tiny edges next to the corners.

That's a nice way to break it down: one set is cut to a depth such that the cut goes through the face centers; the other is equivalent to the shallowest possible cut. However, the two sets are effectively equivalent for the tetrahedron, the octahedron, and the icosahedron; all that's added with the shallow cuts is centers, which don't really add anything.

If you use a spherical cut in the opposite direction of that used on the Cornered Radiolarian you get this:



The red cut surface being just hehind the red face. I like the size of all the pieces here but if you rotate the red face by 60 degrees the problem becomes apparent.



I've also tried pillowing and anti-pillowing (not sure that's the correct word for it) combined with spherical cuts and the problem is still there. See just how small the face center has to be in these.



The heart of the problem seems to be that anything that tries to make the face centers bigger hurts you with regard to the depth of the small edges and vice-versa.

Carl

Yes, that's it! There IS a configuration that technically works, but isn't beautiful or very strong.

Shouldn't pillowing with planar cuts work? I didn't actually try that, because I don't like pillowing, and I thought 2.1.1 was preferable to a pillowed, minimally shallowly cut icosahedron. But it seems like it ought to work.

I thought this looked familiar. Just checked my old files, and found this:



And yes, it looks like the star arms and face pieces will fall out. But I guess that depends on how deeply they are connected.

Yes, I think pillowing would work. But I LOVE the planar icosa shape.

Yes, I just added two to my post above while you were posting this. It can be pillowed or anti-pillowed (or anything inbetween which means no pillowing) but in all cases the face center has to be VERY small and the feet of the small edges also have to be VERY narrow.

Carl

You could use planar cuts... that just makes the small edges smaller. But pillowing doesn't help with regard to the size of the face center, see the animation I posted above.



I like 2.1.1 but to me its a different puzzle. I would sort of like to see one with face centers... even if they don't add much.

Carl

The star arms would fall out... yes. But I think the face pieces could be ancored under the edges.



Pillowing doesn't help... it will work as will a planar puzzle... but the face centers still need to be very small. Note the more pillowed the faces are the shallower the puzzle has to be cut such that the face centers are visible. That's why I tried anti-pillowing as it exposes the face centers and allows the cuts to be deeper. Neither helped very much and you are still stuck with very small face centers if you try to add them.

Carl

In the version that I built, the face pieces can be freely inserted / removed in that configuration. Maybe Jason's is different.


Oh, I see... it's because the cuts are so angled as they hit the surface. Not at all like pillowing a cube. OK.

I know most people seem to dislike them, but could you use magnets? This problem reminds me of the corners on Tony Fisher's Master Skewb.

Yes, in my version the face and star-arm pieces are firmly secured during a half-turn. (I hope I'm answering the question I think you were asking. I'm not sure if I understood you right.) In my version those parts go deeper cut just below the surface, creating floating hidden centers. Even with that trick though, it's still tough to get a good footing for the star arms and face parts, but it works.

It's nice to see my struggles to get a fixed face center, that isn't ugly, validated by others' efforts to do the same. I'd say real "success" would be at least a 10mm edge on the center for a 60mm-edge icosahedron, with stable, firm star arms, and a preference for non-pillowed.

All the puzzles shown in this thread are beautiful! The curvy shapes really give them an exotic aura. Fabulous!