Helix cube puzzle
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- Опубликовано: 19 ноя 2022
- Prototype half frame: shpws.me/TiT4
One tile: shpws.me/TiT7
Full frame: shpws.me/TiT6 (will also require three 25mm long M2 bolts and three M2 nuts)
20 tiles: shpws.me/TiT5
Files for the half frame: www.printables.com/model/3236...
You're absolutely killing it with holonomy. This is simply phenomenal. I'm starting to think about implementing hollonomy into my board game design. Like, maybe a chess variant where the pieces only move forward but after a move they rotate. Bro I got to try that.
Among normal chess pieces, only pawns and bishops seem to have anything to do with holonomy.
You're e ting your own board game?? How did you come up with an idea ?
One game I can think of that involves holonomy is Hyperrogue, a tile-based roguelike on a hyperbolic tiling. Hyperbolic board games aren't very practical in real life though, my table is disappointingly euclidian.
Someone let Oskar van Deventer know about this, he would be so delighted!
I'd be shocked if he doesn't watch this channel religiously already.
I certainly watch his!
Oh boy, another Channel I can subscribe to that will make my brain melt.
@@henryseg Hey Henry off topic but I hope you can respond to my email whenever you get a chance. Thanks.
These are so genius.
Greek inventions were created for entertainment back in those days, for magic tricks and puzzles, because they had no application for them.
I think in a thousand years, your inventions will be used in spaceships and we are witnessing the beginnings
I’d like to see a professional cube solver have a crack at this thing
i don't think you need any cubing knowledge at all (nor is it useful) -
like the rubik's sliding puzzle it looks to me like it's *a lot* more closely related to the 15 puzzle than the rubik's cube - the most obvious giveaway being that you have way finer control than rotating entire layers
And this is why I want to go to school for mechanical engineering. The amount of possibilities we can make with the tools our hands use... simply marvelous. Love this puzzle!
That tetrahedron at the end was real cool in itself!
I've got to say, being able to predict the end result of the holonomy demonstration was extremely satisfying - I did in manually by placing my hand on one face of an imaginary piece and moving it around the frame when you had the blank piece, and then (once I'd managed to get the same result twice - it took me about five goes) I converted it to a rotation angle and a direction based on the angular momentum vector of the transformation (I've switched to using those directions over clockwise and counter-clockwise since angular momentum doesn't care which side you're looking at it from)
And then you demonstrated with the piece starting in a different position so I had to quickly pause and re-orient myself an the angular axis.
OMG, this is beyond genius.
Very nice!
The motion around the ring reminds me of a commutator in group theory.
At 2:12, with x pointing to the right and y pointing up, the motion is (from right to left) -y -x y x
This can also be thought of as -y y^x (-y composed with y conjugate x). The first operation, a y rotation bracketed by an x rotation, is a quarter turn CCW z. The second is a quarter turn CCW y. Together they're equivalent to 120 degrees CCW about [-111].
Yes, exactly, it is a commutator of two rotations.
Ow, my brain
My mind instantly went to group theory too! His question 'is every state achievable from one starting state and if not how many 'components are there' really feels like it wants to be looked at through a group theory lens.
That tile cage is the peak of futuristic man-made tech
I would want this in black, or neon green.
I would absolutely take the time to properly sticker this. I would also sticker the "inside" of all of the pieces, effectively turning it into a puzzle with two start positions.
puzzles are a great use for an otherwise harmful substance such as plastic this is pretty damn sweet
There is a solution to stop rotation at a 5 way junction (where 4 cubes meet).
The tile enters the junction and is captured by a fin in the slot. You move the rocker switch over so a different slot is engaged so you can move the tile out another direction.
Not a passive mechanism sorry but it's the best I can think of.
Like a lazy susan / train railway junction? Because that's what I'm picturing. Pieces could travel along X and rotate into Y but they wouldn't be able to travel in a Z. You could do a really interesting 3x3 with Junctions like these.
Those are amazing puzzles! 😀
You can pretty trivially create more complex shapes by simply restricting it to being made out of exclusively the same 3-edge, 90° corner vertices that you are using for the cube. If you rotate the corners you can create non-convex shapes. The tradeoff with this approach is that you can't always have 2 physically adjacent vertices being connected by a traversable edge.
If you go with that method, you could probably produce the corner sections in bulk and add a mechanism to allow them to snap together so that you can create any sort of shape. Add in a bridge piece to join those non-connected adjacent corners and you have yourself a cool customizable puzzle.
Your 3d printer is dialed in almost perfectly. Those are really nice prints. Did you experience any retraction problems when first printing?
I got these made with selective laser sintering - it’s not a filament based printing process.
Very nice puzzle and very nice idea
In response to the question at 3:45, I don't think it is possible to stop the piece from rotating in place at a 6-way corner, unless the piece is actually 8 pieces bound together in a complex way that allows guide rails to pass through. Even if we remove the twist from the rails, this is probably highly impractical if it is even possible.
Superb.
4:57 a simple way to understnad this. cubes have 6 faces. a cube being twisted 4 times is going to be 360° x 4/6 = 240° from its original orientation. rotating an object 240° counterclockwise = rotating it 120° clockwise.
There exist shapes that prevent rotation in an infinite puzzle grid. My lazy example would be very pointy ("6 pointed stars") cubes that go through a small s turn before the junction. Take this as an existence argument.
Very clever as always
This is a really cool puzzle! Do you have the design patented? I would love to have a metal version but I wouldn't want someone to profit off the design without you guys getting something out of it.
In a hypothetical puzzle where the cube has more free movement, there might be a way to retain the cube while allowing passage. Basically a turnstile, or Geneva mechanism of sorts, but in 3D with more degrees of freedom, though it might better resemble a caltrop. The idea is that a cube can freely push through a set of these caltrop-esque turnstile-like mechanisms, but while a cube is between the set of them the cube cannot freely rotate itself, a compliant gating system. The only issue is that these would be solid free-floating parts, which would require a retention mechanism. On the flip side of this coin, you could also do the inverse, similar concept but instead of a singular solid piece it'd be multiple detached pieces, of which can have compound bi-directional hinges. Another option could be to find some kind of linearly sprung component that can collapse to allow the cubes to pass through and be captured in an orientation. I'm just throwing darts at the wall, I struggle to visualize things due to aphantasia, so I have no idea how any of these would theoretically or practically work, I just know a gating system with some form of compliance to allow movement makes the most sense to me.
Another option is to extend the wireframe edges a bit, so that the cube is forced into linear movement with no twist before entering a vertex,. Then from this have a set of rollers, with a small amount of compliance via swingarms to account for the twisted face of the cube, that would act as rails. The swingarms these rollers are connected to would need compound hinges, so that off-axis movement is still possible, and with springs in these hinges they should be able to retain a cube solidly. It'd be a bit simpler if you could figure out some kind of spherical roller that's mounted on a swingarm that combines the compound axes into a single hinge. The only issue here is how the cube enters this mechanism, there'd have to be some kind of actuator to negatively extend the swingarms of the entrance so that they don't collapse into the vertex, and can swing back in the positive direction to capture the cube on it's back face.
It's definitely not a simple hurdle to overcome.
Awesome concept and presentation as usual. I think I would try it with just the corners first because it looks a bit finicky to push two cubes ( a corner and an edge ) with this build. This could make a nice VR app. A sort of Escher like place. When you walk along an edge your gravity gets twisted 90º. Having 6 edges meet would not be a problem since not twisting is just handled in software.
Everything is easier in software!
That reminds me of "nil" geometry that the developer of Hyperrogue has experimented with. It's really trippy
Man, those 3D printing companies should be paying you SCADS of money to keep doing what you're doing...
To get to any other position, we need to be able to rotate a single cube to the same position, but with only one change.
But the cubes are in a sort of parity where any position can only hold half of cube orientations, so that could disqualify it, but we'll assume that's part of the puzzle at face value.
So now we can rotate a full side of the puzzle by moving 7 pieces, and each piece rotates 1/3rd along an axis, we'll treat these rotations as identical for now.
Because of this we can make 7/3 rotations with each full move.
If we theoretically do this twice then to 6+1, we can rotate one cube by 1/3 and one by 1/6th leaving others in the original position.
Other combinations form 1/3 1/3 1/3
This 3-way parity appears however we combine the cubes for rotation, and it is impossible to add or remove to the 3-way parity by using more combinations of 3-way parity.
So we can conclude that it is impossible to rotate a single 120 degrees without affecting the rest of the cube, so not every position is possible.
These sorts of puzzles tend to be extremely difficult to solve, and have the sort of mechanical problems with pieces getting out of place you mention. The Polo Cube is probably the best of them as a puzzle both mechanically and as a solve experience although as far as I'm aware I'm the only person who's ever solved it. Having a puzzle which is the faces of a cube with one missing and where they can flip through the center is also a fun puzzle but noone has ever made a really great physical realization of it. The thing fundamentally causing the the mechanical problem is that you can't fill out the missing space with smaller pieces like you can with a shelled mechanism. A slight variant on what you've got here which can work is that you can have the pieces on plungers which go through the entire puzzle and rotate the entire line of pieces which they're pushing all at once. That of course gets to be a huge number of pieces and would probably be best as a puzzle with simply two plungers with a single piece of intersection.
*Challenge* Make the _"tiles"_ with a central hub and snap-on faces. Then the faces can be printed in different colors. Then refine the design so it works well.
Bonus points if you design it so the _"tiles"_ can be assembled in the puzzle frame removing the need for screws.
I believe this challenge is significantly more difficult than solving the puzzle. I don't know if the bonus is even possible.
Awesome!
This is super cool puzzle design ! what about a flat "twisted cube" grid (as shown at 2:33) of 3 rows large (if 3:34 problem is solved), and twisted along the shape of a moebius loop ?
3:40 what if the fins act as holders? Extend the fins a little bit so that there is a point where the tile is held by all 12 fins, with a satisfying click. The ends of the slots must have lower walls in order to allow for the fins to click in place.
What if the ball was more of a cross-section and the tracks extended into the intersections? They would only have a slight gap to allow the intersection piece through and travel in a different direction. This wouldn't be as aesthetically pleasing as the ball but it may allow for the tracks to penetrate into the intersection in all directions keeping it from rotating.
This would be the 15 puzzle from the 4th dimension!
They look like, little caramel popcorns
Such a cool idea. How hard is it to solve compared to similar puzzles with strange geometry?
I don’t know - I’ve never tried to solve it!
I'm colorblind and what is this LOL - Beautiful work!!
These pieces rotate by 90 degrees when they move along an edge, but that can probably be changed. Could you make a similar puzzle where they rotate 60, 72, or 120 degrees? A 180 degree rotation wouldn't give holonomy in a cube, but it would on the edges of another platonic solid.
Yes, it would be easy to have a different amount of rotation as the tile goes along an edge. However, the current tile can move in three perpendicular directions from a corner. To do other polyhedra the tile would need to be able to move in other directions, which sounds difficult.
Might be cool to have inlaid tiles, maybe two dots per face
This is just BEGGING for an icosahedral variant
As if the Rubik's slide wasn't already hard enough. I need this. Where can I buy one?
Links in the description, although they are unfortunately not cheap!
even simpler answer: there are four corners but only three colors, of course you'll get the next color in the sequence.
4:12 have you considered model paint (for example acryllic)
Do you have a power style printer at home or just make the whole model in CAD and then order it?
When I was printing custom parts I did always mess something major up like haveing my cad model mirrored and I only spot that after the first layer printed out.
Or do you have a resin/ffm printer at home for this kind of prototyping?
These prints were made on an SLS machine - I order them online. And yes, I have also accidentally ordered mirror image parts more than once.
A neat thing about this design is you could probably be a little bit more creative with the tracks themselves. Like your holonomy sphere as a set of tracks with these pieces in it. With a bridge through the middle to take advantage of the third axis.
One of the tricky parts is that the tile has helical slots built into it. So it cannot just slide without also twisting. A redesign could probably accommodate parts where the tiles twist and parts where they don't, but it wouldn't be as smooth.
@@henryseg Oh, I saw that they had a little bit of wiggle room, so I figured the tracks could arc. Probably not enough to get a good curve.
Would you be able to consider selling 3d printable files for this or others of your puzzles? I do not have the money to buy the finished product, but as a student I'm lucky to have access to a high quality makerspace which would also provide the resources.
Thank you for your consideration!
Here are files for the half-cube prototype: www.printables.com/model/323666-helix-cube-puzzle-prototype
@@henryseg thank you! you have a lot of interesting 3d prints on your printables profile, I did not know.
3:47 can't you make cubes instead of balls and make the routes longer so it will have enough room to spin?
In Firefox with "Play DRM-controlled content" turned off, this video doesn't work, but other videos on RUclips do. Did you accidentally enable DRM on this one?
It would be nice to make a frame of transparent plastic
possible with resin 3d printing and clear resin, and you can also make it without screws and use clear resin to connect the one removable corner with an invisible seam if done properly.
cool game l like it.
If you treat each edge as a pair of perpendicular planes which follow the twist just like the tile, what sort of surface (or presumably collection of surfaces) do you end up with? I can't visualize it (unsurprisingly).
If I understand the question, I think they would be helicoids.
@@henryseg I meant what does the whole cube turn into? I had been thinking "If you follow along an edge, what started as (say) the right face ends up rotating until it's coincident with the top face. So do those faces merge into a single surface?" But no, I realize now that while you're twisting along that edge, the "next" edge is twisting "away from you", such that all the planes remain perpendicular. (Man, words are dreadful for this sort of thing! 😄)
I think you want some sort of global twisting coordinate system. Sounds complicated, but might exist. Might exist more in the three-sphere?
Great Zot! I am disconfombulated!
How be we take all the Veni, vidi, vici out of our schools and replace the Julius Caesar with some Henry Segerman?
What tools do you use to create your designs?
I use the 3D software Rhino, and its scripting environment Grasshopper.
I follow another creator creator that uses grasshopper; it's a cool tool. I've started to outgrow OpenSCAD + Python bindings, but haven't found anything FOSS to create the kinds of geometry I'm interested in, most recently ultralight irregular lattices for 3d printing
@@petervillano3484 Yeah, other than blender, I don't know of anything in this space. You can do a lot with blender though.
Where can i get one of those puzzles?
There are links in the video description.
I've got a better idea for coloring the pieces, just get a set of ink pads like are used for stamps. then stamp the pieces on the pads and let them dry.
Python logo puzzle
my fucking brain
Waste of time such a toys.
crazy how there’s only one mediocre joke in this whole segment.