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 Post subject: Gear Megaminx?
PostPosted: Thu Feb 03, 2011 3:00 pm 
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I just thougt of something you might deem silly. Or stupid.

A Geared Megaminx.

Is this possible?

Thank you! :)

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 Post subject: Re: Gear Megaminx?
PostPosted: Thu Feb 03, 2011 3:04 pm 
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It's not possible, but a gear master pent is :D

- Greg :)

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 Post subject: Re: Gear Megaminx?
PostPosted: Thu Feb 03, 2011 3:22 pm 
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Thanks, that was what I thought ;)

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 Post subject: Re: Gear Megaminx?
PostPosted: Thu Feb 03, 2011 3:23 pm 
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Look at the gear cube. when you turn one side the opposite side turns the other direction. look at the megaminx if there were gears if you turn one side the angles of the puzzle prevent anything from turning the other direction. that would be a cool puzzle though.

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 Post subject: Re: Gear Megaminx?
PostPosted: Thu Feb 03, 2011 3:32 pm 
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I think one of the requirements to make a puzzle "gearable" is to have a depth of cut that includes all the surface part types of the next to deepest cut version of the puzzle. This includes 3x3(master 2x2), master pentultimate, master 24 cube, master skewb, among quite a few others. There may be other criterion for allowing this style of gearing to be added, but I have not given it too much thought, and I'm pretty sure this is one of them.

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 Post subject: Re: Gear Megaminx?
PostPosted: Thu Feb 03, 2011 3:56 pm 
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I do not understand what you are saying because I don't know much on that subject. but, with a little fudging, you might be able to make a gear pyraminx crystal.

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 Post subject: Re: Gear Megaminx?
PostPosted: Thu Feb 03, 2011 4:06 pm 
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I believe it is possible. but not necessarily in the way the gear puzzles we see right now work. It might be possible that it just rotates the edges adjacent to the layer.


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 Post subject: Re: Gear Megaminx?
PostPosted: Thu Feb 03, 2011 6:16 pm 
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gingervergo wrote:
This includes... master 24 cube.

Dare Oskar to make that one.

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 Post subject: Re: Gear Megaminx?
PostPosted: Thu Feb 03, 2011 6:26 pm 
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Rentlix wrote:
gingervergo wrote:
This includes... master 24 cube.

Dare Oskar to make that one.



Isn't the "master 24 cube" just the Etan puzzle? the one Styrene made? There is no real master 24 cube that I know of?


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 Post subject: Re: Gear Megaminx?
PostPosted: Thu Feb 03, 2011 6:29 pm 
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48 Cube is a master 24 cube. Correct me if I'm wrong.

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 Post subject: Re: Gear Megaminx?
PostPosted: Thu Feb 03, 2011 6:45 pm 
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Rentlix wrote:
48 Cube is a master 24 cube. Correct me if I'm wrong.

master 24 cube would be a 3 layer edge turning cube. just like master skewb is a 3 layer corner turning cube



gear megaminx is not possible. gear gigaminx...... well :lol:

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 Post subject: Re: Gear Megaminx?
PostPosted: Thu Feb 03, 2011 9:43 pm 
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My 48 cube is only related to the 24 cube the same way a skewb is related to a 1x1x2.

I think a geared megaminx would work just fine. All you need to do is make a network of gears on the surface conecting both sides.

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 Post subject: Re: Gear Megaminx?
PostPosted: Fri Feb 04, 2011 7:13 am 
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He meant a gear ETHAN

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 Post subject: Re: Gear Megaminx?
PostPosted: Fri Feb 04, 2011 7:29 am 
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ETHAN?

edge turning HAN whats HAN?!

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 Post subject: Re: Gear Megaminx?
PostPosted: Fri Feb 04, 2011 8:15 am 
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rubikcollector123 wrote:
ETHAN?

edge turning HAN whats HAN?!


Edge Turning Hexahedron (with help from) Andreas Nortmann

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 Post subject: Re: Gear Megaminx?
PostPosted: Fri Feb 04, 2011 8:18 am 
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Maybe the corners could be the pieces that spin?

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 Post subject: Re: Gear Megaminx?
PostPosted: Fri Feb 04, 2011 10:37 am 
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RubixFreakGreg wrote:
It's not possible, but a gear master pent is :D

Ok... if we are given that a Gear Master Pentultimate is possible here is how you make a Gear Megaminx...

Image

This picture shows you that a Master Pentultimate contains a Megaminx inside it. So just make your Gear Master Pentultimate and have all the parts outside of the interior Megaminx transparent.

Never say something isn't possible... that is especially true here at TwistyPuzzles. Then again, by calling something impossible you almost assure that someone is going to go off and try to make it.

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 Post subject: Re: Gear Megaminx?
PostPosted: Fri Feb 04, 2011 10:59 am 
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RubixFreakGreg wrote:
rubikcollector123 wrote:
ETHAN?

edge turning HAN whats HAN?!
Edge Turning Hexahedron (with help from) Andreas Nortmann
Thread link for more info.

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 Post subject: Re: Gear Megaminx?
PostPosted: Fri Feb 04, 2011 2:49 pm 
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wwwmwww wrote:
RubixFreakGreg wrote:
It's not possible, but a gear master pent is :D

Ok... if we are given that a Gear Master Pentultimate is possible here is how you make a Gear Megaminx...

Image

This picture shows you that a Master Pentultimate contains a Megaminx inside it. So just make your Gear Master Pentultimate and have all the parts outside of the interior Megaminx transparent.

Never say something isn't possible... that is especially true here at TwistyPuzzles. Then again, by calling something impossible you almost assure that someone is going to go off and try to make it.

Carl


You don't understand, the pieces that have gears have NO connection at all to that megaminx in the middle.

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 Post subject: Re: Gear Megaminx?
PostPosted: Fri Feb 04, 2011 2:54 pm 
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RubixFreakGreg wrote:
You don't understand, the pieces that have gears have NO connection at all to that megaminx in the middle.
Yes they are. You can't turn a Master Pentultimate without turning the Megaminx inside.

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 Post subject: Re: Gear Megaminx?
PostPosted: Fri Feb 04, 2011 3:02 pm 
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GuiltyBystander wrote:
RubixFreakGreg wrote:
You don't understand, the pieces that have gears have NO connection at all to that megaminx in the middle.
Yes they are. You can't turn a Master Pentultimate without turning the Megaminx inside.


I get your point!!! But you can't make a megaminx showing gears, it just won't work

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 Post subject: Re: Gear Megaminx?
PostPosted: Fri Feb 04, 2011 11:33 pm 
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RubixFreakGreg wrote:
I get your point!!! But you can't make a megaminx showing gears, it just won't work

The point was... if you have a Gear Master Pentultimate built up using the shell mech then you HAVE a Gear Megaminx. Just make the outer shells transparent and sticker the inner Megaminx shell as a Megaminx and you DO have a Megaminx showing gears. I'm not saying its easy... just that it ISN'T impossible, but with the right tolerances it WOULD work.

Carl

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 Post subject: Re: Gear Megaminx?
PostPosted: Sat Feb 05, 2011 12:45 am 
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The puzzle you are describing cannot be built up upon edge gears like a normal gear cube, because with the megaminx, the edges border diagonal faces, not opposite faces as they do on the cube. If rotating a face required that all diagonal faces also rotate, these diagonal faces are also adjacent to each other, and these faces would also have to rotate simultaneously, which is physically impossible. However, do not say it cannot be done. The Megaminx analog to the gear cube would be similar to the slice Kilominx, except that opposite faces would spin in the opposite direction. I know for a fact this puzzle would be possible to build from a theoretical design perspective, but would likely be highly impractical to actually produce.

Imagine the core of the Megaminx is a gear housing with six independent sets of differentials.
Link:http://en.wikipedia.org/wiki/Differential_%28mechanical_device%29
A differential is basically a mechanical device which allows opposite ends of an axle to rotate at different speeds. You would need to use a pro-minx style design with a large spherical core. Inside the core, you would need separate differentials for each of the six axes (two faces per axis). This would require many small gears working inside of the core. The gears/axles would likely have to be made of metal, as neither ABS plastic or SLS Nylon would be strong enough to handle the torsion forces on the outer faces of the puzzle.

I would imagine that a gear Kilominx (inverted slice kilominx) of this design would be an extremely difficult to solve, because unlike the Kilominx, opposite corners do not move as pairs and could be commuted anywhere in the puzzle. The megaminx also uses fifth turns rather than the quarter turns of the cube, so solving it would definitely not be a picnic as it is with the Gear Cube. With the gear cube, the quarter turn metric causes the corners to re-align to half-turn metric every time a move is made. Solving one side would actually rescramble the other.

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 Post subject: Re: Gear Megaminx?
PostPosted: Tue Mar 15, 2011 12:51 pm 
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I was talking with Oskar last month and I came with the following idea.

Gear Cube can be seen as:
1- fixed middle layer, with 2 opposite layers turning each side; or
2- fixed bottom layer, with top layer turning 2x faster than the middle layer. (I think this is as Muffet told before)

On Gear 3x3x3, both of views are the same, but on Gear Megaminx, only the second view is possible, as we can see on the picture below (sorry for the bad picture).

The only thing is that, on the second view, the middle layer (yellow) will have to swap the 5 centers, so it's physically impossible on a simple megaminx, but swapping centers happens on a pentultimate.

I can describe this type of twisting and what happens on each turn, but I can't imagine touching this puzzle in real world, it'll be so "twisty"! ^^

This puzzle, made this way, will have a lot more permutations as the Gear Cube, because the top layer turns 2 in 2 positions and, around the turns on 5 faces, it passes into all the 5 orientations (Gear cube passes just in 2 of 4 orientations).

So, if someone make a way to do this puzzle, it will be fantastic!


Attachments:
imagesCAWLYVNG.jpg
imagesCAWLYVNG.jpg [ 38.96 KiB | Viewed 5531 times ]

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 Post subject: Re: Gear Megaminx?
PostPosted: Sat Mar 19, 2011 2:43 pm 
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A fundamental question about gearing a Megaminx is: how many edges should have a gear?

I believe the sweet spot is six.

Oskar
Attachment:
Gear Minx - view 1.jpg
Gear Minx - view 1.jpg [ 134.72 KiB | Viewed 5360 times ]

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Last edited by Oskar on Sat Mar 19, 2011 3:10 pm, edited 1 time in total.

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 Post subject: Re: Gear Megaminx?
PostPosted: Sat Mar 19, 2011 3:06 pm 
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This is incredible, Oskar! Congratulations!!
It doesn't use my concept of changing centers, but it still uses a gear concept that works.
Each of the 12 faces is connected with 5 edges below them, so on the solved position, at least 1 of the 5 edges have to be geared. But 2 faces will share 1 gear, so 6 gears is a good number.
But the geared edges can move when turning a face that includes it. So, when scrambled, it'll have situations of free-turning faces, or situations with more than one geared edges connecting faces, and sometimes being bandaged. But I see that the logic to solve is amazing and a lot more difficult, because it's so dynamic!
Solving each face will change the algorithms to solve the next ones. I even don't know if it has algorithms that always work, because depending on each geared edge position, it will change a lot the way to solve, or maybe it'll be stuck and you'll have to start from beginning.
When approved, I want to see it mass-producted! It'll certainly make success!

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 Post subject: Re: Gear Megaminx?
PostPosted: Sat Mar 19, 2011 5:15 pm 
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I must say this is very similar to what I had in mind, but I had it pictured with all of the edges being geared. Looks as thought it is the same mechanism as the cube, so I would say this has extreme potential to show up at mefferts too, considering how well the gear cube did.


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 Post subject: Re: Gear Megaminx?
PostPosted: Sat Mar 19, 2011 6:06 pm 
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Oskar wrote:
A fundamental question about gearing a Megaminx is: how many edges should have a gear?

I believe the sweet spot is six.

Oskar


Amazing Oskar!

as soon as I saw it a series of questions popped into my head:

can you execute turns in such a way where you position the gears to disallow some turns?

if yes, can this be considered bandaging?

is there a way to look at some higher dimensional analogue of a bandaged megaminx to show the blocking of moves?

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 Post subject: Re: Gear Megaminx?
PostPosted: Sat Mar 19, 2011 7:24 pm 
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gingervergo wrote:
Amazing Oskar!
Agreed... Not the solution I expected, but WOW!
gingervergo wrote:
can you execute turns in such a way where you position the gears to disallow some turns?
I'm about 99.9% sure the answer is yes. I'd almost have to hold the puzzle in my hands to be 100% certain. But I expect Oskar's video when this is printed to show the bandaging.
gingervergo wrote:
if yes, can this be considered bandaging?
Yes, and even without the blocked moves I consider the gear cube itself a type of bandaging that is applied to the 3x3x3. You can think of bandaging as a restriction and on the gear cube you are restricted to turning a face only when the opposite face is turned in the opposite direction.
gingervergo wrote:
is there a way to look at some higher dimensional analogue of a bandaged megaminx to show the blocking of moves?
I expect the coming video to show the blocking just fine in 3D (actually the video itself will be 2D) but to address your question I'll leave that to someone better with 4D analogs them me. The answer is probably yes but I don't think its necessary.

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 Post subject: Re: Gear Megaminx?
PostPosted: Sun Mar 20, 2011 2:37 am 
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With 6 gears there will 593775 different GearMinxes. Ignoring symmetries there are round about 5000 variants left. I have to see how many can be made equivalent. :shock:
But I will do that LATER.


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 Post subject: Re: Gear Megaminx?
PostPosted: Sun Mar 20, 2011 5:14 am 
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Oskar wrote:
A fundamental question about gearing a Megaminx is: how many edges should have a gear?

I believe the sweet spot is six.

Oskar
Attachment:
Gear Minx - view 1.jpg


Amazing! I never imagine like it!
I can't wait to see a printable model.

-JEC-

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 Post subject: Re: Gear Megaminx?
PostPosted: Sun Mar 20, 2011 6:47 am 
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Yes! I hadn't even thought about the possibility of doing an extreme-style mod. The ideal way to place six gears on the megaminx is to arrange them in a cubic formation when the megaminx is solved. Anyone who has played with a Skewb Ultimate will no that the square faces each correspond to an edge.
Image
If the starting position has six gearsin this cube face position, then each face will rotate in tandem with exactly one other face. meaning that no move is initially blocked. However, once you disturb the relative positions of the gear edges, wierd things will ultimately start happening. It's not impossible that a face could be connected via the gears diagonally to two faces. Provided these other two faces are not adjacent, and are also not connected to themselves or other faces by any additional gears, then it would be possible for a maximum of three faces to be daisy-chained together and rotate in tandem. Four faces moving simultaneously is not possible because the fourth face would be physically adjacent to the others. I would imagine that this puzzle would start to bind very quickly during the scrambling process.

I predict that this monster will either be fiendishly difficult to solve, or it will be impossible to scramble, with most moves leading to dead ends requiring the puzzler to backtrack as the only viable option.

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 Post subject: Re: Gear Megaminx?
PostPosted: Sun Mar 20, 2011 9:28 am 
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stardust4ever is correct. I see a puzzle that can be twisted in many ways, with one face turning independent, other 2 faces turning together, other 3 faces turning together, and other faces that doesn't turn.
The problem is: when you make one move, almost ALL of the others will chance the way to turn! So, this puzzle will be as difficult as discovering the meaning of life!!! :lol:
Good luck, Oskar! You created a monster!! :mrgreen:

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 Post subject: Re: Gear Megaminx?
PostPosted: Sun Mar 20, 2011 11:23 am 
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Finding the meaning of life took about ten million years. This puzzle won't be solved unless... Let's hope the Vogons decide to pass us by...

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 Post subject: Re: Gear Megaminx?
PostPosted: Sun Mar 20, 2011 11:37 am 
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Oskar, great to see that you have decided to prototype this! :mrgreen:

I took a quick look at your prototype render and noticed something else about it: Twist parity will be very easy to fix once the pieces are solved into their start positions. Unlike the Gear Cube Extreme, any gear on the gear megaminx can easily be rotated one 60 degree turn counterclockwise for every full 360 degree clockwise revolution of the adjacent faces. So while solving this beast will be the ultimate challenge, getting the gear rotation parity fixed at the end of the solve will be a cake-walk. This also means that it will be possible to flip only a single strait edge.

Oskar, please give us a report on how easy it scrambles. I have the feeling that if this puzzle is difficult to fully scramble, then it will be mind-numbing to solve it again. At least the mechanics will be a lot of fun to twist around and see how it works, even if you can't solve it.

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 Post subject: Re: Gear Megaminx?
PostPosted: Sun Mar 20, 2011 11:51 am 
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stardust4ever wrote:
... any gear on the gear megaminx can easily be rotated one 60 degree turn counterclockwise for every full 360 degree clockwise revolution of the adjacent faces.
Are you sure? The gearing ratio is 6:20. So I would expect only multiples of 120 degrees (2 teeth) for the edge gears. Can you be sure that an edge gear is never off by 1, 3 or 5 teeth?

Oskar

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 Post subject: Re: Gear Megaminx?
PostPosted: Sun Mar 20, 2011 12:57 pm 
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Oskar wrote:
stardust4ever wrote:
... any gear on the gear megaminx can easily be rotated one 60 degree turn counterclockwise for every full 360 degree clockwise revolution of the adjacent faces.
Are you sure? The gearing ratio is 6:20. So I would expect only multiples of 120 degrees (2 teeth) for the edge gears. Can you be sure that an edge gear is never off by 1, 3 or 5 teeth?

Oskar
:scrambled: Okay, you win. I jumped the gun a little bit, assuming that the gear ratio (per single twist) was the same as the cube. When you do a quarter turn on the cube, the gear rotates by 5/6. I did my calculation assuming that the gear minx corners had 3 teeth like the gear cube. Now it is clear to me from looking at the picture the gear minx corners only have two teeth like the edges, making four teeth per twist instead of five. Funny thing, that a 360 degree rotation on the minx has the same number of teeth (5 twists x 4 teeth), 20, as are on the cube (4 twists x 5 teeth). You could still do a half turn by flipping it, but like a normal minx you just can't flip one by itself. This puzzle's gonna be insane. :shock:

I hope you can convince Meffert's or Tomy to mass-produce it. The Gear Cube proved a success, and megaminx's are right up Meffert's alley, so why not? :mrgreen:

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 Post subject: Re: Gear Megaminx?
PostPosted: Fri Mar 25, 2011 1:32 pm 
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Andreas Nortmann wrote:
With 6 gears there will 593775 different GearMinxes. Ignoring symmetries there are round about 5000 variants left. I have to see how many can be made equivalent.
But I will do that LATER.
Time for an update.
After some number crunching I got the following results.
We have:
2^30 = 1073741824 ways to place up to 30 gears.
8948032 different variants when symmetries are deleted.
1309 different variants when shape variants are deleted.
77 variants where every side can be twisted in at least one state.
73 variants without additional implicitly set gears.

1 variant with 0 gears.
1 variant with 1 gear.
1 variant with 2 gears.
1 variant with 3 gears.
1 variant with 4 gears.
1 variant with 5 gears.
1 variant with 6 gears. This is the one with the highest degree of symmetry.
1 variant with 7 gears.
1 variant with 8 gears.
1 variant with 9 gears.
2 variants with 10 gears.
7 variants with 11 gears.
44 variants with 12 gears.
8 variants with 13 gears.
1 variant with 14 gears.
1 variant with 15 gears.


Last edited by Andreas Nortmann on Sat Mar 26, 2011 1:53 am, edited 1 time in total.

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 Post subject: Re: Gear Megaminx?
PostPosted: Fri Mar 25, 2011 6:42 pm 
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stardust4ever wrote:
It's not impossible that a face could be connected via the gears diagonally to two faces. Provided these other two faces are not adjacent, and are also not connected to themselves or other faces by any additional gears, then it would be possible for a maximum of three faces to be daisy-chained together and rotate in tandem. Four faces moving simultaneously is not possible because the fourth face would be physically adjacent to the others.


To expand a little here, it is possible to have four sets of three connected faces. Pick four corners which also form the corners of a regular tetrahedron, and for each of these connect the second closest set of three faces to each other (not the 3 faces which meet at that corner, but the faces which lie closest to the corner apart from those). Unless I've made a mistake, this should cover all 12 faces. I realise this was probably implied, but just in case it wasn't I didn't want this idea to be lost as it seems like it would make a cool puzzle.


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 Post subject: Re: Gear Megaminx?
PostPosted: Sat Mar 26, 2011 10:01 pm 
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If you want to play the Gear Megaminx, you can download this.
http://cclx.webs.com/3dcube32.rar

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 Post subject: Re: Gear Megaminx?
PostPosted: Mon Mar 28, 2011 4:18 pm 
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bobthegiraffemonkey wrote:
stardust4ever wrote:
It's not impossible that a face could be connected via the gears diagonally to two faces. Provided these other two faces are not adjacent, and are also not connected to themselves or other faces by any additional gears, then it would be possible for a maximum of three faces to be daisy-chained together and rotate in tandem. Four faces moving simultaneously is not possible because the fourth face would be physically adjacent to the others.


To expand a little here, it is possible to have four sets of three connected faces. Pick four corners which also form the corners of a regular tetrahedron, and for each of these connect the second closest set of three faces to each other (not the 3 faces which meet at that corner, but the faces which lie closest to the corner apart from those). Unless I've made a mistake, this should cover all 12 faces. I realise this was probably implied, but just in case it wasn't I didn't want this idea to be lost as it seems like it would make a cool puzzle.

To connect three faces, you'll need two gears, so connecting four sets of three faces would require eight gears, correct? Oskar's version only has six, so the last set set of three would have to have free rotation.

@ Chilen: Great job with your applet. I noticed that there is a lot of garbled text though. Also, I keep trying to click the faces on some of the puzzles, sometimes the faces rotate, sometimes they don't. I use Windows XP SP2.

Keep the progress!

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 Post subject: Re: Gear Megaminx?
PostPosted: Mon Mar 28, 2011 9:22 pm 
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stardust4ever wrote:
@ Chilen: Great job with your applet. I noticed that there is a lot of garbled text though. Also, I keep trying to click the faces on some of the puzzles, sometimes the faces rotate, sometimes they don't. I use Windows XP SP2.

Keep the progress!


Sorry for the garbled text.
You can use the keyboard to control.
(arrow key and F V C B Z X ....)

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