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 Post subject: How the size of a puzzle scales with Order...
PostPosted: Sun Sep 01, 2013 6:46 pm 
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I'm working on a puzzle and a thought crossed my mind this weekend and I wanted some input on.

I believe the standard Rubik's Cube is 57mm cubed... correct? I have a Rubik's Pocket Cube and a Rubik's Revenge but they are currently still burred in boxes. I know they don't maintain he same size cubies as the 2x2x2 has larger cubies then a 3x3x3 and a 4x4x4 has smaller cubies. So the first question is could someone provide the standard edge length for the various Rubik band cubes? How about the edge length of the various cubic (non-pillowed) V-cubes? I'm curious if there is a good rule for the size a puzzle should be as the order (pick any definition you like) of the puzzle goes up.

Does any one have the edge lengths of the mass produced Megaminx, Gigaminx, Teraminx, and Petaminx? How close do they come to using the same rule as the cubic puzzles?

I'm mostly curious about mass produced puzzles as I know when it comes to Shapeways the trend is to make things small to keep costs down and I'm more interested in ideal size then cost at the moment.

If there is a nice function that fits the edge length of the various mass produced NxNxN puzzles then I would be curious how close something like Oskar's Over-The-Top 17x17x17 comes to falling on that curve. Though there were many only factors affecting its size that I don't necessarily expect it to fall on the same curve.

Thanks,
Carl

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 Post subject: Re: How the size of a puzzle scales with Order...
PostPosted: Sun Sep 01, 2013 7:23 pm 
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The size of a 3x3x3 rubiks cube is 57mm. It's volume is not 57mm cubed. :)


I think the 4x4x4 is 60mm. I'm not sure about the 5x5x5

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 Post subject: Re: How the size of a puzzle scales with Order...
PostPosted: Sun Sep 01, 2013 8:05 pm 
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I think the 5x5 is either 62mm or 65mm to an edge. Following this trend, the 6x6 would be either 68mm or 70mm to an edge.

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 Post subject: Re: How the size of a puzzle scales with Order...
PostPosted: Sun Sep 01, 2013 8:15 pm 
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rubikcollector123 wrote:
The size of a 3x3x3 rubiks cube is 57mm. It's volume is not 57mm cubed. :)
Well it should be (57mm)^3... of course its not 57 (mm)^3.

Thanks,
Carl

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 Post subject: Re: How the size of a puzzle scales with Order...
PostPosted: Mon Sep 02, 2013 10:20 am 
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Megaminx: 32mm
Gigaminx: 41mm
Teraminx: 49mm
Petaminx: 59mm

2x2: 48mm
3x3: 55mm
4x4: 58mm
5x5: 61mm
6x6: 67mm
7x7: 68mm

And just for fun
11x11: 96mm

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 Post subject: Re: How the size of a puzzle scales with Order...
PostPosted: Mon Sep 02, 2013 12:49 pm 
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Letti wrote:
Megaminx: 32mm
Gigaminx: 41mm
Teraminx: 49mm
Petaminx: 59mm


Interestingly, that follows the exact A187093 sequence.

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 Post subject: Re: How the size of a puzzle scales with Order...
PostPosted: Mon Sep 02, 2013 1:20 pm 
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Yes, there is a basic rule-

1. Where technology and costs allow it should fit into your hand perfectly for turning.
2. If no.1 means parts are too small increase overall size until parts are no longer too small.

Sorry if that's not the maths you were looking for.

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 Post subject: Re: How the size of a puzzle scales with Order...
PostPosted: Mon Sep 02, 2013 2:57 pm 
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Tony Fisher wrote:
Yes, there is a basic rule-

1. Where technology and costs allow it should fit into your hand perfectly for turning.
2. If no.1 means parts are too small increase overall size until parts are no longer too small.

Sorry if that's not the maths you were looking for.
I tend to agree... but it appears most manufactures don't follow something quite so simple. If the ideal cubic puzzle is (57mm)^3 then why isn't the 2x2x2 also (57mm)^3?

Anyways... googling I've found all of these reported at the edge length of the "classic" Rubik's cube (55mm, 56mm, 57mm, 59mm, and 2.2 inches). Not sure if there was that much variability in the manufacturing process or what but I did find that odd.

There is also the question of when is a part "too small". Does it interfere with function/turning? Is its surface area too small for a sticker to reliability stay stuck? Are they in danger of being lost should the puzzle pop? Likely some combination of all these factors.
Granted these are all very subjective questions and they will very based on the method of production too (injected molded, 3D printed, cast, etc.).

I wasn't expecting a hard fixed rule everyone was following but I was curious what if anything the general trend might tell us.

Thanks,
Carl

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 Post subject: Re: How the size of a puzzle scales with Order...
PostPosted: Mon Sep 02, 2013 3:00 pm 
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wwwmwww wrote:
I tend to agree... but it appears most manufactures don't follow something quite so simple. If the ideal cubic puzzle is (57mm)^3 then why isn't the 2x2x2 also (57mm)^3?

I think it might have to do more with the size of the cubies. The cubies on a 2x2 are much larger than that on a 3x3, so the 2x2 is made smaller overall. Just a guess though.

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