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 Post subject: 4x4x4 ball
PostPosted: Thu Apr 07, 2005 5:26 pm 
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Joined: Sun Mar 27, 2005 7:37 pm
Finally finished a project I've been doing on and off for sometime. Kind of got a bit bored with it when I realised rotational movement would be poor. Not totally spherical and stickers didn't go on too well. Apart from that I'm perfectly happy with it. Unlikely to make more. Next puzzle will be better!


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 Post subject:
PostPosted: Thu Apr 07, 2005 6:03 pm 
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Joined: Mon Jan 15, 2001 12:30 am
Location: Montreal, Canada
Hi Tony,

First things first, I do not own any of your puzzles mods,
but i still admire all of what you have done to twisty puzzles over the years.

In the Twisty puzzle world, you are certainly a "reference" when it comes to
puzzles mods, but on the other hand, no one knows much about you.

Sine you are now a member of this forum, i'm permitting myself to ask you
what compelled you to become a member ?

_Over the years you have came up with several different new designs,
and at the same time several ideas have came up from fellow members,
and other puzzles builders around the world, and curiously no one has
produced similar puzzles, so i was wondering if any of the work here in the database will help inspire you ?

Michael
:wink:


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 Post subject:
PostPosted: Fri Apr 08, 2005 7:13 am 
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Joined: Mon Aug 02, 2004 7:03 am
Location: Koblenz, Germany
I like this sphere!
What is its diameter?

Question to everyone: How many possibilities has this sphere compared to the 4x4x4?

Andreas


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 Post subject:
PostPosted: Fri Apr 08, 2005 7:26 am 
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Joined: Wed Mar 15, 2000 9:11 pm
Location: Delft, the Netherlands
entor_perdia wrote:
Question to everyone: How many possibilities has this sphere compared to the 4x4x4?


Let's see:
corners: 8! positions, no orientations.
edges: Occur in eight triplets, so 24!/8!^3 positions.
centres: Occur in eight triplets, so 24!/8!^3 positions.

This leads to 3612507214902104046528000 positions for any fixed spacial orientation of the whole puzzle. There are no fixed centres, so divide by 24 to get 150521133954254335272000 positions.

Note that because the corners are all different, there aren't any positions that remain the same by some rotation of the whole puzzle, and so this division by 24 should give the exact answer.

_________________
Jaap

Jaap's Puzzle Page:
http://www.jaapsch.net/puzzles/


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 Post subject:
PostPosted: Fri Apr 08, 2005 12:53 pm 
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Joined: Sun Mar 27, 2005 7:37 pm
The diameter is 6.6cm, the same as the Master cube it was made from. None of it has been built up though if I were to make another I might consider it as the cuts are so close to the mechanism.
The main reason I joined Twisty now is because in January I purchased my first computer (unless you count a Commodore 64). Up until then I'd followed the discussions and looked at the database but only once a week in my local library.
I usually try to make puzzles that haven't been made before. I can do this by keeping in touch with other makers and checking sites like this, though it doesn't always work. Both Katsuhiko Okamoto and myself made 3x3x5s last year.
The data base can be an inspiration but to be honest most of my ideas I had years ago. Also, I spend so much time looking at and working with puzzles often a new idea will just come to me. The Overlapping cube for example came about when I was dissmantling some Eastsheen 4x4x4s and realised the "centres" were in two parts and the puzzle still worked without the top bits.


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 Post subject:
PostPosted: Fri Apr 08, 2005 8:26 pm 
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Joined: Sat Dec 02, 2000 8:27 pm
Location: Wilmington, NC, USA
Well, this 4x4x4 sphere idea is unique. You, Tony, have a way of looking at possibilities that never occur to the rest of us.

By the way, that characteristic is extremely valuable in the marketplace.


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 Post subject:
PostPosted: Sat Apr 09, 2005 6:11 am 
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Joined: Mon Aug 02, 2004 7:03 am
Location: Koblenz, Germany
jaap wrote:
corners: 8! positions, no orientations.
edges: Occur in eight triplets, so 24!/8!^3 positions.
centres: Occur in eight triplets, so 24!/8!^3 positions.

Divide by 24 to get 150521133954254335272000 positions.


Hrrm.
Is this correct?
Shouldn't the number of positions for the edges be 24!/(3!^8) ?
The same fits to the positions of the centres?

This seems to be the number of positions for the eight color Revenge:
http://twistypuzzles.com/cgi-bin/puzzle.cgi?pid=1221
On the sphere: Don't we have to take the orientations of the centres into account? Or is the orientation defined by the position?

Andreas


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 Post subject:
PostPosted: Sat Apr 09, 2005 8:34 am 
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entor_perdia wrote:
On the sphere: Don't we have to take the orientations of the centres into account? Or is the orientation defined by the position?


You've never seen the inside of a 4x4, have you? :D Yes, orientation is always fixed. The mechanism makes it obvious, but it's not necessary. If you mark the "inside corner" of all center cubie stickers and make any turn then the marks will still be at the inside corners everywhere.

I think you're right with the 3! vs 8!. Nice comparison to the eight color cube :)


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 Post subject:
PostPosted: Sat Apr 09, 2005 8:18 pm 
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Joined: Fri Jun 04, 2004 7:37 am
Location: Japan
Welcome, Tony.
I am happy we can meet you on the Internet.
I had been waiting for this time.

I am sorry to be a late greeting.
I thought that it might be the event of April Fool.

> Both Katsuhiko Okamoto and myself made 3x3x5s last year.

Yes.

Your new works, Truncated 5x5x5 cuboctahedron and 4x4x4 ball are very nice and beautiful.

I will be glad if you visit my site.
I regret that my English is poor.

Katsuhiko Okamoto


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 Post subject:
PostPosted: Sat Apr 09, 2005 8:38 pm 
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Joined: Sun Mar 27, 2005 7:37 pm
Hi Katsuhiko,
As far as I'm concerned you are the king of puzzle transformation. I still have no idea how you created the master pyraminx and the small cuboids. By the way, I attempted to make a 3x4x5 but ran in to difficulties, maybe you could succeed where I failed.


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 Post subject:
PostPosted: Sun Apr 10, 2005 3:48 am 
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Joined: Fri Jun 04, 2004 7:37 am
Location: Japan
Dear Tony,

Thank you for your response.

> As far as I'm concerned you are the king of puzzle transformation.

Oh, thank you, I am proud of your calling so.
But, real King is you.
It will obtain everybody's consent.

I beg your continued patronage.

Katsuhiko Okamoto


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 Post subject:
PostPosted: Mon Apr 11, 2005 1:08 am 
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Joined: Wed Mar 15, 2000 9:11 pm
Location: Delft, the Netherlands
entor_perdia wrote:
jaap wrote:
edges: Occur in eight triplets, so 24!/8!^3 positions.


Hrrm.
Is this correct?
Shouldn't the number of positions for the edges be 24!/(3!^8) ?
The same fits to the positions of the centres?


Doh!
You're right. It should be:
8! * 24!/(3!^8) * 24!/(3!^8) / 24 = 2.29e+38

entor_perdia wrote:
On the sphere: Don't we have to take the orientations of the centres into account? Or is the orientation defined by the position?


Orientation of the centres (and also the edges) is defined by their position. This is obvious when you take a 4x4x4 cube apart. In this 4x4x4 ball the design on the triplets of centres/corners is identical, so they can be interchanged without any visible effect.

_________________
Jaap

Jaap's Puzzle Page:
http://www.jaapsch.net/puzzles/


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