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How can you make this ball?
Posted: 14 September 2012 05:06 AM   [ Ignore ]
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Hello friends.
I need help.
It is possible to realize a ball as shown in figure?
I can not.
I can not.
I can not.
etc. etc.

thanks.
Ciao

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“Il principio della scienza della pittura è il punto, il secondo è la linea, il terzo è la superficie, il quarto è il corpo che si veste di tal superficie”
Leonardo da Vinci

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Posted: 14 September 2012 07:29 AM   [ Ignore ]   [ # 1 ]
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A sphere cannot be made from equal hexagons.

“Geodesic Discrete Global Grid Systems” by Kevin Sahr, Denis White, and A. Jon Kimerling

http://webpages.sou.edu/~sahrk/dgg/pubs/gdggs03.pdf

Kendall

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Posted: 14 September 2012 08:12 AM   [ Ignore ]   [ # 2 ]
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Can’t be done, MM. You can’t make a sphere using only hexagons.

The problem is that when you project a plane figure onto a sphere, you get distortion and the angles change.

If you start with a hexagon as a polar cap, you can surround it with hexagons, but since the sphere is spreading out as you lay them, the hexagon’s edges furthest from the starting point must also spread out. When you add another row of hexagons, the edges start spreading so far that there’s no room to fit the needed hexagons. You can start squeezing them together, but then you no longer have hexagons, you have funny looking 6-sided shapes.

You can see this effect easily on a globe of the earth. Towards the equator, a single block outlined by 2 adjacent parallels and 2 adjacent longitudes approximate a square. But if you trace from that square upwards, the “tops” of the squares get progressively narrower, and you end up with narrow strips near the pole.

One of the slickest tricks for covering a sphere with repeating geometric shapes comes from soccer, which uses 12 identical pentagons and 20 identical hexagons.

 

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Posted: 14 September 2012 10:55 AM   [ Ignore ]   [ # 3 ]
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afreaginname - 14 September 2012 08:12 AM

One of the slickest tricks for covering a sphere with repeating geometric shapes comes from soccer, which uses 12 identical pentagons and 20 identical hexagons.

 

The Traveller Role playing game took the soccer ball idea and expanded on it. They recombined and subdivided the hexagons & pentagons to create many more hexagons and make the pentagons much smaller. Here is a picture of that pattern projected onto an icosahedron and unfolded.

I have no idea how to go from this to a sphere. If you did there would be some variation in the size of the hexagons. If I had to do it, I would start with the soccerball layout and subdivide from there.

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Posted: 14 September 2012 12:36 PM   [ Ignore ]   [ # 4 ]
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pwiecek - 14 September 2012 10:55 AM

The Traveller Role playing game took the soccer ball idea and expanded on it. They recombined and subdivided the hexagons & pentagons to create many more hexagons and make the pentagons much smaller. Here is a picture of that pattern projected onto an icosahedron and unfolded

That’s fascinating as hell, but I must be getting old…

I stared at that thing for 10 minutes trying to figure out where the pentagons were before I realized that there were only 5 “sawtooth” points top and bottom, not 6 (the old “forest/trees” thngy…). So that gave me the 2 “polar” pentagons. As I was folding it in my mind, It took me a few more minutes to realize that the “hexagons” I was seeing at the unfolded apexes were an illusion - they’re each pentagons with a split side.

So curiously, even at the reduced size/increased counts of the polys, there are STILL only 12 pentagons as in the soccer ball, but many more hexagons (looks like 240?), and I strongly doubt that inflating the assembled icosahedron into a sphere would result in any notable distortion of any of the polys.

Thanks for posting that, Pwiecek! A very interesting exercize!  smile

 

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Posted: 15 September 2012 01:27 AM   [ Ignore ]   [ # 5 ]
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Many thanks to all.
I have to translate ....
Bye

Molte grazie a tutti.
Devo tradurre….
Ciao

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“Il principio della scienza della pittura è il punto, il secondo è la linea, il terzo è la superficie, il quarto è il corpo che si veste di tal superficie”
Leonardo da Vinci

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Posted: 15 September 2012 01:31 AM   [ Ignore ]   [ # 6 ]
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long face

I translated

long face

Ho tradotto

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“Il principio della scienza della pittura è il punto, il secondo è la linea, il terzo è la superficie, il quarto è il corpo che si veste di tal superficie”
Leonardo da Vinci

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Posted: 15 September 2012 07:44 AM   [ Ignore ]   [ # 7 ]
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No doubt what you have written is very interesting.
I admire your culture.
Thank you for the information.

However, with Hexagon is not possible to model a golf ball?
In the golf ball there is some imperfection .......6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,5,6,6,6,6,6,6,6,6,6,5 etc. etc. etc.

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“Il principio della scienza della pittura è il punto, il secondo è la linea, il terzo è la superficie, il quarto è il corpo che si veste di tal superficie”
Leonardo da Vinci

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Posted: 15 September 2012 07:54 AM   [ Ignore ]   [ # 8 ]
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shock

I’m going to get a breath of fresh air.
(Vado a prendere una boccata di aria fresca)

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“Il principio della scienza della pittura è il punto, il secondo è la linea, il terzo è la superficie, il quarto è il corpo che si veste di tal superficie”
Leonardo da Vinci

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Posted: 15 September 2012 08:00 AM   [ Ignore ]   [ # 9 ]
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shock

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“Il principio della scienza della pittura è il punto, il secondo è la linea, il terzo è la superficie, il quarto è il corpo che si veste di tal superficie”
Leonardo da Vinci

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Posted: 15 September 2012 08:20 AM   [ Ignore ]   [ # 10 ]
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afreaginname - 14 September 2012 12:36 PM

...................... and I strongly doubt that inflating the assembled icosahedron into a sphere would result in any notable distortion of any of the polys..

Due to inflating being based on vertex direction, you do get a change in size of the Hexagons. Maybe better to take the icosahedron up to 40 faces? But even then, I think the sizes will differ enough to very noticeable.

I did quickly make the icosahedron based on the image posted, and inflated to sphere to check (no, not done in Hexagon).

 

 

 

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Posted: 15 September 2012 09:56 AM   [ Ignore ]   [ # 11 ]
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Steve athome - 15 September 2012 08:20 AM
afreaginname - 14 September 2012 12:36 PM

...................... and I strongly doubt that inflating the assembled icosahedron into a sphere would result in any notable distortion of any of the polys..

Due to inflating being based on vertex direction, you do get a change in size of the Hexagons

True, but by “notable” (not to be confused with “noticeable”), I simply meant I doubted it would be great enough to worry about.

Maybe better to take the icosahedron up to 40 faces?  But even then, I think the sizes will differ enough to very noticeable.
I did quickly make the icosahedron based on the image posted, and inflated to sphere to check (no, not done in Hexagon)

And a fine looking sphere it is!  smile

There may be noticeable distortion to some hexagons as you rotate the sphere, but the general aesthetics are still very pleasing.

BTW: What was the program you used to do that? It really is a good looking sphere.

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Posted: 15 September 2012 10:08 AM   [ Ignore ]   [ # 12 ]
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m_m_italy - 15 September 2012 07:44 AM

However, with Hexagon is not possible to model a golf ball? In the golf ball there is some imperfection .......6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,5,6,6,6,6,6,6,6,6,6,5 etc. etc. etc.

Golf balls can get REALLY weird!! Check this out:

http://www.google.com/patents?id=MiwvAAAAEBAJ&printsec=abstract&zoom=4#v=onepage&q&f;=false


Have fun!  smile

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Posted: 15 September 2012 10:14 AM   [ Ignore ]   [ # 13 ]
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afreaginname - 15 September 2012 09:56 AM

BTW: What was the program you used to do that? It really is a good looking sphere.

Nvil (Voidworld), it is currently free. http://voidworld.cmcproductions.co.uk/index.php?board=2.0

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Posted: 15 September 2012 10:21 AM   [ Ignore ]   [ # 14 ]
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Steve athome - 15 September 2012 10:14 AM

Nvil (Voidworld), it is currently free. http://voidworld.cmcproductions.co.uk/index.php?board=2.0

Huh! I saw that name in another thread, too. I’ll have to grab a copy and play with it.

Thanks!

 

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Posted: 17 September 2012 12:34 AM   [ Ignore ]   [ # 15 ]
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......devo tradurre…..

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“Il principio della scienza della pittura è il punto, il secondo è la linea, il terzo è la superficie, il quarto è il corpo che si veste di tal superficie”
Leonardo da Vinci

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