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How can you make this ball?

m_m_italym_m_italy Posts: 386
edited December 1969 in Hexagon Discussion

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

Comments

  • Kendall SearsKendall Sears Posts: 2,995
    edited December 1969

    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

  • emfederin_9bc0c524c8emfederin_9bc0c524c8 Posts: 0
    edited December 1969

    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.

  • pwiecekpwiecek Posts: 1,537
    edited December 1969

    afreaginname said:
    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.

    Hexsphere.jpg
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  • emfederin_9bc0c524c8emfederin_9bc0c524c8 Posts: 0
    edited December 1969

    pwiecek said:
    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! :)

  • m_m_italym_m_italy Posts: 386
    edited December 1969

    Many thanks to all.
    I have to translate ....
    Bye

    Molte grazie a tutti.
    Devo tradurre....
    Ciao

  • m_m_italym_m_italy Posts: 386
    edited December 1969

    :long:

    I translated

    :long:

    Ho tradotto

  • m_m_italym_m_italy Posts: 386
    edited September 2012

    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.

    Post edited by m_m_italy on
  • m_m_italym_m_italy Posts: 386
    edited December 1969

    :ahhh:

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

    enigma_della_sfera.png
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  • m_m_italym_m_italy Posts: 386
    edited December 1969

    :ahhh:

    dilemma_della_sfera.png
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  • stem_athomestem_athome Posts: 514
    edited September 2012

    afreaginname said:
    ...................... 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).

    icos_01.png
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    Post edited by stem_athome on
  • emfederin_9bc0c524c8emfederin_9bc0c524c8 Posts: 0
    edited September 2012

    Steve athome said:
    afreaginname said:
    ...................... 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! :)

    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.

    Post edited by emfederin_9bc0c524c8 on
  • emfederin_9bc0c524c8emfederin_9bc0c524c8 Posts: 0
    edited December 1969

    m_m_italy said:
    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! :)

  • stem_athomestem_athome Posts: 514
    edited December 1969

    afreaginname said:
    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

  • emfederin_9bc0c524c8emfederin_9bc0c524c8 Posts: 0
    edited December 1969

    Steve athome said:
    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!

  • m_m_italym_m_italy Posts: 386
    edited December 1969

    ......devo tradurre.....

  • m_m_italym_m_italy Posts: 386
    edited December 1969

    Thanks again to everyone.
    Give me time to translate.
    For now I say:
    1 I'm sorry because I have not explained well
    2 I had no doubt you would have found a solution
    3 I also solved the problem but I have no time to stop and show the result

    thank you, thank you thank you

    .....devo tradurre.....

    Bye

  • m_m_italym_m_italy Posts: 386
    edited December 1969

    Steve athome said:
    afreaginname said:
    ...................... 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).

    Ciao Steve.
    I will (but I have to finish) with the hexagon.
    The super golf ball is like that.

    Grazie per l'aiuto

    icos_01.png
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  • m_m_italym_m_italy Posts: 386
    edited December 1969

    afreaginname said:
    Steve athome said:
    afreaginname said:
    ...................... 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! :)

    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.


    With patience and about ten hours of work builds with exagagon.

  • m_m_italym_m_italy Posts: 386
    edited December 1969

    afreaginname said:
    m_m_italy said:
    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! :)

    Calcolato: dieci (10) ore di lavoro......
    :long:

    :-)

    Ciao e grazie for link.....molto molto interessante and utile

  • pwiecekpwiecek Posts: 1,537
    edited December 1969

    afreaginname said:
    pwiecek said:
    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! :)

    Well, There has to be SOME distortion of the hexagons. If they were perfect they would tessellate onto a plane. As it is, I believe the centers of the 20 triangles are going to bulge out a little making the center hexes a little larger. The more hexes, the less difference in size. But the biggest difference is going to be between the hexagons and the pentagons.

  • m_m_italym_m_italy Posts: 386
    edited December 1969

    W.I.P.......

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  • m_m_italym_m_italy Posts: 386
    edited December 1969

    .....50% sfera.....

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  • HopperHopper Posts: 2
    edited December 1969

    I built this golf ball with Hexagon some time ago if anyone needs one: http://www.turbosquid.com/3d-models/golf-ball-3d-obj/366748

  • m_m_italym_m_italy Posts: 386
    edited December 1969

    Hopper said:
    I built this golf ball with Hexagon some time ago if anyone needs one: http://www.turbosquid.com/3d-models/golf-ball-3d-obj/366748

    Bravo.
    Thank you.
    But I want to finish my work.

    Bye

  • m_m_italym_m_italy Posts: 386
    edited December 1969

    :-)
    Grazie a tutti.
    Ciao

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