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I am trying to build a wire-frame model and I'm looking for the angle of the hex-hex edge compared to the adjoining pentagon face, and the pent-hex edge to the adjoining hexagon face. Are there any good math resources to find these? I would prefer formulas, but angle measurements would be sufficient.
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According to an old book I have here, the ratio of the length of an edge of a truncated icosahedron to the radius of a CIRCUMSCRIBED sphere is 2*sin(theta/2), where theta is the angle subtended by an edge (in this case, about 23° 17'), or about 0.4036. For an inscribed or "interscribed" sphere,
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I already know the dihedral angles, I need the angles made by the edges leaving the face, not the edges of the face. For example, if a pentagon is sitting flat on a table, at what angle does the hex-hex edge (the edge that goes to the next pentagon) need to be relative to the table?
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P.S. You could get the same result from the data provided in the article, that the radius of the circumscribed sphere is sqrt(9φ + 10) (where "φ"=φ = (1+√5)/2) when the edges have length 2. My calculator gives 0.40354821233519770308113433897167 as the ratio...
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I tried playing around with layout--in IE on my screen there are weird white spaces that I can't seem to correct. (The white spaces were there even before I edited it.) It looks OK in Opera, but even there the football pic winds up all alone under the table.
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This article is substantially duplicated by a piece in an external publication. Since the external publication copied
Knowledge rather than the reverse, please do not flag this article as a copyright violation of the following source:
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is: "All balls must be: spherical, made of suitable material, of a circumference of between 68 cm (27 ins) and 70 cm (28 ins)..." nowhere does it state the number of panels. Older balls didn't have 32 panels (see eg
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of the truncated icosahedral graph is 2, but this is wrong, since it is not a bipartite graph. On the other hand, since it is planar, the chromatic number must be no greater than 4. So is it 3 or 4?
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Ok I need to add that there's a formula that follows 10E8 which shows that if a fullerene is to the soccer ball as the soccer ball is to the earth.. someone please articulate this and add it thanks!
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Yea I figured it was the corners after looking at a catagory and opening 8 articles that were truncated polyhedra of some sort. Looks like about 80% of the articles link to
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http://www.google.com/search?q=cache:5VOWiB_N3LgJ:www.fkf.mpg.de/andersen/fullerene/scale.html+c60+soccer+scale&hl=en&gl=us&ct=clnk&cd=1&client=firefox-a
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All of the couple dozen google hits trace back to this talk page or - via mention of his name, or repetition of his phrases - to one Rob Farley. Too obscure for inclusion.
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I just tried entering "chromatic number of truncated icosahedral graph" into
Wolfram Alpha, and got "Result: 3", so there's that! Here is the same computation in
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I don't have a source with that, looked at Atlas of Graphs. MathWorld lists 2 other potential sources. Probably the field should be removed unless someone knows.
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Source: Harland, Andy; Hanson, Henry (2016). "Soccer Ball
Dynamics". In Strudwick, Tony (ed.). Soccer Science. Human Kinetics. p.
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Given the diameter of a
Truncated Icosahedron sphere, how to figure out the side length of associated hexagons and pentagons?--
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appeared as a configuration of the lenses used for focusing the explosive shock waves of the detonators in both
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I think that the "tritium" (or its container) in Spider Man 2 had the shape of a truncated icosahedron... --
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I'll bite. Why put two constructions, mostly independent of each other, in one paragraph? It lacks flow.
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There's ennumerable improvements like this, and you have no disagreement from me, just time. Probably
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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Source: Rhodes, Richard (1996). Dark Sun: The Making of the
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is a truncated icosahedron. if someone could verify and add to the article, that would be nice!
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Is there an article on the naming nomenclature of plyhedra or
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Are there any sources for this jocular term for this polyhedron? Seems worthy of inclusion.
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Why does the soccer ball must have 32 faces? Why not 36 or 40 or any number of face?
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The following is an archived discussion of the DYK nomination of the article below.
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https://en.wikipedia.org/Ball_(association_football)#/media/File:Fussball_1936.jpg)
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Hydrothermal
Syntheses of Gold Nanocrystals: From Icosahedral to Its Truncated Form
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to figure any of these angles. Good luck. I've not seen that published anywhere.
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I'll go ahead and put the field back in with the value set to 3.
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has eight. 32 panel is just a common, recognizable design.
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sage: g = graphs.BuckyBall() sage: g.chromatic_number() 3
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The rule book doesn't state this at all. Rule 2 in IFAB's
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