Talk:Truncated icosahedron

Soccer ball

Why does the soccer ball must have 32 faces? Why not 36 or 40 or any number of face? — Preceding unsigned comment added by 153.20.95.69 (talk • contribs) 04:05, 8 September 2004 (UTC)

Because the rulebook states that a soccerball must be a truncated icosahedron. All sports have arbitrary rules such as the 18 holes on golf as oppsed to 22 or some other number.

--

Ŭalabio 05:24, 2004 Dec 30 (UTC)

The rule book doesn't state this at all. Rule 2 in IFAB's Laws of the Game (association football) 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 https://en.wikipedia.org/wiki/Ball_(association_football)#/media/File:Fussball_1936.jpg) and many recent ones don't either: see eg the Adidas Teamgeist has 14, the Adidas Jabulani has eight. 32 panel is just a common, recognizable design. Bazzargh (talk) 15:39, 15 December 2022 (UTC)

Layout

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. 4.236.78.198 17:32, 21 October 2005 (UTC)

What does the Truncated part mean?

Is there an article on the naming nomenclature of plyhedra or Archimedean solids or whatever? Dalf | Talk 06:45, 2 February 2006 (UTC)

Meaning of the names certainly could/should be described in Archimedean solid. Truncated means you take a polyhedron and slice off the corners, cutting original edges into 1/3rds, so middle third of original edges remain and original faces get doubled - triangles into hexagons in this case. Tom Ruen 07:03, 2 February 2006 (UTC)

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 truncated or truncate which is a read link. I think [[Truncation (geometry) might be a better name though as there is no article at any of the location I suppose Tuncation would be as good a place as any. The 1/3 thing and other details should be explained somehwere, and if it does not deserv its own article one or emore of the above articles shludl be redirected to whereever it is explained. Dalf | Talk 08:28, 2 February 2006 (UTC)

There's ennumerable improvements like this, and you have no disagreement from me, just time. Probably polyhedron is the best place to describe terminology. Tom Ruen 08:38, 2 February 2006 (UTC)

Truncation (geometry) article added now. Tom Ruen 00:57, 26 April 2006 (UTC)

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!

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

Dome construction using Truncated Icosahedron

Given the diameter of a Truncated Icosahedron sphere, how to figure out the side length of associated hexagons and pentagons?--Jdpan 19:39, 14 February 2007 (UTC)

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, the results would be different... AnonMoos (talk) 19:54, 14 February 2007 (UTC)

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... AnonMoos 12:16, 15 February 2007 (UTC)

A popular culture reference

I think that the "tritium" (or its container) in Spider Man 2 had the shape of a truncated icosahedron... --Itub 15:16, 13 March 2007 (UTC)

Vertex Angles

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. --SDSpivey (talk) 22:07, 15 December 2008 (UTC)

The book The Geometrical Foundation of Natural Structure is a great reference if you can find it. It has the dihedral angles, given numerically:

• 5-6: 142°37'21"
• 6-6: 138°11'22"

p.s. Used copies on amazon.com

Tom Ruen (talk) 22:44, 15 December 2008 (UTC)

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? --SDSpivey (talk) 05:03, 16 December 2008 (UTC)

You should be able to use some trigonometry and the Truncated_icosahedron#Canonical_coordinates to figure any of these angles. Good luck. I've not seen that published anywhere. Tom Ruen (talk) 17:54, 17 December 2008 (UTC)

I was able to find what I was looking for, Finding the Angles of the Truncated Icosahedron --SDSpivey (talk) 05:29, 20 December 2008 (UTC)

"Isoccerhedron"

Are there any sources for this jocular term for this polyhedron? Seems worthy of inclusion.
--Koro Neil (talk) 16:25, 24 July 2011 (UTC)

   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.
   (Did you already know that? Or do you know him?)
--Jerzy•t 03:33, 28 March 2013 (UTC)

chromatic number of truncated icosahedral graph

The current version of the article includes a figure which claims that the chromatic number 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? Noamz (talk) 20:35, 5 June 2017 (UTC)

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. Tom Ruen (talk) 22:59, 5 June 2017 (UTC)

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 SageMath:

sage: g = graphs.BuckyBall()
sage: g.chromatic_number()
3

I'll go ahead and put the field back in with the value set to 3. Noamz (talk) 10:32, 6 June 2017 (UTC)

Applications:

"this shape" seems to refer not only to truncated icosahedrons, but also to to icosahedrons themselves. [And some of the applications are only applications of icosahedrons, and not truncated icosahedrons.] — Preceding unsigned comment added by 65.130.74.174 (talk) 04:34, 27 August 2019 (UTC)

popular culture reference?

I believe the origin ball from Pokemon Legends: Arceus is a truncated icosahedron. if someone could verify and add to the article, that would be nice! QuantumChaosTheory (talk) 20:55, 28 March 2024 (UTC)

this is intended as one single paragraph

I'll bite. Why put two constructions, mostly independent of each other, in one paragraph? It lacks flow. —Tamfang (talk) 06:08, 11 July 2024 (UTC)

Did you know nomination

The following is an archived discussion of the DYK nomination of the article below. Please do not modify this page. Subsequent comments should be made on the appropriate discussion page (such as this nomination's talk page, the article's talk page or Wikipedia talk:Did you know), unless there is consensus to re-open the discussion at this page. No further edits should be made to this page.

The result was: rejected by reviewer, closed by Narutolovehinata5 talk 02:32, 27 July 2024 (UTC)

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• Comment or view
• Article history

)

The truncated icosahedron (left) compared with an association football

• ... that the football resembling a spherical truncated icosahedron was designed during the World Cup in 1970, but superseded in 2006?

• Source: Harland, Andy; Hanson, Henry (2016). "Soccer Ball Dynamics". In Strudwick, Tony (ed.). Soccer Science. Human Kinetics. p. 205. ISBN 978-1-4504-9679-7.

• ALT1: ... that the shape of a truncated icosahedron appeared as a configuration of the lenses used for focusing the explosive shock waves of the detonators in both the gadget and Fat Man atomic bombs? Source: Rhodes, Richard (1996). Dark Sun: The Making of the Hydrogen Bomb. Touchstone Books. p. 195. ISBN 0-684-82414-0.
• Reviewed:

Created by Dedhert.Jr (talk). Number of QPQs required: 0. Nominator has less than 5 past nominations.

Dedhert.Jr (talk) 13:16, 25 July 2024 (UTC).

• Sorry, but to qualify for DYK, the article must have been recently created, expanded fivefold, or promoted to GA. Since the article is neither, it doesn't qualify. Perhaps try bringing this one to GA? Thanks — PerfectSoundWhatever (t; c) 17:25, 26 July 2024 (UTC)