Talk:Icosahedron

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The stellations of the icosahedron are described in University of Toronto Studies Number 6 - The Fifty-Nine Icosahedra - by HSM Coxeter, P Du Val, HT Flather, and JF Petrie - University of Toronto Press 1938 (Derek Locke)

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[edit] New stat table

I replace stat table with template version, which uses tricky nested templates as a "database" which allows the same data to be reformatted into multiple locations and formats. See here for more details: User:Tomruen/polyhedron_db_testing

Tom Ruen 00:54, 4 March 2006 (UTC)

[edit] volume vs dodecahedron

(Comment from Trevor: I'd LOVE to see a proof on this. Til then, I don't buy it.) —Preceding unsigned comment added by Btrevoryoung (talk • contribs) 12:38, 14 June 2006


If you refer to the table of volumes in Platonic solid it is relatively easy to calculate. R, the circumradius, corresponds to the radius of the sphere that the polyhedron is inscribed in. If you do some calculations you will find that (volume of dodecahedron with circumradius R)/(volume of sphere with radius R) is greater than (volume of icosahedron with circumradius R)/(volume of sphere with radius R). This is an alternative way of explaining what the article states. This may be counter-intuitive to some because it is unlike the similar situation in regards to circles and polygons. I will leave the math to you.

[edit] Proofs for Surface Area and Volume

Proofs for the surface area and volume of an icosahedron can be found here: http://mathworld.wolfram.com/Icosahedron.html David Mitchell 17:19, 31 October 2006 (UTC)

[edit] Icosahedron in 2-D

Shouldn't an icosahedron in two dimensions be a pentagon? Because if you take the tetrahedrons vertex figur, you'll see that it is a triangel, which is in the same family as the tetrahedron. It's the same thing with the octahedron. Another proof is its dual, the dodecahedron, which has pentagonal faces. I couldn't find any of this in the article, so i brought it up here.Chagi 14:33, 28 April 2007 (UTC)

A 2D analogy of the icosahedron? You could consider either facets or vertex figures. If considering vertex figures, the cube {4,3} and dodecahedron {5,3} are then 3D extensions of the triangle {3,3}, like the tetrahedron. And the octahedron {3,4} extends from a square, and icosahedron {3,5} from a pentagon. I don't see much value in this overall. If you have any geometry books that talk about this, feel free to expand this idea here. Tom Ruen 21:31, 28 April 2007 (UTC)
What I ment was, polyhedra (platonic solids only?) with triangles as faces use their vertex figure as a two-dimensional analog of themselfs, and since the icosahedron has triangles, then why would it be diffrent? While the cube in other hands, uses it face as a 2-d analog, then shouldn't the dodecahedron do the same? Chagi 22:20, 28 April 2007 (UTC)
I wasn't aware that "polyhedra ... use their vertex figure as a two-dimensional analog of themselfs". Must everything have an analogue in every domain? —Tamfang 01:13, 2 May 2007 (UTC)
I didn't say that everything must have a analog, but if it's possible to figure something out, why not do it? Secondly, I wasn't saying that polyhedra uses their vertex figure as a two-dimensional analog, I was suggesting that polyhedra with equilateral triangles use their vertex figurwe as a 2D analog.Chagi 19:37, 8 May 2007 (UTC)