Talk:Truncated icosidodecahedron

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Polyhedra

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Somebody should make a soccer ball shaped like this ^_^ Of course, it would be much more expensive...but would look so much cooler! I wonder if the aerodynamics would be significantly different...?

Cartesian coordinates

I don't care, didn't add the original term, but it is used ALL over, if you want to change it. Tom Ruen 06:20, 7 February 2006 (UTC)[reply]

I'll change them when I happen to visit the pages ... or maybe, who knows, I'll get ambitious. ;) —Tamfang 18:24, 7 February 2006 (UTC)[reply]

I wonder what we both meant by that. —Tamfang (talk) 04:58, 20 April 2018 (UTC)[reply]

Indeed! Tom Ruen (talk) 17:41, 20 April 2018 (UTC)[reply]

to put that another way

If we multiply everything by φ, the edge length becomes 2 and the coordinates are the even permutations of

(\pm 1,\pm 1,\pm (4\phi +1))

(\pm 2,\pm \phi ^{2},\pm (3\phi +2))

(\pm 1,\pm \phi ^{3},\pm (2\phi +3))

(\pm (\phi +2),\pm 2\phi ,\pm (3\phi +1))

(\pm \phi ^{2},\pm 3\phi ,\pm 2\phi ^{2})

—Tamfang (talk) 04:58, 20 April 2018 (UTC)[reply]

I'd go with that! Tom Ruen (talk) 17:41, 20 April 2018 (UTC)[reply]

Error in the area formula

The solid has 30 square, 20 hexagonal and 12 decagonal faces in total, so its area should be

$A_{O}=30a^{2}\left(1+{\sqrt {3}}+{\sqrt {5+2{\sqrt {5}}}}\right)$

It is equal to 174.2920303 in estimation.

Please check the calculation, it is quite simple, and if I am right, correct the formula (and remove this talk).

31.11.242.188 (talk) 00:21, 1 January 2015 (UTC)[reply]

The formula used now is referenced on Mathworld [1], and comes out to 175.031044596 by my calculator, while a reference book The Geometrical Foundation of Natural Structure: A Source Book of Design, shows a decimal 174.2880, close!?. How hard could it be!?

Area of regular n-gon, edge length 1 = n/(4*tan(pi/n))

30 {4} - 4/(4*tan(pi/4))*30 = 1*30 = 30

20 {6} - 6/(4*tan(pi/6))*20 = 51.961524

12 {10} - 10/(4*tan(pi/10))*12 = 92.330506

Total 174.29203

So I'm in agreement with 31.11.242.188, although it would be better to have SOURCE to reference! Tom Ruen (talk) 02:21, 1 January 2015 (UTC)[reply]

I don't think so, look here : https://www.slideshare.net/hcr1991/mathematical-analysis-of-great-rhombicosidodecahedron-the-largest-archimedean-solid/ InternetowyGołąb (talk) 13:18, 3 July 2017 (UTC)[reply]

The meaning and origin of "rhombi-"

On several Wikipedia pages, regarding the naming of solids, it is claimed—in all instances, without citation—that the prefix "rhombi-" comes from the fact that some or all of the faces of the solid in question lie in the same plane as the faces of another solid (e.g., the rhombic dodecahedron) that happens to have the name "rhombic" in it. I think this can be shown to be specious (even though I've found this claim on one non-Wikipedia page, but also unsourced there) for several reasons:

(1) See http://www.geom.uiuc.edu/~teach95/kt95/KTL12t.html. This page says, "What does rhombi mean in the name of a polyhedron? Answer: The true answer to this is a bit complex. Students should make a connection between the red (medium shaded) squares that arise in the polyhedra with rhombi in the naming. You could make the connection that the etymology of rhombi meant a square."

(2) The most obvious meaning of "rhomb-" is related to squares or rhombuses (rhombi). All the polyhedra with "rhomb-" prefixes have square faces. (And there's something special about them, which I'll explain later.)

(3) An alternate name for the cuboctahedron is "rhombitetratetrahedron," but the cuboctahedron does not have any set of faces that happen to lie in the same plane as another solid with "rhombic" in its name.

(4) I'm guessing (but can't source this) that many of the "rhombi-" names were in use BEFORE the names of the solids that supposedly gave rise to their "rhomb-" prefixes.

(5) A logical explanation (hinted at in the above link) is that the square faces came as the result of distortion into a "rhombic" shape (i.e., their square shape, which are quadrilaterals with equal-length sides) after the solid was generated by a geometric operation, such as expansion. For example, the rhombi-truncated cuboctahedron is generated by truncation of the cuboctahedron, but this leaves rectangles instead of square faces. The "rhombi-" prefix clarifies that the truncated shape must be deformed into the Archimedean solid that has square faces instead of rectangles. You can easily find an explanation like this for all solids that have "rhomb" in their names or alternate names.

(6) It just seems odd that the coincidence of planes for some faces should justify a name, when there's often no other direct connection to the named-after solid, especially when there are usually many other solids with closer geometrical connections that did not affect the naming of the new solid. For example, there are many solids that have faces that lie in the same plane as dodecahedra (or tetrahedra, or cubes), yet they don't have some form or portion of the word "dodecahedron" (or "tetrahedron," or "cube") in their name. If anyone can confirm the information as written, please do so. Otherwise, I may change the text and cite the link I have provided above.Holy (talk) 01:28, 24 February 2017 (UTC)[reply]