Talk:Rhombicuboctahedron

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I have made some pictures of the various solids mentioned in the article. They aren't especially nice, in as much as they are orthogonal projections without any shading or glenzing whatsoever, but are quick to make and so could easily be done for all sorts of polyhedra, and would be ok to have until better images come along. See some here. My question is, how many of them do we want? Having several pictures for each of the Archimedean solids seems like it might be wasting space that could be better used for something else. --JG

They aren't very big, so it's probably OK if you want to do this. You can save quite a bit of space (about 35%) by recoding the PNGs as paletted PNGs, instead of 24-bit PNGs. None of your PNGs used more than 8 colours, so this can be done losslessly. I've uploaded a zip file of the recoded PNGs to http://www.zundark.btinternet.co.uk/joshpngs.zip --Zundark, 2001 Nov 9

Streetlamps in Mainz[edit]

Street lamp mainz.jpg

I took this picture of a street lamp in Mainz, shaped like a rhombicuboctahedron. Maybe it is too trivial to include in the article, but I think it is interesting. :) --Itub 13:27, 4 September 2007 (UTC)

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Pseudo­rhombi­cubocta­hedron in the book "De divina proportione"[edit]

As can be seen in http://www.scientificamerican.com/article.cfm?id=davinci-mathematical-slip-up, it was in reality the pseudo­rhombi­cubocta­hedron which was illustrated in the book "De divina proportione". — Preceding unsigned comment added by Saung Tadashi (talkcontribs) 03:31, 24 July 2013 (UTC)

translation problem[edit]

A recent addition:

In the book "De divina proportione", this shape was given the latin name "Vigintisexbasium Planum Vacuum" meaning regular solid with twenty-six faces.

Viginti sex basium would make sense, "of 26 bases". But I can't get "regular solid" out of planum vacuum, which seems to mean either "flat vacuum" or "empty plane". —Tamfang (talk) 04:24, 24 July 2013 (UTC)

and it's not even regular. suspect planum vacuum refers to the Leonardo-style drawing with just the edges shown (the faces are empty). Double sharp (talk) 14:35, 26 July 2013 (UTC)

Problem with "Pyritohedral Symmetry" section[edit]

In this section, there are five images. Four of them supplement the text. The fifth one, of a compound of two icosahedra, doesn't seem to be there for any good reason. I suggest that either, (a) the image be removed, or (b) the wording of the article changed to justify the inclusion of this image, if, in fact, it should be here. RobertLovesPi (talk) 01:29, 23 June 2015 (UTC)

The compound arises from both alternated positions of the snub octahedron. I added more description. Tom Ruen (talk) 02:52, 23 June 2015 (UTC)

The meaning and origin of "rhombi-"[edit]

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) 01:21, 24 February 2017 (UTC)
On this solid specifically, the name goes back to Kepler. (in 'The Harmony of the worlds, 1618)
p.119 "... Therefore eight triangles and eighteen (that is, twelve and six) squares join up to make an icosihexahedron [26-hedron], which I call a truncated cuboctahedral rhombus, or a rhombicuboctahedron."
p.123 for the rhombicosidodecahedron: "One trigon angle, two tetragon angles, thirty tetragons and twelve pentagons will fit together to make a hexacontadyhedron [62-hedron], which I call a rhombicosidodecahedron or a truncated icosidodecahedral rhombus."
I see topologically the rhombicuboctahedron is indeed a full truncation (or rectification) of a rhombic dodecahedron (Kepler's cuboctahedral rhombus, and also called a twelve plane rhombi). Tom Ruen (talk) 02:18, 24 February 2017 (UTC)
Rhombic dodecahedron rectified to rhombicuboctahedron.png
Thank you—great stuff! You have swept away the false reason and provided the real history!Holy (talk) 06:17, 24 February 2017 (UTC)