Talk:Truncated cuboctahedron

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Polyhedra

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Great rhombicuboctahedron

I'm quite surprised it's also called a great rhombicuboctahedron, as it isn't a stellation of the rhombicuboctahedron. Professor M. Fiendish 03:42, 23 August 2009 (UTC)[reply]

I'm not sure who the original source of this usage of small/great to distinguish between the rectified and cantellated forms: small rhombicuboctahedron and great rhombicuboctahedron. Robert Williams uses these names in The Geometric Foundations of Natural Structure. Peter Cromwell also uses this naming in polyhedra. Kepler invented the truncated cuboctahedron name which is topologically correct, even if not a geometric truncation (some say rhombitruncated cuboctahedron to distinguish this as a different sort of truncation.) Norman Johnson (mathematician), discourages the great terminology because of the stellation/nonconvex uniform polyhedron meaning. Tom Ruen (talk) 04:34, 23 August 2009 (UTC)[reply]

Over at the French Wikipedia the polyhedron template has small rhombicuboctahedron and great rhombicuboctahedron (petit rhombicuboctaèdre, grand rhombicuboctaèdre) but the articles themselves are at small rhombicuboctahedron and truncated cuboctahedron (petit rhombicuboctaèdre, cuboctaèdre tronqué). Using one and not the other is pretty inconsistent. Professor M. Fiendish 06:18, 23 August 2009 (UTC)[reply]

We actually do have a polyhedron template: Template:Polyhedron navigator, which is about the only useful contribution added by banned users User:Euclidthegreek and User:Johanneskepler. It's far too unwieldly though. The Johnson solids and near-miss Johnson solids should perhaps be split out into separate templates. Professor M. Fiendish 06:18, 23 August 2009 (UTC)[reply]

I split the Johnsons into Template:Johnson solids navigator. Professor M. Fiendish, Esq. 11:20, 23 August 2009 (UTC)[reply]

orthogonal projections

I do not understand the phrase "Face normal", particularly "Face normal 4-6". —Tamfang (talk) 08:48, 11 January 2014 (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) 01:30, 24 February 2017 (UTC)[reply]