Talk:Facet (geometry)

grammatical morass

 * In geometry, a facet is any of several things closely related to that of a face of a polyhedron or polytope, and in general refers to certain features of a shape that have dimension as large as possible.

What does the first that mean? "Closely related to the thing of a face"?

And then, what does "as large as possible" mean?

How about:


 * a facet is any of several closely related concepts: in general, a feature of a figure of the next higher dimension.

—Tamfang (talk) 19:05, 29 December 2013 (UTC)
 * Better now? —David Eppstein (talk) 19:21, 29 December 2013 (UTC)

Faceting and facets
Does the geometrical process of faceting create new "facets"? Here on Facet (geometry), an editor has just edited out this usage on the basis that Olshevsky does not use "facet" in this sense. However both Bridge and Inchbald, cited in the linked article, both do so. Since these are peer-reviewed papers while Olshevsky is a self-published web site, should we be giving more weight to them? I should note that I am an alias for Inchbald, so should perhaps not personally edit the text that has been changed. &mdash; Cheers, Steelpillow (Talk) 09:52, 21 April 2015 (UTC)
 * I am ok with adding back that usage as long as it has a proper source. When I edited it out, it was unsourced. —David Eppstein (talk) 15:46, 21 April 2015 (UTC)
 * Thank you. I have restored it and added both cites, copied across from faceting. If anybody doesn't like me duplicating existing cites of my work, Bridge's is adequate and mine may be removed without harm. However, it is the more recent and perhaps also the more accessible. &mdash; Cheers, Steelpillow (Talk) 17:06, 21 April 2015 (UTC)

Contradiction
As it is the article contradicts itself in the first two bullet points. In particular the first bullet point starts with "In three-dimensional geometry" whereas the usage of facet described (not a face) cannot be applied to the entire field of 3D geometry. Case in point, the second bullet point also mention "In three-dimensional geometry" and go on to describe another usage of the term, where this times it's a face by generalization from higher dimensions (the only usage I'm familiar with). Maybe the first bullet point is only relevant to crystallography? Joancharmant (talk) 18:15, 14 March 2017 (UTC)

reciprocal vs dual

 * [faceting] is the reciprocal process to stellation

That implies that faceting undoes stellation, and I don't think so: the vertices of stellations of a semiregular solid are generally not those of the parent. So is this a specialized use of reciprocal? – I have often seen it said that faceting and stellation are dual operations. —Tamfang (talk) 22:57, 11 February 2023 (UTC)
 * Firstly, we go by what reliable sources say. The cited work by Coxeter uses the term "reciprocal", as in "two reciprocal processes: stellating and faceting." Failing to check or to understand is no grounds for deletion. Secondly, these processes are geometric constructions which are related via a polar reciprocity about some arbitrary conic curve (for polygons) or quadric surface (for polyhedra), usually a concentric circle or sphere respectively. Such a reciprocity is an example of a duality, and is a consequence of the deep theorem of projective duality. Yes you are right that the vertices of a stellation are generally not those of the parent but, reciprocally, you may recall that the faces of a faceting are generally not the faces of the parent's dual either. So it does work. The two figures are commonly referred to as duals, while the processes are reciprocal. &mdash; Cheers, Steelpillow (Talk) 09:46, 12 February 2023 (UTC)