Spelling and grammar are fine. It's clear and concise enough, and there are wikilinks to required concepts. Verifiable with no original research: One reference is authored by the primary Wikipedia author also nominator.
Merge Proposal[ edit ] Snapshot of monthly views, and daily averages based on month from Feb Posted on talk page here: At the moment, Three-dimensional graph is now a disambiguous page Popcrate talk Probably it could be improved in other ways too.
Michael 7 write about self-dual polyhedra templates talk Polyhedronespecially Talk: Polyhedron Duality and citation. I am asking questions and getting evasive answers. There is so much animosity coming at me that I cannot tell what is ad hominem bile and what is a genuine content issue, but whichever it is, I am unable to have a sensible discussion.
As for the supposed animosity of the discussion, see here and here. Steelpillow February and Talk: But the current content debate is what matters now. If so, then we should honestly inform the reader that this is so. Boris Tsirelson talk Lewis are the two editors I have been trying to engage with.
Can some kind folks please take an independent look at it all? It seems to me, no one thinks "what to do? We know that sometimes different nonequivalent definitions coexist even in most professional mathematics examples were givenjust because mathematical truth is constant in time but its treatment by mortals is not.
In addition, polyhedra are treated in sources of different academic levels; no wonder if terminology varies a little, and default assumptions differ. As far I understand the policies of wikipedia, in such situation we have to represent coexisting approaches with due weights.
Of course, it is somewhat subjective, what are "due weights", and which versions to ignore as marginal or obsolete. Is this the only matter of dispute? They tend to be oppositional but not in a constructive way. Would you care to speak?
I wonder, to what extent you dis agree with my description of the content dispute. Or do you prefer to wait for another "kind folks"? I think that a fair summary, although Wikipedia requires us to pay more attention to what reliable sources have actually said than to the ultimate truth of what they said WP: I have suggested that, since this is an introductory article with only very basic mathematics, we should be guided by reliable secondary and tertiary sources on the subject, only supported by primary sources where necessary to fill in some of the detail, per WP: Such sources typically confine themselves to Euclidean geometry and introduce the convex, star non-convex and dual polyhedra; they consider few if any of the many more specialist definitions in use.
My attempts to describe and cite such sources have been summarily reverted, but I have not been able to get any sensible discussion of what they actually say and support, and how we should reflect that.
Hence the link in my opening post here to the duality and citation discussion. Because additional sources sounds like a useful thing to have. And ironically, the best source I ended up finding for your preferred abstract-based definition is a highly specialist primary source the Burgiel paper.
I posted them again when I started the discussion at Talk: Polyhedron Duality and citationexplaining that they had been reverted and asking why, so it is something of a surprise to me that they have yet to be noticed.
Obviously, it is not possible to defend this by vague hand-waving in the direction of Wikipedia policies about sourcing. Incidentally, Cundy and Rollett is still being used as a source in the article; Wenninger is not, but since its history as a source in this article involves it being introduced to support a statement that it does not actually contain, I have trouble being upset by this.
So if we are to continue using it as a source, it would be helpful to find some other statement that it is actually useful to source I removed one citation instance because the factoid it supported was of no great significance: What matters with Wenninger is whether it supports the current version, and in this diff I was using it to support the claims that "The dual of a uniform polyhedron can also be obtained by the process of polar reciprocation in a concentric sphere.
However, using this construction, in some cases the reciprocal figure is not a proper polyhedron. Similarly with David EppsteinI was citing Cundy and Rollett to verify the basic nature of polyhedral duality and not any headcount.Read "Image Analysis and Computer Vision: , Computer Vision and Image Understanding" on DeepDyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips.
Talk:Dual graph. Jump to navigation Jump to search.
Dual (I think I know the subject well enough to write it without sources, but that way lies original research.) especially given your question in the next section of the review on self-dual graphs. In contrast, the property of having a midsphere is self-dual: the polar of a polyhedron with a midsphere is a dual polyhedron with the same midsphere.
For the other regular polyhedra, the edge length of the dual will be different than the edge length of the primal. Great pentakis dodecahedron topic.
Great pentakis dodecahedron Type Star polyhedron Face Elements F = 60, E = 90V = 24 (χ = −6) Symmetry group I, [5,3], * Index references DU dual polyhedron Small stellated truncated dodecahedron In geometry, the great pentakis dodecahedron is a nonconvex isohedral polyhedron.
Some polyhedra are self-dual, meaning that the dual of the polyhedron is congruent to the original polyhedron. [duality 1] [duality 2] The dual of a convex polyhedron can be obtained by the process of polar reciprocation.
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