Talk:Fundamental polygon

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WikiProject Mathematics (Rated Start-class, Low-priority)
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 Field:  Topology


Need a discussion of, or perhaps a new article about, the Poincare polygon theorem.

Also need higher dimensional articles, about fundamental polyhedra and the Poincare polyhedron theorem.

Perhaps the current article can be upgraded to discuss fundamental polyhedra as well, with the current text as its core.

--Mosher 11:52, 21 September 2005 (UTC)

If you set out to do this, then please create a new article for fundamental polyhedra. I beleive that WP articles work better if they can be kept short, in byte-size pieces. The reader should be trusted to follow whatever links are needed to get any background material hey may be missing. linas 22:00, 21 September 2005 (UTC)

For Those of Us Lacking Brain Cells....[edit]

It would be more introductional to state that the 2n sequence corresponds to the 2n edges of the polygon in question. Also, a point, it would be nice to know if the genus of the manifold/shape/closed surface correspond to the number of edges (by, say, something like a silly factor of 4 when dealing with simple surfaces - though I have never seen a proof of this, it does seem geometrically clear). MrASingh 03:05, 27 March 2007 (UTC)

The fundamental polygon for the klein bottle...[edit]

... is not the one shown (which is actually the torus). If anyone can locate or recreate the correct one please do so! -A13ean (talk) 18:25, 26 February 2008 (UTC)


The terminology "genus k projective plane" or "genus k Klein bottle" is something I've never heard in years of working with non-orientable surfaces in graph theory. The terminology I've always seen is "non-orientable surface of (non-orientable) genus k". Zaslav (talk) 05:52, 29 July 2009 (UTC)