semi-Hamiltonian paths in planar triangulations
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From: Yann David on 21 Jun 2010 19:47 Hum, is your "augmented" octahedron still planar though? How would you draw it in the plane?
From: Jasen Betts on 24 Jun 2010 01:18 On 2010-06-21, Yann David <yann_david(a)hotmail.com> wrote: > Hum, is your "augmented" octahedron still planar though? How would you > draw it in the plane? Any graph that can be inscribed on the surface of a sphere can be translated to a planar graph quite easily. Immagine the sphere to be a elastic membrane (like a rubber baloon) piece a face of the figure(ie at a point distant from edges and vertices) and stretch this opening until the sphereical shell is a flat membrane. --- news://freenews.netfront.net/ - complaints: news(a)netfront.net ---
From: bill on 24 Jun 2010 21:41 On Jun 21, 4:47 pm, Yann David <yann_da...(a)hotmail.com> wrote: > Hum, is your "augmented" octahedron still planar though? How would you > draw it in the plane? Start with a hexagon. Number the vertices 1 thru 6 sequentially. Add edges 13, 35, 51, 24, 46 and 62. This is a planar embedding of an octahedron. To get the "augmented" version add a vertex to each of the 7 interior faces of the graph, but no vertex in the external face.
From: spudnik on 25 Jun 2010 14:29
all convex polyhedra are readily projected to the plane, from a vertex or a face -- usually the latter, so as not to have lines going off of the paper; "Schlaffli diagrams?" > Start with a hexagon. Number the vertices 1 thru 6 > sequentially. Add edges 13, 35, 51, 24, 46 and 62. This is a planar > embedding of an octahedron. To > get the "augmented" version add a vertex to each of the > 7 interior faces of the graph, but no vertex in the > external face. thus&so: well it's a good experiment, "coking" water and calcium carbonate to make these hydrocarbs "up to 20 carbons," but I misread the statement about "oil theory with currect [sic] genesis." presumably, the neologism indicates that the current "impact theory" of lunar genesis is neither here nor there nor correct, being based really on computerized simulacra and a gross lack of data (no space program in the USA ... no energy policy, either, but cap&trade on CO2, a-hem; also, who told me that all of the USA seismometers etc. from Apollo were arbitrarily turned-off, supposedly with no recourse toe turn them back, on? anyway, given the low seismic inactivity of Moon, it is hard to see active seeps on it, as in Gulf or off of Redondo Beach, Calif., which seems to be a requirement of the abiotic theory, which seems to propose that the T & P are ultimately due to fission (also, fusion?) within Earth. > > This abiotic oil theory along with the currect genesis thus&so: the acolyte of Hubbard at Shell, wrote a couple of books that lay-out many of the indsutry's assumptions, _Peak Oil_ and _Beyond Oil_, if somewhat Greeny -- and very-much "better late, than never." presumably the processing of biogenic oil in the tectonic system would degrade the chirality etc.; I mean, there are all sorts of organic plastics in the sediment, and enormous production of it on Earth. so, is one really to presume that none of this gets into the system -- that it is somehow to be called, fossilized fuels (TM) ?? --BP loves Waxman-Obama cap&trade (at least circa Kyoto, or Waxman's '91 cap&trade on NOX and SO2) -- how about a tiny tax, instead of the Last Bailout of Wall Street and the "City of London?" http://larouchepub.com/pr_lar/2010/lar_pac/100621pne_nordyke.html --le theoreme prochaine du Fermatttt! http://wlym.com |