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| [[image:Compound of two tetrahedra.png|thumb|right|Two desmic tetrahedra. The third tetrahedron of this system is not shown, but has one vertex at the center and the other three on the plane at infinity.]] | | Buddies call her [http://Www.Bing.com/search?q=Maryalice+Finkbeiner&form=MSNNWS&mkt=en-us&pq=Maryalice+Finkbeiner Maryalice Finkbeiner] and she fully digs that title. For many years she's been performing as a [http://www.guardian.Co.uk/search?q=postal+services postal services] worker. Her partner would not like it the way she does but what she definitely likes undertaking is karaoke and now she is attempting to earn money with it. North Dakota is where by her residence is. See what is new on her web page here: http://www.agrupacionmusicalalbeniz.com/cgi-bin/comprar/sandalias-calvin-klein.php<br><br> |
| [[File:Reye configuration.svg|thumb|left|The [[Reye configuration]] with the same 12 vertices as a desmic system]]
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| In [[projective geometry]], a '''desmic system''' is a set of three [[tetrahedron|tetrahedra]] in 3-dimensional [[projective space]], such that any two are '''desmic''', (i.e. related such that each edge of one cuts a pair of opposite edges of the other). It was introduced by {{harvs|txt|authorlink=Cyparissos Stephanos|last=Stephanos|year=1879}}. The three tetrahedra of a desmic system are contained in a [[Pencil (mathematics)|pencil]] of [[quartic surface]]s. The name "desmic" comes from the [[Greek language|Greek]] word δεσμός, meaning band or chain, referring to the pencil of quartics.
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| Every line that passes through two vertices of two tetrahedra in the system also passes through a vertex of the third tetrahedron.
| | My web-site [http://www.agrupacionmusicalalbeniz.com/cgi-bin/comprar/sandalias-calvin-klein.php sandalias Calvin Klein] |
| The 12 vertices of the desmic system and the 16 lines formed in this way are the points and lines of a [[Reye configuration]].
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| ==Example==
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| The three tetrahedra given by the equations
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| *<math>\displaystyle (w^2-x^2)(y^2-z^2) = 0</math>
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| *<math>\displaystyle (w^2-y^2)(x^2-z^2) = 0</math>
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| *<math>\displaystyle (w^2-z^2)(y^2-x^2) = 0</math>
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| form a desmic system, contained in the pencil of quartics
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| *<math>\displaystyle a(w^2x^2+y^2z^2) + b(w^2y^2+x^2z^2) + c (w^2z^2+x^2y^2) = 0</math>
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| for ''a'' + ''b'' + ''c'' = 0.
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| ==References==
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| *{{Citation | last1=Borwein | first1=Peter B | authorlink = Peter Borwein | title=The Desmic conjecture | doi=10.1016/0097-3165(83)90022-5 | mr=704251 | year=1983 | journal=[[Journal of Combinatorial Theory]] | series = Series A | volume=35 | issue=1 | pages=1–9}}.
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| *{{Citation | authorlink=R. W. H. T. Hudson | last1=Hudson | first1=R. W. H. T. | title=Kummer's quartic surface | publisher=[[Cambridge University Press]] | series=Cambridge Mathematical Library | isbn=978-0-521-39790-2 | mr=1097176 | year=1990|url=http://www.archive.org/details/184605691}}.
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| *{{Citation | last1=Stephanos | first1=Cyparissos | title= Sur les systèmes desmiques de trois tétraèdres | url=http://www.numdam.org/item?id=BSMA_1879_2_3_1_424_1 | id={{JFM|11.0431.01}} | year=1879 | journal=Bulletin des sciences mathématiques et astronomiques, Sér. 2 | volume=3 | issue=1 | pages= 424–456 }}.
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| == External links ==
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| * [http://members.home.nl/fg.marcelis/desmic.htm Desmic tetrahedra]
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| [[Category:Projective geometry]]
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Buddies call her Maryalice Finkbeiner and she fully digs that title. For many years she's been performing as a postal services worker. Her partner would not like it the way she does but what she definitely likes undertaking is karaoke and now she is attempting to earn money with it. North Dakota is where by her residence is. See what is new on her web page here: http://www.agrupacionmusicalalbeniz.com/cgi-bin/comprar/sandalias-calvin-klein.php
My web-site sandalias Calvin Klein