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| | Eusebio Stanfill is what's blogged on my birth records although it is not necessarily quite the name on my birth certificate. Idaho is our birth room. I work as an get clerk. As a man what When i really like is representing but I'm thinking on top of starting something new. You will probably find my website here: http://prometeu.net<br><br>Feel free to visit my web page :: [http://prometeu.net clash of clans hacks] |
| !bgcolor=#e7dcc3 colspan=2|Deltoidal icositetrahedron
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| |align=center colspan=2|[[Image:deltoidalicositetrahedron.jpg|280px|Deltoidal icositetrahedron]]<br>''Click on picture for large version.''<br>''Click ''[[:image:deltoidalicositetrahedron.gif|here]]'' for spinning version.''
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| |bgcolor=#e7dcc3|Type||[[Catalan solid|Catalan]]
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| |bgcolor=#e7dcc3|Coxeter diagram||{{CDD|node_f1|4|node|3|node_f1}}
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| |bgcolor=#e7dcc3|Face polygon||[[kite (geometry)|kite]]
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| |bgcolor=#e7dcc3|Faces||24
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| |bgcolor=#e7dcc3|Edges||48
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| |bgcolor=#e7dcc3|Vertices||26 = 6 + 8 + 12
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| |bgcolor=#e7dcc3|[[Face configuration]]||V3.4.4.4
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| |bgcolor=#e7dcc3|[[List of spherical symmetry groups|Symmetry group]]||[[Octahedral symmetry|''O''<sub>''h''</sub>]], BC<sub>3</sub>, [4,3], *432
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| |bgcolor=#e7dcc3|[[Point_groups_in_three_dimensions#Rotation_groups|Rotation group]]||O, [4,3]<sup>+</sup>, (432)
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| |bgcolor=#e7dcc3|[[Dihedral angle]]||138° 7' 5"<br><math>\arccos(-\frac{7 + 4\sqrt{2}}{17})</math>
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| |bgcolor=#e7dcc3|[[Dual polyhedron]]||[[rhombicuboctahedron]]
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| |bgcolor=#e7dcc3|Properties||convex, [[face-transitive]]
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| |align=center colspan=2|[[Image:Deltoidalicositetrahedron net.png|280px|Deltoidal icositetrahedron]]<br>[[Net (polyhedron)|Net]]
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| In [[geometry]], a '''deltoidal icositetrahedron''' (also a '''trapezoidal icositetrahedron''' and ''tetragonal icosikaitetrahedron'') is a [[Catalan solid]] which looks a bit like an overinflated [[cube (geometry)|cube]]. Its [[dual polyhedron]] is the [[rhombicuboctahedron]].
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| ==Dimensions ==
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| The 24 faces are deltoids or [[kite (geometry)|kites]], also called ''trapezia'' in the US and ''trapezoids'' in Britain. The short and long edges of each kite are in the ratio 1:1.292893...
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| If its smallest edges have length 1, its surface area is <math>\scriptstyle{6\sqrt{29-2\sqrt{2}}}</math> and its volume is <math>\scriptstyle{\sqrt{122+71\sqrt{2}}}</math>.
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| ==Occurrences in nature and culture==
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| The deltoidal icositetrahedron is a [[crystal habit]] often formed by the mineral [[analcime]] and occasionally [[garnet]]. The shape is often called a trapezohedron in mineral contexts, although in [[solid geometry]] that name [[trapezohedron|has another meaning]].
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| ==Related polyhedra==
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| The deltoidal icositetrahedron is topologically equivalent to a [[cube]] whose faces are divided in quadrants.
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| :[[Image:Partial cubic honeycomb.png|160px]]
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| The [[great triakis octahedron]] is a stellation of the deltoidal icositetrahedron.
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| == Related polyhedra and tilings ==
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| The deltoidal icositetrahedron is one of a family of duals to the uniform polyhedra related to the cube and regular octahedron.
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| {{Octahedral truncations}}
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| This polyhedron is topologically related as a part of sequence of deltoidal polyhedra with face figure (V3.4.n.4), and continues as tilings of the [[Hyperbolic space|hyperbolic plane]]. These [[face-transitive]] figures have (*n32) reflectional [[Orbifold notation|symmetry]].
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| {{Expanded table}}
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| ==See also==
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| *[[Deltoidal hexecontahedron]]
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| *"[[The Haunter of the Dark]]", a story by H.P. Lovecraft, whose plot involves this figure
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| == References ==
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| *{{The Geometrical Foundation of Natural Structure (book)}} (Section 3-9)
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| *{{Citation |last=Wenninger |first=Magnus |authorlink=Magnus Wenninger |title=Dual Models |publisher=[[Cambridge University Press]] |isbn=978-0-521-54325-5 |mr=730208 |year=1983}} (The thirteen semiregular convex polyhedra and their duals, Page 23, Deltoidal icositetrahedron)
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| *''The Symmetries of Things'' 2008, John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, ISBN 978-1-56881-220-5 [http://www.akpeters.com/product.asp?ProdCode=2205] (Chapter 21, Naming the Archimedean and Catalan polyhedra and tilings, page 286, tetragonal icosikaitetrahedron)
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| ==External links==
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| *{{Mathworld2 |urlname=DeltoidalIcositetrahedron |title=Deltoidal icositetrahedron |urlname2=CatalanSolid |title2=Catalan solid}}
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| *[http://polyhedra.org/poly/show/36/trapezoidal_icositetrahedron Deltoidal (Trapezoidal) Icositetrahedron] – Interactive Polyhedron model
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| {{Polyhedron navigator}}
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| [[Category:Catalan solids]]
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Eusebio Stanfill is what's blogged on my birth records although it is not necessarily quite the name on my birth certificate. Idaho is our birth room. I work as an get clerk. As a man what When i really like is representing but I'm thinking on top of starting something new. You will probably find my website here: http://prometeu.net
Feel free to visit my web page :: clash of clans hacks