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| {{Semireg dual polyhedra db|Semireg dual polyhedron stat table|dtT}}
| | Hello, I'm Domingo, a 19 year old from Frederiksberg C, Denmark.<br>My hobbies include (but are not limited to) Slot Car Racing, Rugby league football and watching Game of Thrones.<br><br>my blog :: [http://minecraft.cardcodes.net Free Minecraft] |
| In [[geometry]], a '''triakis tetrahedron''' is an [[Archimedean solid|Archimedean dual]] solid, or a [[Catalan solid]]. Its dual is the [[truncated tetrahedron]].
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| It can be seen as a [[tetrahedron]] with [[triangular pyramid]]s added to each face; that is, it is the [[Kleetope]] of the tetrahedron. This interpretation is expressed in the name.
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| If the triakis tetrahedron has shorter edge lengths 1, it has area <math>\tfrac{5}{3} \scriptstyle{\sqrt{11}}</math> and volume <math>\tfrac{25}{36} \scriptstyle{\sqrt{2}}</math>.
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| == Orthogonal projections ==
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| {| class=wikitable
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| |+ [[Orthogonal projection]]
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| !Centered by
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| !Edge normal
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| !Face normal
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| !Edge
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| !Face/vertex
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| |- align=center
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| !Truncated<BR>[[tetrahedron]]
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| |[[File:tetrahedron t01 ae.png|100px]]
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| |[[File:tetrahedron t01 af36.png|100px]]
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| |[[File:3-simplex t01.svg|100px]]
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| |[[File:3-simplex t01 A2.svg|100px]]
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| |- align=center
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| !Triakis<BR>tetrahedron
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| |[[File:Dual tetrahedron t01 ae.png|100px]]
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| |[[File:Dual tetrahedron t01 af36.png|100px]]
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| |[[File:Dual tetrahedron t01.png|100px]]
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| |[[File:Dual tetrahedron t01 A2.png|100px]]
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| |- align=center
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| |- align=center
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| !Projective<BR>symmetry
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| ![1]
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| ![1]
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| ![3]
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| ![4]
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| |}
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| ==Variations==
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| A triakis tetrahedron with equilateral triangle faces represents a [[polyhedral net|net]] of the four-dimensional regular polytope known as the [[5-cell]].
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| ==Stellations==
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| :[[File:Stellation of triakis tetrahedron.png|160px]]
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| This chiral figure is one of thirteen [[stellation]]s allowed by [[The Fifty-Nine Icosahedra#Miller's rules|Miller's rules]].
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| == Related polyhedra ==
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| The triakis tetrahedron is a part of a sequence of polyhedra and tilings, extending into the hyperbolic plane. These [[face-transitive]] figures have (*n32) reflectional [[Orbifold notation|symmetry]].
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| {{Truncated figure1 table}}
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| {{Tetrahedron family}}
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| ==See also==
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| *[[Truncated triakis tetrahedron]]
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| ==References==
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| *{{The Geometrical Foundation of Natural Structure (book)}} (Section 3-9)
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| *{{Citation |last1=Wenninger |first1=Magnus |author1-link=Magnus Wenninger |title=Dual Models |publisher=[[Cambridge University Press]] |isbn=978-0-521-54325-5 |id={{MathSciNet |id=730208}} |year=1983}} (The thirteen semiregular convex polyhedra and their duals, Page 14, Triakistetrahedron)
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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 284, Triakis tetrahedron )
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| ==External links==
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| *{{Mathworld2 |urlname=TriakisTetrahedron |title=Triakis tetrahedron |urlname2=CatalanSolid |title2=Catalan solid}}
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| {{Polyhedron navigator}}
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| [[Category:Catalan solids]]
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| {{Polyhedron-stub}}
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Hello, I'm Domingo, a 19 year old from Frederiksberg C, Denmark.
My hobbies include (but are not limited to) Slot Car Racing, Rugby league football and watching Game of Thrones.
my blog :: Free Minecraft