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| | Hi there. Allow me start by introducing the writer, her name is Myrtle Cleary. Years in the past we moved to North Dakota. Playing baseball is the hobby he will never stop doing. Hiring is his profession.<br><br>Also visit my website :: [http://Dinky.in/?dietfooddelivery78594 healthy meals delivered] |
| !bgcolor=#e7dcc3 colspan=2|Disdyakis triacontahedron
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| |align=center colspan=2|[[Image:disdyakistriacontahedron.jpg|240px|Disdyakis triacontahedron]]<br>''Click on picture for large version''<br>
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| [[:image:disdyakistriacontahedron.gif|spinning version]]''
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| |bgcolor=#e7dcc3|Type||[[Catalan solid|Catalan]]
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| |bgcolor=#e7dcc3|Coxeter diagram||{{CDD|node_f1|5|node_f1|3|node_f1}}
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| |bgcolor=#e7dcc3|Face polygon||[[scalene triangle]]
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| |bgcolor=#e7dcc3|Faces||120
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| |bgcolor=#e7dcc3|Edges||180
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| |bgcolor=#e7dcc3|Vertices||62 = 12 + 20 + 30
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| |bgcolor=#e7dcc3|[[Face configuration]]||V4.6.10
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| |bgcolor=#e7dcc3|[[List of spherical symmetry groups|Symmetry group]]||I<sub>h</sub>, H<sub>3</sub>, [5,3], (*532)
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| |bgcolor=#e7dcc3|[[Point_groups_in_three_dimensions#Rotation_groups|Rotation group]]||I, [5,3]<sup>+</sup>, (532)
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| |bgcolor=#e7dcc3|[[Dihedral angle]]||164° 53' 17"
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| |bgcolor=#e7dcc3|[[Dual polyhedron]]||[[truncated icosidodecahedron]]
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| |bgcolor=#e7dcc3|Properties||convex, [[face-transitive]]
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| |align=center colspan=2|[[Image:disdyakistriacontahedron net.png|240px|Disdyakis triacontahedron]]<BR>[[Net (polyhedron)|Net]]
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| In [[geometry]], a '''disdyakis triacontahedron''', or '''hexakis icosahedron''' is a [[Catalan solid]] with 120 faces and the dual to the [[Archimedean solid|Archimedean]] [[truncated icosidodecahedron]]. As such it is face uniform but with irregular face polygons. It looks a bit like an inflated [[rhombic triacontahedron]]—if one replaces each face of the rhombic triacontahedron with a single vertex and four triangles in a regular fashion one ends up with a disdyakis triacontahedron. That is, the disdyakis triacontahedron is the [[Kleetope]] of the rhombic triacontahedron. It also has the most faces among the Archimedean and Catalan solids, with the [[snub dodecahedron]], with 92 faces, in second place.
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| ==Symmetry==
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| The edges of the polyhedron projected onto a sphere form ten [[great circle]]s, and represent all ten mirror planes of reflective ''I<sub>h</sub>'' [[icosahedral symmetry]], as shown in this image. Combining pairs of light and dark triangles define the fundamental domains of the nonreflective (''I'') icosahedral symmetry.
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| {|class=wikitable width=240
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| |[[File:Icosahedral reflection domains.png|120px]]
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| |[[File:Disdyakis triacontahedron.png|120px]]
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| ==Related polyhedra==
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| {{Icosahedral truncations}}
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| It is topologically related to a polyhedra sequence defined by the [[face configuration]] ''V4.6.2n''. This group is special for having all even number of edges per vertex and form bisecting planes through the polyhedra and infinite lines in the plane, and continuing into the hyperbolic plane for any <math>n \ge 7.</math>
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| With an even number of faces at every vertex, these polyhedra and tilings can be shown by alternating two colors so all adjacent faces have different colors.
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| Each face on these domains also corresponds to the fundamental domain of a [[symmetry group]] with order 2,3,n mirrors at each triangle face vertex.
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| {{Omnitruncated table}}
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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 25, Disdyakistriacontahedron )
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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 285, kisRhombic triacontahedron )
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| ==External links==
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| *{{Mathworld2 |urlname=DisdyakisTriacontahedron |title=Disdyakis triacontahedron |urlname2=CatalanSolid |title2=Catalan solid}}
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| *[http://polyhedra.org/poly/show/43/hexakis_icosahedron Disdyakis triacontahedron (Hexakis Icosahedron)] – Interactive Polyhedron Model
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| {{Polyhedron navigator}}
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| [[Category:Catalan solids]]
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Hi there. Allow me start by introducing the writer, her name is Myrtle Cleary. Years in the past we moved to North Dakota. Playing baseball is the hobby he will never stop doing. Hiring is his profession.
Also visit my website :: healthy meals delivered