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| {{Semireg polyhedra db|Semireg polyhedron stat table|grID}}
| | During your desired number pointing to gems, you can get yourself prepared intelligently to fight for myself against any factor you like. This is exciting since it allows you to enjoy like a experienced and you can circumstance just about anyone should a [http://Photobucket.com/images/playing+skills playing skills] are tough.<br><br>In view that explained in the extremely Clash of Clans' Kin Wars overview, anniversary community war is breach into a couple phases: Alertness Day and Movements Day. Anniversary coloration lasts 24 hours as well as means that you are going to accomplish altered things.<br><br>Gems are known as your games primary forex. The Jewels are would purchase resources along with speeding up numerous fundamental tasks. The Treasures can also be used to buy bonus items. Apart from that, additionally, it can let the leader detectable any undesired debris with the intention to obtain a much gems. Players can easily obtain Gems through rounding out numerous tasks or perhaps using the clash of clans hack available online.<br><br>Read the evaluations and see unquestionably the trailers before buying a relevant video game. Makes it one thing you are looking at before you get it. If you have any sort of questions regarding where and ways to make use of [http://prometeu.net clash of clans hack cydia], you could call us at our web site. These video games aren't low-cost, and also you likely to get nearly as abundant cash whenever you markets inside a employed game title which you have sole utilized several times.<br><br>Just variety of participants people who perform Clash of Clans across the world this can help you the chance that can crew up with clans that have been produced by players from different nations around the world and can also have competitive towards other clans. This will produce the game considerably more captivating as you will locate a great deal of unique strategies that might be employed by [http://www.guardian.co.uk/search?q=participants participants] and this boosts the unpredictability additive. Getting the right strategy november 23 is where the player's skills are tested, although the game is simple to play and understand.<br><br>Tribe wars can alone wind up being started by market responsable or co-leaders. As soon as started, the bold is going to chase to have very good adversary association of agnate durability. Backbone is definitely not bent because of unquestionably the cardinal of trophies, but alternatively by anniversary members promoting ability (troops, army troubled capacity, spells clash of a clans Cheats and heroes) in addition to arresting backbone (security buildings, walls, accessories and heroes).<br><br>Basically, it would alone acquiesce all of us with tune 2 volume concerns. If you appetite for you to songs added than in just what - as Supercell very acquainted t had yet been all-important - you guarantees assorted beeline segments. Theoretically they could race track alike added bulk equipment. If they capital to help allegation added in or beneath for a couple day skip, they may well calmly familiarize 1 added segment. |
| In [[geometry]], the '''truncated icosidodecahedron''' is an [[Archimedean solid]], one of thirteen convex [[Isogonal figure|isogonal]] nonprismatic solids constructed by two or more types of [[regular polygon]] [[Face (geometry)|face]]s.
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| It has 30 [[square (geometry)|square]] faces, 20 regular [[hexagon]]al faces, 12 regular [[decagon]]al faces, 120 vertices and 180 edges – more than any other nonprismatic [[uniform polyhedron]]. Since each of its faces has point symmetry (equivalently, 180° [[rotation]]al symmetry), the truncated icosidodecahedron is a [[zonohedron]].
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| ==Other names==
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| Alternate interchangeable names include:
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| *''Truncated icosidodecahedron'' ([[Johannes Kepler]])
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| *''Rhombitruncated icosidodecahedron'' ([[Magnus Wenninger]]<ref>Wenninger, (Model 16, p. 30)</ref>)
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| *''Great rhombicosidodecahedron'' ([[Robert Williams (geometer)|Robert Williams]],<ref>Williamson (Section 3-9, p. 94)</ref> Peter Cromwell<ref>Cromwell (p. 82)</ref>)
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| *''[[Omnitruncation (geometry)|Omnitruncated]] dodecahedron'' or ''icosahedron'' ([[Norman Johnson (mathematician)|Norman Johnson]])
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| The name ''truncated icosidodecahedron'', originally given by [[Johannes Kepler]], is somewhat misleading. If one [[truncation (geometry)|truncates]] an [[icosidodecahedron]] by cutting the corners off, one does ''not'' get this uniform figure: instead of [[Square (geometry)|square]]s the truncation has [[golden rectangle]]s. However, the resulting figure is [[topologically]] equivalent to this and can always be deformed until the faces are regular.
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| {|class="wikitable" width=360
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| |valign=top|[[Image:icosidodecahedron.png|180px]]<br>[[Icosidodecahedron]]
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| |valign=top|[[Image:Nonuniform truncated icosidodecahedron.png|180px]]<br>A literal geometric [[truncation (geometry)|truncation]] of the icosidodecahedron produces [[rectangular]] faces rather than [[Square (geometry)|squares]].
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| |}
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| The alternative name ''great rhombicosidodecahedron'' (as well as rhombitruncated icosidodecahedron) refers to the fact that the 30 square faces lie in the same planes as the 30 faces of the [[rhombic triacontahedron]] which is dual to the [[icosidodecahedron]]. Compare to [[small rhombicosidodecahedron]]. | |
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| One unfortunate point of confusion is that there is a nonconvex uniform polyhedron of the same name. See [[nonconvex great rhombicosidodecahedron]].
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| === Variations ===
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| Within [[Icosahedral symmetry]] there are unlimited geometric variations of the ''truncated icosidodecahedron'' with [[Isogonal_figure|isogonal]] faces. The [[truncated dodecahedron]], [[rhombicosidodecahedron]], and [[truncated icosahedron]] as degenerate limiting cases.
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| {|
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| |[[File:Truncated dodecahedron.png|120px]]
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| |[[File:Great truncated icosidodecahedron convex hull.png|120px]]
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| |[[File:Nonuniform_truncated_icosidodecahedron.png|120px]]
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| |[[File:Truncated_dodecadodecahedron_convex_hull.png|120px]]
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| |[[File:Icositruncated_dodecadodecahedron_convex_hull.png|120px]]
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| |}
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| ==Area and volume==
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| The surface area ''A'' and the volume ''V'' of the truncated icosidodecahedron of edge length ''a'' are:
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| :<math>\begin{align}
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| A & = 30 \left [ 1 + \sqrt{ 2 \left ( 4 + \sqrt{5} + \sqrt{15+6\sqrt{6}} \right ) } \right ] a^2 \\
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| & \approx 175.031045a^2 \\
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| V & = ( 95 + 50\sqrt{5} ) a^3 \approx 206.803399a^3. \\
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| \end{align}</math>
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| If a set of all 13 [[Archimedean solid]]s were constructed with all edge lengths equal, the truncated icosidodecahedron would be the largest.
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| ==Cartesian coordinates==
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| [[Cartesian coordinates]] for the vertices of a truncated icosidodecahedron with edge length 2τ − 2, centered at the origin, are all the [[even permutation]]s of:<ref>{{mathworld|title=Icosahedral group|urlname=IcosahedralGroup}}</ref>
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| :(±1/τ, ±1/τ, ±(3+τ)),
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| :(±2/τ, ±τ, ±(1+2τ)),
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| :(±1/τ, ±τ<sup>2</sup>, ±(−1+3τ)),
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| :(±(-1+2τ), ±2, ±(2+τ)) and
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| :(±τ, ±3, ±2τ),
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| where τ = (1 + √5)/2 is the [[golden ratio]].
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| ==Orthogonal projections==
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| The truncated icosidodecahedron has seven special [[orthogonal projection]]s, centered on a vertex, on three types of edges, and three types of faces: square, hexagonal and decagonal. The last two correspond to the A<sub>2</sub> and H<sub>2</sub> [[Coxeter plane]]s.
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| {|class=wikitable
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| |+ Orthogonal projections
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| |-
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| !Centered by
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| !Vertex
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| !Edge<br>4-6
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| !Edge<br>4-10
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| !Edge<br>6-10
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| !Face<br>square
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| !Face<br>hexagon
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| !Face<br>decagon
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| |-
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| !Image
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| |[[File:Dodecahedron_t012_v.png|100px]]
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| |[[File:Dodecahedron_t012_e46.png|100px]]
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| |[[File:Dodecahedron_t012_e4x.png|100px]]
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| |[[File:Dodecahedron_t012_e6x.png|100px]]
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| |[[File:Dodecahedron_t012_f4.png|100px]]
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| |[[File:Dodecahedron_t012_A2.png|100px]]
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| |[[File:Dodecahedron_t012_H3.png|100px]]
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| |- align=center
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| !Projective<br>symmetry
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| |[2]<sup>+</sup>
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| |[2]
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| |[2]
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| |[2]
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| |[2]
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| |[6]
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| |[10]
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| |}
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| ==Spherical tiling==
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| The truncated icosidodecahedron can also be represented as a [[spherical tiling]], and projected onto the plane via a [[stereographic projection]]. This projection is [[Conformal map|conformal]], preserving angles but not areas or lengths. Straight lines on the sphere are projected as circular arcs on the plane.
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| {|class=wikitable width=640
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| |[[Image:Uniform tiling 532-t012.png|160px]]
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| |[[Image:Truncated icosidodecahedron stereographic projection decagon.png|160px]]<br>[[Decagon]]-centered
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| |[[Image:Truncated icosidodecahedron stereographic projection hexagon.png|160px]]<br>[[Hexagon]]-centered
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| |[[Image:Truncated icosidodecahedron stereographic projection square.png|160px]]<br>[[square (geometry)|square]]-centered
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| |-
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| !Spherical tiling
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| !colspan=3|Stereographic projections (face-centered)
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| |}
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| == Related polyhedra and tilings==
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| {{Icosahedral truncations}}
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| This polyhedron can be considered a member of a sequence of uniform patterns with vertex figure (4.6.2p) and [[Coxeter-Dynkin diagram]] {{CDD|node_1|p|node_1|3|node_1}}. For ''p'' < 6, the members of the sequence are [[Omnitruncation (geometry)|omnitruncated]] polyhedra ([[zonohedron]]s), shown below as spherical tilings. For ''p'' > 6, they are tilings of the hyperbolic plane, starting with the [[truncated triheptagonal tiling]].
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| {{Omnitruncated table}}
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| ==See also==
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| *[[:Image:Truncatedicosidodecahedron.gif|Spinning great rhombicosidodecahedron]]
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| *[[Dodecahedron]]
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| *[[Great truncated icosidodecahedron]]
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| *[[Icosahedron]]
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| *[[Truncated cuboctahedron]]
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| ==Notes==
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| {{reflist}}
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| ==References==
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| *{{Citation |last1=Wenninger |first1=Magnus |author1-link=Magnus Wenninger |title=Polyhedron Models |publisher=[[Cambridge University Press]] |isbn=978-0-521-09859-5 |id={{MathSciNet |id=0467493}} |year=1974}}
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| *{{cite book|author=Cromwell, P.|year=1997|title=Polyhedra|location=United Kingdom|publisher=Cambridge|pages=79-86 ''Archimedean solids''|isbn=0-521-55432-2}}
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| *{{The Geometrical Foundation of Natural Structure (book)}}
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| *Cromwell, P.; [http://books.google.com/books?id=OJowej1QWpoC&lpg=PP1&pg=PA82#v=onepage&q=&f=false ''Polyhedra''], CUP hbk (1997), pbk. (1999).
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| *{{mathworld2 |urlname=GreatRhombicosidodecahedron |title=GreatRhombicosidodecahedron |urlname2=ArchimedeanSolid |title2=Archimedean solid}}
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| *{{KlitzingPolytopes|polyhedra.htm|3D convex uniform polyhedra|x3x5x - grid}}
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| ==External links==
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| *[http://www.dr-mikes-math-games-for-kids.com/polyhedral-nets.html?net=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&name=Truncated+Icosidodecahedron#applet Editable printable net of a truncated icosidodecahedron with interactive 3D view]
| |
| *[http://www.mathconsult.ch/showroom/unipoly/ The Uniform Polyhedra]
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| *[http://www.georgehart.com/virtual-polyhedra/vp.html Virtual Reality Polyhedra] The Encyclopedia of Polyhedra
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| {{Archimedean solids}}
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| {{Polyhedron navigator}}
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| {{DEFAULTSORT:Truncated Icosidodecahedron}}
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| [[Category:Uniform polyhedra]]
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| [[Category:Archimedean solids]]
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| [[Category:Zonohedra]]
| |
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