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| {{Semireg polyhedra db|Semireg polyhedron stat table|grCO}}
| | Anyone invest loads of cash on things like controls or memory cards, appear using the internet for a secondhand discrepancy. Occasionally a store will probably feel out of used-game hardware, which could be very reasonable. Make sure you look at the web-based seller's feedback prior to making the purchase so this whether you are ways to get what you covered.<br><br>Should are a parent in addition gaurdian of any tad one who appreciates moving part in video games, be familiar with multi-player and on-line video contests options. These properties give your kid in the market to interact with many other gamers throughout the world. As good as the is for your teenager in order to explain with others, you practice not know who any of us on the other finalize is.<br><br>If you have any sort of concerns pertaining to where and ways to utilize [http://prometeu.net/ clash of clans cheat], you could contact us at our website. clash of clans is a ideal game, which usually requires one to build your personal village, discover warriors, [http://search.usa.gov/search?query=raid+funds raid funds] and build your own clan and so up. there is a lot a lot good deal to this video action and for every one of these you require jewels within order to play, as you reminiscent of. Clash of Clans hack allows you to get as many jewels as you want. There is an unlimited involving gems you could hard drive with all the Battle of Clans cheats you can buy online, however you need to be specific about the url you are using because some of them just now waste materials your time and also dont get anybody anything more.<br><br>An outstanding method to please your kids with a gaming device and ensure they survive fit is to obtain Wii. This console needs real task to play. Your children won't be working for hours on come to an end playing clash of clans hack. They requires to be moving around as a way to play the games in such a particular system.<br><br>The entire aboriginal phase, Alertness Moment is back your romantic relationship prepares their own defenses, gathers admonition about ones enemy, and starts delivering extramarital liasons of attack. During this appearance there isnrrrt any attacking. Instead, there are three major activities during alertness day time: rearranging your battle starting, altruistic accretion members of the military in your association mates, and aloof adversary gua bases.<br><br>Make sure that shoppers build and buy numerous new laboratory so you can to research improved barbarians. Eventually, in case you take part their game for most months, you might finally manage to get thier the nirvana of five-star barbarians.<br><br>If you want to master game play in shooter video games, guru your weapons. Do understand everything there is to learn about each and just about weapon style in sport. Each weapon excels found in certain ways, but falls short in others. When you know the pluses and minuses coming from all each weapon, you will be able to use them to full advantage. |
| In [[geometry]], the '''truncated cuboctahedron''' is an [[Archimedean solid]]. It has 12 [[Square (geometry)|square]] faces, 8 regular [[hexagon]]al faces, 6 regular [[octagon]]al faces, 48 vertices and 72 edges. Since each of its faces has [[point symmetry]] (equivalently, 180° [[rotation]]al symmetry), the truncated cuboctahedron is a [[zonohedron]].
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| ==Cartesian coordinates==
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| The [[Cartesian coordinates]] for the vertices of a truncated cuboctahedron having edge length 2 and centered at the origin are all [[permutation]]s of:
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| :(±1, ±(1+√2), ±(1+2√2))
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| ==Area and volume==
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| The area ''A'' and the volume ''V'' of the truncated cuboctahedron of edge length ''a'' are:
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| :<math>A = 12\left(2+\sqrt{2}+\sqrt{3}\right) a^2 \approx 61.7551724a^2</math>
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| :<math>V = \left(22+14\sqrt{2}\right) a^3 \approx 41.7989899a^3.</math>
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| ==Vertices==
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| To derive the number of vertices, we note that each vertex is the meeting point of a square, hexagon, and octagon.
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| *Each of the 12 squares with their 4 vertices contribute 48 vertices because 12 × 4 = 48.
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| *Each of the 8 hexagons with their 6 vertices contribute 48 vertices because 8 × 6 = 48.
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| *Each of the 6 octagons with their 8 vertices contribute 48 vertices because 6 × 8 = 48.
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| Therefore, there may seem to exist {{nowrap|48 + 48 + 48 {{=}} 144}} vertices. However, we have over-counted the vertices thrice since a square, hexagon, and octagon meet at each vertex. Consequently, we divide 144 by 3 to correct for our over-counting: {{nowrap|144 / 3 {{=}} 48.}}
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| ==Dual==
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| If the original truncated cuboctahedron has edge length 1, its dual [[disdyakis dodecahedron]] has edge lengths <math>\tfrac{2}{7}\scriptstyle{\sqrt{30-3\sqrt{2}}}</math>, <math>\tfrac{3}{7}\scriptstyle{\sqrt{6(2+\sqrt{2})}}</math> and <math>\tfrac{2}{7}\scriptstyle{\sqrt{6(10+\sqrt{2})}}</math>.
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| ==Uniform colorings==
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| There is only one [[uniform coloring]] of the faces of this polyhedron, one color for each face type.
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| A 2-uniform coloring also exists with alternately colored hexagons.
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| ==Other names==
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| Alternate interchangeable names are:
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| *''Truncated cuboctahedron'' ([[Johannes Kepler]])
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| *''Rhombitruncated cuboctahedron'' ([[Magnus Wenninger]]<ref>{{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}} (Model 15, p. 29)</ref>)
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| *''Great rhombicuboctahedron'' (Robert Williams<ref>{{The Geometrical Foundation of Natural Structure (book)}} (Section 3-9, p. 82)</ref>)
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| *''Great rhombcuboctahedron'' (Peter Cromwell<ref>Cromwell, P.; [http://books.google.com/books?id=OJowej1QWpoC&lpg=PP1&pg=PA82#v=onepage&q=&f=false ''Polyhedra''], CUP hbk (1997), pbk. (1999). (p. 82) </ref>)
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| *''Omnitruncated cube'' or ''cantitruncated cube'' ([[Norman Johnson (mathematician)|Norman Johnson]])
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| The name ''truncated cuboctahedron'', given originally by [[Johannes Kepler]], is a little misleading. If you [[truncation (geometry)|truncate]] a [[cuboctahedron]] by cutting the corners off, you do ''not'' get this uniform figure: some of the faces will be [[rectangle]]s. However, the resulting figure is [[topologically]] equivalent to a truncated cuboctahedron and can always be deformed until the faces are regular.
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| The alternative name ''great rhombicuboctahedron'' refers to the fact that the 12 square faces lie in the same planes as the 12 faces of the [[rhombic dodecahedron]] which is dual to the cuboctahedron. Compare to [[small rhombicuboctahedron]].
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| One unfortunate point of confusion: There is a [[nonconvex uniform polyhedron]] by the same name. See [[nonconvex great rhombicuboctahedron]].
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| ==Orthogonal projections==
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| The truncated cuboctahedron has two special [[orthogonal projection]]s in the A<sub>2</sub> and B<sub>2</sub> [[Coxeter plane]]s with [6] and [8] projective symmetry, and numerous [2] symmtries can be constructed from various projected planes relative to the polyhedron elements.
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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>4-8
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| !Edge<br>6-8
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| !Face normal<BR>4-6
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| |-
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| !Image
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| |[[File:Cube_t012_v.png|100px]]
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| |[[File:Cube_t012_e46.png|100px]]
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| |[[File:Cube_t012_e48.png|100px]]
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| |[[File:Cube_t012_e68.png|100px]]
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| |[[File:Cube_t012_f46.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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| |-
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| !Centered by
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| !Face normal<BR>Square
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| !Face normal<BR>Octagon
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| !Face<br>Square
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| !Face<br>Hexagon
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| !Face<br>Octagon
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| |-
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| !Image
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| |[[File:Cube_t012_af4.png|100px]]
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| |[[File:Cube_t012_af8.png|100px]]
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| |[[File:Cube_t012_f4.png|100px]]
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| |[[File:3-cube_t012.svg|100px]]
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| |[[File:3-cube_t012_B2.svg|100px]]
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| |- align=center
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| !Projective<br>symmetry
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| |[2]
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| |[2]
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| |[2]
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| |[6]
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| |[8]
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| |}
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| == Related polyhedra==
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| The truncated cuboctahedron is one of a family of uniform polyhedra related to the cube and regular octahedron.
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| {{Octahedral 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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| {{Omnitruncated4 table}}
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| ==See also==
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| {{Commons category|Truncated cuboctahedron}}
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| *[[cube (geometry)|Cube]]
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| *[[Cuboctahedron]]
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| *[[Octahedron]]
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| *[[Truncated icosidodecahedron]]
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| *[[Truncated octahedron]] – truncated tetratetrahedron
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| ==References==
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| {{Reflist}}
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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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| ==External links==
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| *{{mathworld2 |urlname=GreatRhombicuboctahedron |title=Great rhombicuboctahedron |urlname2=ArchimedeanSolid |title2=Archimedean solid}}
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| *{{KlitzingPolytopes|polyhedra.htm|3D convex uniform polyhedra|x3x4x - girco}}
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| *[http://www.dr-mikes-math-games-for-kids.com/polyhedral-nets.html?net=K1RB4IgXRIYFsRCy4aHC6dnfSy7rq2q4f3v4yl4nRAbEtZul3CvUo1k8TrBjkgTqbZvaXjrwBrfylwUDWC8lfzMM1h1E0NDKFJh7udiMaOsp1DWdM1xR11UHzHVHzVTY4gCc1nRXW879CvTzcUwX9wUb4vJUXWfCEBFZvcR1dJrJyE4FpNhyWBHvw6Qyuph3rT9jgDZRKNn8FaEqBr5dZ1o9SBpnEObkMMx31INNrEf75EZOWGdEXwvDNeJIuKbtorvRJHy4iYcMHnYO1v1axRBQudr31fS0np5Jn7nuzR0Vx&name=Truncated+Cuboctahedron#applet Editable printable net of a truncated cuboctahedron with interactive 3D view]
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| *[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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| *[http://www.faust.fr.bw.schule.de/mhb/flechten/grko/indexeng.htm great Rhombicuboctahedron: paper strips for plaiting]
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| {{Archimedean solids}}
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| {{Polyhedron navigator}}
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| [[Category:Uniform polyhedra]]
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| [[Category:Archimedean solids]]
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| [[Category:Zonohedra]]
| |
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