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| {{Semireg polyhedra db|Semireg polyhedron stat table|tC}}
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| In [[geometry]], the '''truncated cube''', or '''truncated hexahedron''', is an [[Archimedean solid]]. It has 14 regular faces (6 [[octagon]]al and 8 [[triangle (geometry)|triangular]]), 36 edges, and 24 vertices.
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| If the truncated cube has unit edge length, its dual [[triakis octahedron]] has edges of lengths 2 and <math>\scriptstyle {2+\sqrt{2}}</math>.
| | Have a look at my blog [http://wiki.geigw.de/index.php/Xbox_360_Emulator_-_Official_Free_Pcx360_Emulator_For_Pc xbox 360 emu] |
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| ==Area and volume==
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| The area ''A'' and the [[volume]] ''V'' of a truncated cube of edge length ''a'' are:
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| :<math>A = 2\left(6+6\sqrt{2}+\sqrt{3}\right)a^2 \approx 32.4346644a^2</math>
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| :<math>V = \frac{1}{3}\left(21+14\sqrt{2}\right)a^3 \approx 13.5996633a^3.</math>
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| ==Orthogonal projections==
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| The ''truncated cube'' has five special [[orthogonal projection]]s, centered, on a vertex, on two types of edges, and two types of faces: triangles, and octagons. The last two correspond to the B<sub>2</sub> and A<sub>2</sub> [[Coxeter plane]]s.
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| {|class=wikitable width=640
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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>3-8
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| !Edge<br>8-8
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| !Face<br>Octagon
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| !Face<br>Triangle
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| |-
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| !Truncated<BR>cube
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| |[[File:Cube t01 v.png|100px]]
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| |[[File:Cube t01 e38.png|100px]]
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| |[[File:Cube t01 e88.png|100px]]
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| |[[File:3-cube t01_B2.svg|100px]]
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| |[[File:3-cube t01.svg|100px]]
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| |-
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| ![[Triakis octahedron|Triakis<BR>octahedron]]
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| |[[File:Dual truncated cube t01 v.png|100px]]
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| |[[File:Dual truncated cube t01 e8.png|100px]]
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| |[[File:Dual truncated cube t01 e88.png|100px]]
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| |[[File:Dual truncated cube t01_B2.png|100px]]
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| |[[File:Dual truncated cube t01.png|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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| |[4]
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| |[6]
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| |}
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| ==Cartesian coordinates==
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| The following [[Cartesian coordinates]] define the vertices of a [[Truncation (geometry)|truncated]] [[hexahedron]] centered at the origin with edge length 2ξ:
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| :(±ξ, ±1, ±1),
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| :(±1, ±ξ, ±1),
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| :(±1, ±1, ±ξ)
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| where ξ = <math>\scriptstyle {\sqrt2 - 1}</math>
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| == Vertex arrangement==
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| It shares the [[vertex arrangement]] with three [[nonconvex uniform polyhedra]]:
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| {|class="wikitable" width="400" style="vertical-align:top;text-align:center"
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| |[[Image:Truncated hexahedron.png|100px]]<br>Truncated cube
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| |[[Image:Uniform great rhombicuboctahedron.png|100px]]<br>[[Nonconvex great rhombicuboctahedron]]
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| |[[Image:Great cubicuboctahedron.png|100px]]<br>[[Great cubicuboctahedron]]
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| |[[Image:Great rhombihexahedron.png|100px]]<br>[[Great rhombihexahedron]]
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| |}
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| ==Related polyhedra==
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| The truncated cube 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 is topologically related as a part of sequence of uniform [[Truncation (geometry)|truncated]] polyhedra with [[vertex configuration]]s (3.2n.2n), and [n,3] [[Coxeter group]] symmetry.
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| {{Truncated figure1 table}}
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| It is topologically related to a series of polyhedra and tilings with [[face configuration]] V''n''.6.6.
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| {{Truncated figure4 table}}
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| === Alternated truncation===
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| A cube can be [[Alternation (geometry)|alternately]] truncated producing [[tetrahedral symmetry]], with six hexagonal faces, and four triangles at the truncated vertices. It is one of a sequence of [[Truncated rhombic dodecahedron#related polyhedra|alternate truncations of polyhedra and tiling]].
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| :[[File:Alternate_truncated_cube.png|100px]]
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| == Related polytopes ==
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| The ''[[Truncation (geometry)|truncated]] [[cube]]'', is second in a sequence of truncated [[hypercube]]s:
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| {{Truncated hypercube polytopes}}
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| ==See also==
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| *[[:Image:Truncatedhexahedron.gif|Spinning truncated cube]]
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| *[[Cube-connected cycles]], a family of graphs that includes the [[skeleton (topology)|skeleton]] of the truncated cube
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| ==References==
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| *{{The Geometrical Foundation of Natural Structure (book)}} (Section 3-9)
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| * Cromwell, P. ''Polyhedra'', CUP hbk (1997), pbk. (1999). Ch.2 p.79-86 ''Archimedean solids''
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| ==External links==
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| *{{mathworld2 |urlname=TruncatedCube |title=Truncated cube |urlname2=ArchimedeanSolid |title2=Archimedean solid}}
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| *{{KlitzingPolytopes|polyhedra.htm|3D convex uniform polyhedra|o3x4x - tic}}
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| *[http://www.dr-mikes-math-games-for-kids.com/polyhedral-nets.html?net=621wh65c7Ey8v4cRpEVhGs0pPxZ5raM9uNf8HcBUgOyrp6acSwZGvkvEcL6m06RDKxmSAduYsvTvoCvEDokvHrjyVEqlGVdIH8WamnxFO1qnGpUtgt7K0ZD57RlX&name=Truncated+Cube#applet Editable printable net of a truncated cube 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] www.georgehart.com: The Encyclopedia of Polyhedra
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| **[[VRML]] [http://www.georgehart.com/virtual-polyhedra/vrml/truncated_cube.wrl model]
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| **[http://www.georgehart.com/virtual-polyhedra/conway_notation.html Conway Notation for Polyhedra] Try: "tC"
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| {{Archimedean solids}}
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| {{Polyhedron navigator}}
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| {{Polyhedron-stub}}
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| [[Category:Uniform polyhedra]]
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| [[Category:Archimedean solids]]
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