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| {{Infobox polyhedron
| | Friends call him Royal Cummins. Kansas is our beginning location and my parents reside nearby. One of the issues I adore most is climbing and now I have time to consider on new things. The job he's been occupying for years is a messenger.<br><br>My blog post ... [http://Www.sharkz-Fifa.de/index.php?mod=users&action=view&id=10274 sharkz-fifa.de] |
| |image=square_cupola.png
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| |type=[[Johnson solid|Johnson]]<br>[[triangular cupola|J<sub>3</sub>]] - '''J<sub>4</sub>''' - [[pentagonal cupola|J<sub>5</sub>]]
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| |faces=4 [[triangle]]s<br>1+4 [[Square (geometry)|square]]s<br>1 [[octagon]]
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| |edges=20
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| |vertices=12
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| |symmetry=''C''<sub>4v</sub>, [4], (*44)
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| |rotation_group=''C''<sub>4</sub>, [4]<sup>+</sup>, (44)
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| |vertex_config=8(3.4.8)<br>4(3.4<sup>3</sup>)
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| |dual=-
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| |properties=[[convex set|convex]]
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| |net=Johnson_solid_4_net.png
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| }}
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| In [[geometry]], the '''square [[cupola (geometry)|cupola]]''', sometimes called '''lesser dome''', is one of the [[Johnson solid]]s (''J''<sub>4</sub>). It can be obtained as a slice of the [[rhombicuboctahedron]]. As in all cupolae, the base [[polygon]] has twice as many [[edge (geometry)|edge]]s and [[vertex (geometry)|vertices]] as the top; in this case the base polygon is an [[octagon]].
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| {{Johnson solid}}
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| ==Formulae==
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| The following [[formula]]e for [[volume]], [[surface area]], and [[circumscribed sphere|circumradius]] can be used if all [[faces (geometry)|faces]] are [[regular polygon|regular]], with edge length ''a'':<ref>[[Stephen Wolfram]], "[http://www.wolframalpha.com/input/?i=Square+cupola Square cupola]" from [[Wolfram Alpha]]. Retrieved July 20, 2010.</ref> | |
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| <math>V=(1+\frac{2\sqrt{2}}{3})a^3\approx1.94281...a^3</math> | |
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| <math>A=(7+2\sqrt{2}+\sqrt{3})a^2\approx11.5605...a^2</math>
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| <math>C=(\frac{1}{2}\sqrt{5+2\sqrt{2}})a\approx1.39897...a</math>
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| == Related polyhedra ==
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| {{Cupolae}}
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| == Dual polyhedron ==
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| The dual of the square cupola has 16 triangular faces:
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| {| class=wikitable width=320
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| |- valign=top
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| !Dual square cupola
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| !Net of dual
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| |- valign=top
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| |[[File:Dual square cupola.png|160px]]
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| |[[File:Dual square cupola net.png|160px]]
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| |}
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| ==References==
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| {{Reflist}}
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| ==External links==
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| * {{Mathworld2 | urlname =SquareCupola| title =Square cupola | urlname2 = JohnsonSolid | title2 = Johnson solid}}
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| [[Category:Prismatoid polyhedra]]
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| [[Category:Johnson solids]]
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| {{Polyhedron-stub}}
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Friends call him Royal Cummins. Kansas is our beginning location and my parents reside nearby. One of the issues I adore most is climbing and now I have time to consider on new things. The job he's been occupying for years is a messenger.
My blog post ... sharkz-fifa.de