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| {{Infobox polyhedron
| | Claude is her name and she completely digs that name. Interviewing is how I make a residing and it's some thing I truly appreciate. Her spouse and her chose to reside in Alabama. The factor she adores most is to play handball but she can't make it her profession.<br><br>my weblog ... extended auto warranty ([http://numismaticforums.com/tiki-index.php?page=UserPagegeniedyringmrhrworyc official statement]) |
| |image=triangular_cupola.png
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| |type=[[Johnson solid|Johnson]]<br>[[pentagonal pyramid|J<sub>2</sub>]] - '''J<sub>3</sub>''' - [[square cupola|J<sub>4</sub>]]
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| |faces=1+3 [[triangle]]s<br>3 [[Square (geometry)|square]]s<br>1 [[hexagon]]
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| |edges=15
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| |vertices=9
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| |symmetry=''C''<sub>3v</sub>
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| |vertex_config=6(3.4.6)<br>3(3.4.3.4)
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| |dual=-
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| |properties=[[convex set|convex]]
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| |net=Triangular cupola net.PNG
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| }}
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| In [[geometry]], the '''triangular [[cupola (geometry)|cupola]]''' is one of the [[Johnson solid]]s (''J''<sub>3</sub>). It can be seen as half a [[cuboctahedron]].
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| {{Johnson solid}}
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| ==Formulae==
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| The following [[formula]]e for the [[volume]] and [[surface area]] can be used if all [[face (geometry)|face]]s are [[regular polygon|regular]], with edge length ''a'':<ref>[[Stephen Wolfram]], "[http://www.wolframalpha.com/input/?i=Triangular+cupola Triangular cupola]" from [[Wolfram Alpha]]. Retrieved July 20, 2010.</ref>
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| <math>V=(\frac{5}{3\sqrt{2}})a^3\approx1.17851...a^3</math>
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| <math>A=(3+\frac{5\sqrt{3}}{2})a^2\approx7.33013...a^2</math>
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| === Dual polyhedron ===
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| The dual of the triangular cupola has 12 triangular faces:
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| {| class=wikitable width=320
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| |- valign=top
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| !Dual triangular cupola
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| !Net of dual
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| |- valign=top
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| |[[File:Dual triangular cupola.png|160px]]
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| |[[File:Dual triangular cupola net.png|160px]]
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| |}
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| == Related polyhedra == | |
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| The ''triangular cupola'' can be [[Augmentation (geometry)|augmented]] by 3 [[square pyramid]]s, leaving adjacent coplanar faces. This isn't a [[Johnson solid]] because of its coplanar faces. Merging those coplanar triangles into larger ones, topologically this is another ''triangular cupola'' with [[isosceles trapezoid]]al side faces. If all the triangle are retained and the base hexagon is replaced by 6 triangles, it generates a coplanar [[Deltahedron#Non-strictly convex cases|deltahedron]] with 22 faces.
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| :[[File:Augmented triangular cupola.png|240px]]
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| The family of [[Cupola (geometry)|cupolae]] with regular polygons exists up to 5-sides, and higher for isosceles triangle version.
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| {{Cupolae}}
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| ==References==
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| {{Reflist}}
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| ==External links==
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| * {{Mathworld2 | urlname =TriangularCupola| title = Triangular cupola | urlname2 = JohnsonSolid | title2 = Johnson solid}}
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| {{Polyhedron-stub}}
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| [[Category:Prismatoid polyhedra]]
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| [[Category:Johnson solids]]
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Claude is her name and she completely digs that name. Interviewing is how I make a residing and it's some thing I truly appreciate. Her spouse and her chose to reside in Alabama. The factor she adores most is to play handball but she can't make it her profession.
my weblog ... extended auto warranty (official statement)