Calibrated airspeed: Difference between revisions

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{{Infobox polyhedron
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|image=pentagonal_cupola.png
|type=[[Johnson solid|Johnson]]<br>[[square cupola|J<sub>4</sub>]] - '''J<sub>5</sub>''' - [[pentagonal rotunda|J<sub>6</sub>]]
|faces=5 [[triangle]]s<br>5 [[Square (geometry)|square]]s<br>1 [[pentagon]]<br>1 [[decagon]]
|edges=25
|vertices=15
|symmetry=''C''<sub>5v</sub>, [5], (*55)
|rotation_group=''C''<sub>5</sub>, [5]<sup>+</sup>, (55)
|vertex_config=10(3.4.10)<br>5(3.4.5.4)
|dual=-
|properties=[[convex set|convex]]
|net=Pentagonal Cupola.PNG
}}
In [[geometry]], the '''pentagonal [[cupola (geometry)|cupola]]''' is one of the [[Johnson solid]]s (''J''<sub>5</sub>). It can be obtained as a slice of the [[rhombicosidodecahedron]]. The pentagonal cupola consists of 5 [[equilateral triangle]]s, 5 [[Square (geometry)|square]]s, 1 [[pentagon]], and 1 [[decagon]].
 
{{Johnson solid}}
 
==Formulae==
The following [[formula]]e for [[volume]], [[surface area]] and [[circumscribed sphere|circumradius]] can be used if all [[face (geometry)|faces]] are [[regular polygon|regular]], with edge length ''a'':<ref>[[Stephen Wolfram]], "[http://www.wolframalpha.com/input/?i=Pentagonal+cupola Pentagonal cupola]" from [[Wolfram Alpha]]. Retrieved July 21, 2010.</ref>
 
<math>V=\left(\frac{1}{6}\left(5+4\sqrt{5}\right)\right)a^3\approx2.32405...a^3</math>
 
<math>A=\left(\frac{1}{4}\left(20+5\sqrt{3}+\sqrt{5(145+62\sqrt{5})}\right)\right)a^2=\left(\frac{1}{4}\left(20+\sqrt{10\left(80+31\sqrt{5}+\sqrt{15(145+62\sqrt{5})}\right)}\right)\right)a^2\approx16.5797...a^2</math>
 
<math>C=\left(\frac{1}{2}\sqrt{11+4\sqrt{5}}\right)a\approx2.23295...a</math>
 
== Related polyhedra==
=== Dual polyhedron ===
 
The dual of the pentagonal cupola has 10 triangular faces and 5 kite faces:
{| class=wikitable width=320
|- valign=top
!Dual pentagonal cupola
!Net of dual
|- valign=top
|[[File:Dual pentagonal cupola.png|160px]]
|[[File:Dual pentagonal cupola net.png|160px]]
|}
 
{{Cupolae}}
 
==References==
{{Reflist}}
 
==External links==
* {{mathworld | urlname = JohnsonSolid | title = Johnson solid}}
* {{mathworld | urlname =PentagonalCupola| title =Pentagonal cupola}}
 
[[Category:Prismatoid polyhedra]]
[[Category:Johnson solids]]
 
 
{{Polyhedron-stub}}

Latest revision as of 09:56, 18 August 2014

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