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<div>{{Infobox polyhedron<br />
|image=pentagonal_gyrocupolarotunda.png<br />
|type=[[Johnson solid|Johnson]]<br>[[pentagonal orthocupolarotunda|''J''<sub>32</sub>]] -''' J<sub>33</sub>''' - [[pentagonal orthobirotunda|J<sub>34</sub>]]<br />
|faces=3×5 [[triangle]]s<br>5 [[Square (geometry)|square]]s<br>2+5 [[pentagon]]s<br />
|edges=50<br />
|vertices=25<br />
|symmetry=''C''<sub>5v</sub>|<br />
|vertex_config=10(3<sup>2</sup>.4.5)<br>5(3.4.5.4)<br>2.5(3.5.3.5)<br />
|dual=-<br />
|properties=[[convex set|convex]]<br />
|net=Johnson solid 33 net.png<br />
}}<br />
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In [[geometry]], the '''pentagonal gyrocupolarotunda''' is one of the [[Johnson solid]]s (''J''<sub>33</sub>). Like the [[pentagonal orthocupolarotunda]] (''J''<sub>32</sub>), it can be constructed by joining a [[pentagonal cupola]] (''J''<sub>5</sub>) and a [[pentagonal rotunda]] (''J''<sub>6</sub>) along their [[decagon]]al bases. The difference is that in this solid, the two halves are rotated 36 degrees with respect to one another.<br />
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{{Johnson solid}}<br />
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==Formulae==<br />
The following [[formula]]e for [[volume]] and [[surface area]] 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=Pentagonal+gyrocupolarotunda Pentagonal gyrocupolarotunda]" from [[Wolfram Alpha]]. Retrieved July 24, 2010.</ref><br />
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<math>V=\frac{5}{12}(11+5\sqrt{5})a^3\approx9.24181...a^3</math><br />
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<math>A= (5+\frac{15}{4}\sqrt{3}+\frac{7}{4}\sqrt{25+10\sqrt{5}}) a^2\approx23.5385...a^2</math><br />
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==References==<br />
{{Reflist}}<br />
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==External links==<br />
* {{MathWorld|title=Johnson solid|urlname=JohnsonSolid}}<br />
* {{MathWorld | urlname=PentagonalGyrocupolarotunda | title=Pentagonal gyrocupolarotunda}}<br />
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[[Category:Johnson solids]]<br />
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{{Polyhedron-stub}}</div>83.213.59.160