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| {{Infobox polyhedron
| | Hello and welcome. My title is Ling. She is presently a cashier but soon she'll be on her own. Bottle tops collecting is the only pastime his spouse doesn't approve of. Alabama has always been his house and his family members enjoys it.<br><br>Check out my webpage; [http://www.Dabber.com/u2b/uprofile.php?UID=519913 extended car warranty] |
| |image=elongated_pentagonal_orthobicupola.png
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| |type=[[Johnson solid|Johnson]]<br>[[elongated square gyrobicupola|''J''<sub>37</sub>]] -''' J<sub>38</sub>''' - [[elongated pentagonal gyrobicupola|J<sub>39</sub>]]
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| |faces=10 [[triangle]]s<br>2.5+10 [[Square (geometry)|square]]s<br>2 [[pentagon]]s
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| |edges=60
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| |vertices=30
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| |symmetry=''D''<sub>5h</sub>
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| |vertex_config=20(3.4<sup>3</sup>)<br>10(3.4.5.4)
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| |dual=-
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| |properties=[[convex set|convex]]
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| |net=Johnson solid 38 net.png
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| }}
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| In [[geometry]], the '''elongated pentagonal orthobicupola''' is one of the [[Johnson solid]]s (''J''<sub>38</sub>).<ref>http://mathworld.wolfram.com/ElongatedPentagonalOrthobicupola.html</ref> As the name suggests, it can be constructed by elongating a [[pentagonal orthobicupola]] (''J''<sub>30</sub>) by inserting a [[decagonal prism]] between its two congruent halves. Rotating one of the cupolae through 36 degrees before inserting the prism yields an [[elongated pentagonal gyrobicupola]] (''J''<sub>39</sub>).
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| {{Johnson solid}}
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| ==Formulae==
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| 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=Elongated+pentagonal+orthobicupola Elongated pentagonal orthobicupola]" from [[Wolfram Alpha]]. Retrieved July 25, 2010.</ref>
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| <math>V=\frac{1}{6}(10+8\sqrt{5}+15\sqrt{5+2\sqrt{5}})a^3\approx12.3423...a^3</math>
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| <math>A=(20+\sqrt{\frac{5}{2}(10+\sqrt{5}+\sqrt{75+30\sqrt{5}})})a^2\approx27.7711...a^2</math>
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| ==References==
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| {{Reflist}}
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| ==External links==
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| * {{Mathworld2 | urlname = ElongatedPentagonalOrthobicupola | title = Elongated pentagonal orthobicupola | urlname2 = JohnsonSolid | title2 = Johnson solid }}
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| {{Polyhedron-stub}}
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| [[Category:Johnson solids]]
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Revision as of 16:53, 16 February 2014
Hello and welcome. My title is Ling. She is presently a cashier but soon she'll be on her own. Bottle tops collecting is the only pastime his spouse doesn't approve of. Alabama has always been his house and his family members enjoys it.
Check out my webpage; extended car warranty