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Pentagonal gyrocupolarotunda
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Pentagonal gyrocupolarotunda : ウィキペディア英語版
Pentagonal gyrocupolarotunda

In geometry, the pentagonal gyrocupolarotunda is one of the Johnson solids (''J''33). Like the pentagonal orthocupolarotunda (''J''32), it can be constructed by joining a pentagonal cupola (''J''5) and a pentagonal rotunda (''J''6) along their decagonal bases. The difference is that in this solid, the two halves are rotated 36 degrees with respect to one another.
==Formulae==
The following formulae for volume and surface area can be used if all faces are regular, with edge length ''a'':〔Stephen Wolfram, "(Pentagonal gyrocupolarotunda )" from Wolfram Alpha. Retrieved July 24, 2010.〕
V=\frac(11+5\sqrt)a^3\approx9.24181...a^3
A= (5+\frac\sqrt+\frac\sqrt{25+10\sqrt{5}}) a^2\approx23.5385...a^2

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