Pentagonal orthobicupola

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In geometry, the pentagonal orthobicupola is one of the Johnson solids ( $J 30$ Script error: No such module "Check for unknown parameters".). As the name suggests, it can be constructed by joining two pentagonal cupolae ( $J 5$ Script error: No such module "Check for unknown parameters".) along their decagonal bases, matching like faces. A 36-degree rotation of one cupola before the joining yields a pentagonal gyrobicupola ( $J 31$ Script error: No such module "Check for unknown parameters".).

The pentagonal orthobicupola is the third in an infinite set of orthobicupolae.

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File:J30 pentagonal orthobicupola.stl

3D model of a pentagonal orthobicupola

Formulae

The following formulae for volume and surface area can be used if all faces are regular, with edge length a:^[1]

V = \frac{1}{3} (5 + 4 \sqrt{5}) a^{3} \approx 4.64809 . . . a^{3}

A = (10 + \sqrt{\frac{5}{2} (10 + \sqrt{5} + \sqrt{75 + 30 \sqrt{5}})}) a^{2} \approx 17.7711 . . . a^{2}

References

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↑ Stephen Wolfram, "Pentagonal orthobicupola" from Wolfram Alpha. Retrieved July 23, 2010.

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External links

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