Elongated pentagonal orthobicupola

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In geometry, the elongated pentagonal orthobicupola or cantellated pentagonal prism is one of the Johnson solids ( $J 38$ Script error: No such module "Check for unknown parameters".).^[1] As the name suggests, it can be constructed by elongating a pentagonal orthobicupola ( $J 30$ Script error: No such module "Check for unknown parameters".) 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 ( $J 39$ Script error: No such module "Check for unknown parameters".).

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File:J38 elongated pentagonal orthobicupola.stl

3D model of an elongated pentagonal orthobicupola

Formulae

The following formulae for volume and surface area can be used if all faces are regular, with edge length a:^[2]

V = \frac{1}{6} (10 + 8 \sqrt{5} + 15 \sqrt{5 + 2 \sqrt{5}}) a^{3} \approx 12.3423 . . . a^{3}

A = (20 + \sqrt{\frac{5}{2} (10 + \sqrt{5} + \sqrt{75 + 30 \sqrt{5}})}) a^{2} \approx 27.7711 . . . a^{2}

References

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↑ Stephen Wolfram, "Elongated pentagonal orthobicupola" from Wolfram Alpha. Retrieved July 25, 2010.

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External links

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[1] Script error: No such module "citation/CS1".

[2] Stephen Wolfram, "Elongated pentagonal orthobicupola" from Wolfram Alpha. Retrieved July 25, 2010.

[1]

[2]

Elongated pentagonal orthobicupola

Formulae

References

External links

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