Elongated pentagonal rotunda

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In geometry, the elongated pentagonal rotunda is one of the Johnson solids (J₂₁). As the name suggests, it can be constructed by elongating a pentagonal rotunda (J₆) by attaching a decagonal prism to its base. It can also be seen as an elongated pentagonal orthobirotunda (J₄₂) with one pentagonal rotunda removed.

Formulae

The following formulae for volume and surface area can be used if all faces are regular, with edge length a:<ref>Stephen Wolfram, "Elongated pentagonal rotunda" from Wolfram Alpha. Retrieved July 22, 2010.</ref>

<math>V=\frac{1}{12}\left(45+17\sqrt{5}+30\sqrt{5+2\sqrt{5}}\right)a^3\approx14.612...a^3</math>

<math>A=\frac{1}{2}\left(20+\sqrt{5\left(145+58\sqrt{5}+2\sqrt{30\left(65+29\sqrt{5}\right)}\right)}\right)a^2\approx32.3472...a^2</math>

Dual polyhedron

The dual of the elongated pentagonal rotunda has 30 faces: 10 isosceles triangles, 10 rhombi, and 10 quadrilaterals.

Dual elongated pentagonal rotunda	Net of dual
File:Dual elongated pentagonal rotunda.png	File:Dual elongated pentagonal rotunda net.png

External links

• Template:Mathworld2