Elongated pentagonal gyrobirotunda

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In geometry, the elongated pentagonal gyrobirotunda or elongated icosidodecahedron is one of the Johnson solids (Template:Math). As the name suggests, it can be constructed by elongating a "pentagonal gyrobirotunda," or icosidodecahedron (one of the Archimedean solids), by inserting a decagonal prism between its congruent halves. Rotating one of the pentagonal rotundae (Template:Math) through 36 degrees before inserting the prism yields an elongated pentagonal orthobirotunda (Template:Math).

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 gyrobirotunda" from Wolfram Alpha. Retrieved July 26, 2010.</ref>

<math>V=\frac{1}{6}\left(45+17\sqrt{5}+15\sqrt{5+2\sqrt{5}}\right)a^3 \approx 21.5297 a^3</math>

<math>A=\left(10+\sqrt{30\left(10+3\sqrt{5}+\sqrt{75+30\sqrt{5}}\right)}\right)a^2 \approx 39.306 a^2</math>

External links

• Template:Mathworld2