Elongated pentagonal gyrobirotunda

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:

$V=\frac{1}{6}(45+17\sqrt{5}+15\sqrt{5+2\sqrt{5}})a^3\approx 21.5297a^3$

$A=(10+\sqrt{30(10+3\sqrt{5}+\sqrt{75+30\sqrt{5}})})a^2\approx 39.306a^2$

External links

• Template:Mathworld2