Pentagonal rotunda

In geometry, the pentagonal rotunda is one of the Johnson solids (Template:Math). It can be seen as half of an icosidodecahedron, or as half of a pentagonal orthobirotunda. It has a total of 17 faces.

Formulae

The following formulae for volume, surface area, circumradius, and height are valid if all faces are regular, with edge length a:

$V=\left(\frac{1}{12}(45+17\sqrt{5})\right)a^3\approx 6.91776...a^3$

$\begin{array}{cc}A& =\left(\frac{1}{2}\sqrt{5(145+58\sqrt{5}+2\sqrt{30(65+29\sqrt{5})})}\right)a^2\\ & =\left(\frac{1}{2}(5\sqrt{3}+\sqrt{10(65+29\sqrt{5})})\right)a^2\approx 22.3472...a^2\end{array}$

$R=\left(\frac{1}{2}(1+\sqrt{5})\right)a\approx 1.61803...a$

$H=\left(\sqrt{1+\frac{2}{\sqrt{5}}}\right)a\approx 1.37638...a$

External links

• Template:MathWorld2