Pentagonal gyrocupolarotunda

In geometry, the pentagonal gyrocupolarotunda is one of the Johnson solids (Template:Math). Like the pentagonal orthocupolarotunda (Template:Math), it can be constructed by joining a pentagonal cupola (Template:Math) and a pentagonal rotunda (Template:Math) along their decagonal bases. The difference is that in this solid, the two halves are rotated 36 degrees with respect to one another.

Template:Johnson solid File:J33 pentagonal gyrocupolarotunda.stl

Formulae

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

$V=\frac{5}{12}(11+5\sqrt{5})a^3\approx \mathrm{9.24181...}{a}^3$

$A=(5+\frac{15}{4}\sqrt{3}+\frac{7}{4}\sqrt{25+10\sqrt{5}})a^2\approx \mathrm{23.5385...}{a}^2$

External links

• Template:MathWorld2