Truncated icosahedron composed by twelve regular pentagons and twenty regular hexagons.

Polyhedron with thirty two faces: twelve regular pentagons and twenty regular hexagons. It has ninety edges and sixty vertices. It is a Archimedean solid as it is a convex uniform polyhedra composed of regular polygons meeting in identical vertices, excluding the five Platonic solids (which are composed of only one type of polygon) and excluding the prisms and antiprisms.

The surface area of a truncated icosahedron with edge length a is given by the formula:

\text{Surface area}=\left(20 \times \frac{3}{2} \sqrt{3}+12 \times \frac{5}{4} \sqrt{1+ \frac{2}{\sqrt{5}}} \right) a^2

The volume of a truncated icosahedron with edge length a is given by the formula:

\text{Volume}=\frac{125+43 \sqrt{5}}{4} a^3

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