Snub dodecahedron composed by twelve regular pentagons and eighty equilateral triangles.

Polyhedron with ninety two faces: twelve regular pentagons and eighty equilateral triangles. It has one hundred fifty 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 snub dodecahedron with edge length 1 is given by the formula:

Surface area=203+325+105\text{Surface area}=20 \sqrt{3}+3 \sqrt{25+10 \sqrt{5}}

The volume of a snub dodecahedron with edge length aa is given by the formula:

Volume=12ξ2(3ϕ+1)ξ(36ϕ+7)(53ϕ+6)6(3ξ2)3a3\text{Volume}=\frac{12 \xi^2 \left( 3 \phi + 1 \right) – \xi \left( 36\phi + 7 \right) – \left( 53 \phi + 6 \right)}{6\left( \sqrt{3-\xi^2}\right)^3}a^3

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