Dodecahedron

A dodecahedron is a solid shape that has 12 surfaces. Each face is a pentagon (has five edges). In total there are 20 corners (also called vertices) and 30 edges altogether. A dodecahedron which looks exactly the same from all faces is also a platonic solid.

A dodecahedron

Surface area and volume

If a is the length of one of its edges, the surface area and volume of a regular dodecahedron are:

A=3{\sqrt {25+10{\sqrt {5}}}}a^{2}

V={\frac {15+7{\sqrt {5}}}{4}}a^{3}

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