# Icosahedron

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One of the five regular polytopes. An icosahedron has 20 (triangular) faces, 30 edges and 12 vertices (at each of which 5 edges meet). If $a$ is the length of an edge of the icosahedron, then its volume is given by

$$V=\frac{5}{12}a^3(3+\sqrt5)\cong2.1817a^3.$$

Figure: i050020a