In geometry, an icosahedron (plural: icosahedra) is a polyhedron with twenty faces, thirty edges, and twelve vertices. The term is most commonly used to refer to the regular icosahedron, a Platonic solid composed of twenty equivalent equilateral triangles, four of which meet at each vertex.

Edge: a

Radius of inscribed circle: r

Radius of circumscribed circle: R

Surface area: S

Volume: V

- $r={√3(3+√5)}/12\ a$
- $R=√{2(5+√5)}/4\ a$
- $S=5√3\ a^2$
- $V={5(3+√5)}/12\ a^3$

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