Icosahedron Formulas

Posted In: Mathematics

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.

Icosahedron


Edge: a
Radius of inscribed circle: r
Radius of circumscribed circle: R
Surface area: S
Volume: V

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

Post Tags: Geometry


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