Icosahedron Calculator

About this calculator

A regular icosahedron is a Platonic solid made of twenty equilateral triangular faces, thirty edges and twelve vertices where five faces meet at each point. Its volume follows V = (5/12)(3+√5)·a³ and its surface area is 5√3·a², both governed entirely by the edge length a because of the solid's uniform symmetry; it is the dual of the regular dodecahedron.

Structural biologists use icosahedral symmetry to describe the protein shells of many viruses, including adenovirus and the HIV capsid, since this shape encloses the maximum volume with the fewest identical repeating subunits. Architects and engineers borrow the same geometry for geodesic domes popularized by Buckminster Fuller, while game designers use the icosahedron as the classic twenty-sided die.