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 herpes simplex virus, since this symmetry lets a closed shell be assembled from many copies of a few identical proteins. 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.