It has the highest ratio of volume to surface area and, according to Plato, symbolizes water. Each has 30 edges and 20 equilateral triangle faces with five meeting at each of its twelve vertices. Formula to find Area and Volume of Icosahedron: Let a be the side of Icosahedron, then For any regular polyhedron, three spheres can be commonly defined: one that passes through all the vertices, called circumscribed sphere or circumsphere, one that passes through the centroids of all faces, called inscribed sphere or insphere, and one that passes through the middles of all edges, called midsphere. window.jQuery || document.write('