It has degree 5, with 12 vertices and 30 edges.
It has girth 3, diameter 3 and radius 3.
Its symmetry group has 120 elements.
It is not bipartite.
It is Hamiltonian.
It is symmetric.
It is 1-arc-transitive.
icosahedron is the skeleton of S4:{5,5}
icosahedron is the skeleton of N14.3′
icosahedron is the skeleton of the icosahedron
icosahedron is the dual of dodecahedron in the plane