It does represent correctly the icosahedron as a graph, but its drawing (green) contains even greater geometric errors than it could be acceptable for a hand-drawn picture on a blackboard (or it deliberately shows irregular polyhedra). For each vertex, the set of 5 adjacent vertices should form a regular pentagon which lies on a plane. Look at two pentagons which contain the lowermost vertical green edge (solid), and at two pentagons which contain the uppermost vertical green edge (dashed). They do not look like any affine projection of a regular pentagon can look.