Adjacency Matrices of PSL(2,5) and Resemblance of Its Coset Diagrams with Fullerene C60

The action of PSL(2,ℤ) on PL(F5n) yields PSL(2,5). In this paper, we use the adjacency matrices of the abstract group PSL(2,5), eventually of fullerene C60, to draw the coset diagram and investigate various properties of the diagram with reference to the intransitivity of the action and the number of orbits.