A Dodecahedral Transport Construction of AT4val[60,6] and its Petersen Line-Graph Quotient

We construct a 60-vertex tetravalent graph from local transport operations on the flag structure of the combinatorial dodecahedron. Starting from the 120 flags of the polyhedron, we identify opposite configurations along edges to obtain 60 chamber states. Two transport moves induce adjacency relations between these states, producing a connected 4-regular graph G_60. The graph admits a free action of the Klein four group V_4, and the quotient graph Q_15 is isomorphic to the line graph of the Petersen graph. Consequently G_60 is a regular V_4-cover of L(Petersen), and coincides with the arc-transitive graph AT4val[60,6] in the census of tetravalent arc-transitive graphs maintained by Primož Potočnik.