Given a graph G with a specified root node r. A spanning tree in G where each node has distance at most 2 from r is called a 2-hop spanning tree. For given edge weights the 2-hop spanning tree problem is to find a minimum weight 2-hop spanning tree. The problem is NP-hard and has some interesting applications. We study a polytope associated with a directed model of the problem give a completeness result for wheels and a vertex description of a linear relaxation. Some classes of valid inequalities for the convex hull of incidence vectors of 2-hop spanning trees are derived by projection techniques.