Shortest road network joining four square towns

Four towns sit at the corners of a square. Roads must be built so that every town can reach every other, using the least total road length. What does the optimal network look like?

A Steiner tree with two internal junctions. Two junction points on the square's centre line connect to a pair of adjacent towns each and to each other, with all roads meeting at $120^\circ$. Its length is $(1+\sqrt3)\approx2.73$ times the side, beating the diagonal cross ($2\sqrt2\approx2.83$).