On the genus of the complete tripartite graph Kn,n,1

For even n we prove that the genus of the complete tripartite graph Kn,n,1 is ⌈(n−1)(n−2)∕4⌉. This is the least number of bridges needed to build a complete n-way road interchange where changing lanes is not allowed. Both the theoretical result, and the surprising link to modelling road intersections are new.