Grid

[dgrimes]

Is there a name for an "n x n" grid with edges added so that it is 4-regular, non-planar. So all variables have an adjacent neighbor above, below and to its left and right. For vertices on the perimeter of degree 3 one edge is added linking it with its symmetrically equivalent perimeter vertex, i.e. if a vertex at the top of the grid has degree 3 then an edge is added linking it to the vertext at the bottom of its column of vertices in the graph, similarly for rows.
So there are 2*n edges added to a normal "n x n" grid to make it so every vertex is of degree 4.
I am trying to find out if there is a specific name for such a "grid"?