Optimal Road Arrangement for Towns Connected by a Polygon

[Natasha1]

If the vertices of a regular polygon represent 4 townships and are all connected by a system of roads.

To keep costs to a minimum, what is the ideal arrangement of roads?

What if not a regular polygon but a quadrilateral, cube, regular solid?

Can someone help me please

 

[Hootenanny]

quadrilateral

By definition, this only has four verticies. HINT: Polygons are two dimensional.

~H