The road surface
that is required to guarantee that a square or pentagonal wheel
will keep its center level is piecewise catenary.
An
equitriangular wheel will CRASH if we try to keep its center level.
A vertex of the rolling triangle hits the road before the vertex reaches
the cusp.
see http://cage.rug.ac.be/~hs/wheels/wheels.html
or http://www.adeptscience.co.uk/maplearticles/f301.html