  Any smooth tropical plane curve contains a distinguished trivalent graph
called its skeleton. In 2020 Morrison and Tewari proved that the so-called big
face graphs cannot be the skeleta of tropical curves for genus $12$ and
greater. In this paper we answer an open question they posed to extend their
result to the prism graphs, proving that they are the skeleton of a smooth
tropical plane curve precisely when the genus is at most $11$. Our main tool is
a classification of lattice polygons with two points than can simultaneously
view all others, without having any one point that can observe all others.
