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
and
greater. In this paper we answer an open question they posed to extend
their result to the prism graphs, proving that a prism graph is the skeleton
of a smooth tropical plane curve precisely when the genus is at most
. Our
main tool is a classification of lattice polygons with two points that can
simultaneously view all others, without having any one point that can observe all
others.
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