Nematic liquid crystals in a polyhedral domain, a prototype for bistable
displays, may be described by a unit-vector field subject to tangent boundary
conditions. Here we consider the case of a rectangular prism. For
configurations with reflection-symmetric topologies, we derive a new lower
bound for the one-constant elastic energy. For certain topologies, called
conformal and anticonformal, the lower bound agrees with a previous result. For
the remaining topologies, called nonconformal, the new bound is an improvement.
For nonconformal topologies we derive an upper bound, which differs from the
lower bound by a factor depending only on the aspect ratios of the prism.Comment: 21 page
