  In this paper we answer positively a question raised by Kapovich and Leeb in
a paper titled "Finsler bordifications of symmetric and certain locally
symmetric spaces". Specifically, we show that for a finite-dimensional vector
space with a polyhedral norm, its horofunction compactification is homeomorphic
to the dual unit ball of the norm by an explicit map. To prove this, we
establish a criterion for converging sequences in the horofunction
compactification and generalize the basic notion of the moment map in the
theory of toric varieties.
