  The aim of this note is to present two results that make the task of finding
equivalent polyhedral norms on certain Banach spaces, having either a Schauder
basis or an uncountable unconditional basis, easier and more transparent. The
hypotheses of both results are based on decomposing the unit sphere of a Banach
space into countably many pieces, such that each one satisfies certain
properties. Some examples of spaces having equivalent polyhedral norms are
given.
