On Extreme Points of the Dual Ball of a Polyhedral Space

We prove that every separable polyhedral Banach space X is isomorphic to a
polyhedral Banach space Y such that, the set ext BY ∗ cannot be covered by a sequence of
balls B(yi, ²i) with 0 < ²i < 1 and ²i → 0. In particular ext BY ∗ cannot be covered by
a sequence of norm compact sets. This generalizes a result from [7] where an equivalent
polyhedral norm |||·||| on c0 was constructed such that ext B(c0,|||·|||)∗ is uncountable but
can be covered by a sequence of norm compact sets.