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.