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 Bᵧ ∗cannot be covered by a sequence of balls B (i; i) with 0 < i < 1 and i ⟶ 0. In particular ext Bᵧ ∗ 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 extB(c0;⦀· ⦀)∗ is uncountable but can be covered by a sequence of norm compact sets.peerReviewe