Complete metric absolute neighborhood retracts

We characterize complete metric absolute (neighborhood) retracts in terms of existence of certain maps of CW-polytopes. Using our result, we prove that a compact metric space with a convex and locally convex simplicial structure is an AR. This answers a question of Kulpa from [Topology Proc. 22 (1997) 211–235]. As another application, we prove that the hyperspace of closed subsets of a separable Banach space endowed with the Wijsman topology is an absolute retract.