The achromatic number for a graph G = (V,E) is the largest integer m such that there is a partition of V into disjoint independent sets (V1, ... ,Vm) such that for each pair of distinct sets Vi , Vj , Vi ∪ Vj is not an independent set in G In this paper we present an 0(1)-approximation algorithm to determine the achromatic number of Hex derived networks. © 2011 Springer-Verlag.