This paper explores the design modelling issues of the Petaweb, an optical network architecture that provides fully meshed connectivity between electronic edge nodes. The Petaweb is simple to manage, simplifies key networking functions such as routing and addressing and can offer a total capacity of several Petabits per second. From the topology standpoint, it is an unusual structure as the backbone nodes are totally disconnected whereas the edge nodes are all reachable in one-hop. The network design problem leads to a very hard combinatorial problem. We propose a model and a heuristic approach that is based on repeated matchings. Computational results concerning the modelling issues will be presented and thoroughly discussed.