Attractive pi-pi interactions between two of the four outside cavity faces of 1,3-bis-pyridylmethylcalix[4]arene (1) and both faces of 1,4-diiodotetrafluorobenzene (2a) form infinite one-dimensional non-covalent ribbons where the two modules alternate. These ribbons are cross-linked by electron donor-acceptor interactions between picolyl nitrogen atoms of calixarene 1 in one chain and iodine atoms of perfluoroarene 2a in another chain and the two-dimensional supramolecular network 3a is formed. A similar behaviour is also shown by 1,4-dibromotetrafluorobenzene (2b). The halogen bonding and the attractive pi-pi interactions occur in directions which are nearly orthogonal each other. Diiodotetrafluorobenzene, being involved in both these interactions, appears to be a particularly interesting tecton. The ability of electron-poor arenes to elicit the exo-receptor potential of calixarene module by connecting their outside faces through pi-pi interactions may be developed as a new and general binding protocol in calixarene self-assembly processes.