The lateral and longitudinal profiles of hadronic showers detected by a prototype of the ATLAS Iron-Scintillator Tile Hadron Calorimeter have been investigated. This calorimeter presents a unique longitudinal configuration of scintillator tiles. Using a fine-grained pion beam scan at 100 GeV, a detailed picture of transverse shower behaviour is obtained. The underlying radial energy densities for the four depth segments and for the entire calorimeter have been reconstructed. A three-dimensional hadronic shower parametrization has been developed. The results presented here are useful for understanding the performance of iron-scintillator calorimeters, for developing fast simulations of hadronic showers, for many calorimetry problems requiring the integration of a shower energy deposition in a volume and for future calorimeters design.