The demand in the medical industry for load bearing materials is ever increasing. The techniques currently used for the manufacture of such materials are not optimized in terms of porosity and mechanical strength. This study adopts a microstructural shape design approach to the production of open porous materials, which utilizes spatial periodicity as a simple way to generate the models. A set of triply periodic surfaces expressed via trigonometric functions in the implicit form are presented. A geometric description of the topology of the microstructure is necessary when macroscopic properties such as mechanical strength, stiffness and isotropy are required to be optimised for a given value of volume fraction. A distinction between the families of structures produced is made on the basis of topology. The models generated have been used successfully to manufacture both a range of structures with different volume fractions of pores and samples of functional gradient material using rapid prototyping.