Digital rock physics combines microtomographic imaging with advanced numerical simulations of effective material properties. It is used to complement laboratory investigations with the aim to gain a deeper understanding of relevant physical processes related to transport and effective mechanical properties. We apply digital rock physics to reticulite, a natural mineral with a strong analogy to synthetic open-cell foams. We consider reticulite an end-member for high-porosity materials with a high stiffness and brittleness. For this specific material, hydro-mechanical experiments are very difficult to perform. Reticulite is a pyroclastic rock formed during intense Hawaiian fountaining events. The honeycombed network of bubbles is supported by glassy threads and forms a structure with a porosity of more than 80%. Comparing experimental with numerical results and theoretical estimates, we demonstrate the high potential of in situ characterization with respect to the investigation of effective material properties. We show that a digital rock physics workflow, so far applied to conventional rocks, yields reasonable results for high-porosity rocks and can be adopted for fabricated foam-like materials with similar properties. Numerically determined porosities, effective elastic properties, thermal conductivities and permeabilities of reticulite show a fair agreement to experimental results that required exeptionally high experimental efforts.