The category of “extremal materials” has been introduced in the literature to define materials that simultaneously show very soft and very stiff deformation modes (unimode, bimode, trimode, quadramode and pentamode materials, depending on the number of soft modes). This definition applies to a special class of mechanical metamaterials – composite materials, structural foams, cellular materials, etc. – which feature special mechanical properties. Pentamode materials have been proposed for transformation acoustics and elasto-mechanical cloak, but their potential in different engineering fields is still only partially explored. We here present novel versions of pentamode materials: artificial structural crystals showing shear moduli markedly smaller than the bulk modulus. Novel pentamode lattices with tensegrity architecture are designed, through the insertion of actuated struts and/or prestressed cables within basic pentamode lattices. Such systems are proposed as tunable seismic base-isolation devices, profiting from their low and adjustable shear moduli, which can be easily adapted to the dynamic properties of the structure to be isolated.