In this paper, we describe geometrically the domain of elastic materials in terms of invariants of the integrity basis (including the positive defi-niteness condition), prove a theoretical link between those polynomial invari-ants and the Kelvin invariants of the elasticity tensor, to finally introduce the concept of design transformation which leads to subsets of elastic materials having identical Kelvin invariants. As an example of this approach, the set of 2D pentamode materials is fully characterized.