We　analyze　the　problem　of　mass　and　morphological　optimization　for　metamaterials　with　tensegrity-type　cells.　Our　approach　is　based　on　both　local　and　global　instability　analyses.　As　a　meaningful　prototypical　example　we　tassellate　a　compressed　slab　into　periodic　patterns　of　triangular,　square　and　hexagonal　cells.　(C)　2016　Elsevier　Ltd.　All　rights　reserved.