Elastostatics of star-polygon tile-based architectured planar lattices

A panoptic view of architectured planar lattices based on star-polygon tilings was developed. Four star-polygon-based lattice sub-families, formed systematically arranged triangles, squares, or hexagons, were investigated numerically and experimentally. Finite-element-based homogenization allowed computation Poisson's ratio, elastic modulus, shear bulk modulus. comprehensive understanding the range properties micromechanical deformation mechanisms Adjusting angle achieved an over 250-fold in a 10-fold density, $-0.919$ to $+0.988$ for ratio. Additively manufactured lattices, by novel printing strategies, showed good agreement properties. Parametric additive manufacturing procedures all are available \url{www.fullcontrol.xyz/#/models/1d3528}. Three four sub-families exhibited in-plane isotropy. One high stiffness with auxeticity at low density primarily axial mode as opposed bending other three lattices. The achievable properties, demonstrated property maps, proves extension conventional material-property space. Lattice metamaterials Triangle-Triangle, Kagome, Hexagonal, Square, Truncated Archimedean, Triangular, Hexagonal topologies have been studied literature individually. Here, it is shown that these structures belong presented overarching family.