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