A non-pneumatic tire comprising: a generally annular inner ring having an axis of rotation; a deformable generally annular outer ring; and a flexible interconnected web extending between the inner ring and the outer ring, the interconnected web including at least two radially adjacent layers of web elements at every radial cross-section of the tire, the web elements defining a plurality of generally polygonal openings and including a plurality of radial web elements that are angled relative to a plane that extends radially through the axis of rotation and a plurality of distinct tangential web elements that are generally transverse to the radial plane, wherein each generally polygonal opening is defined by a plurality of vertices, wherein when load is applied, a substantial amount of the load is supported by a plurality of the web elements working in tension, and wherein a plurality of the radial web elements in a region above the axis of rotation are subjected to a tensile force while at least some of the radial web elements in a region between the load and a footprint region buckle and a plurality of the tangential web elements distribute the load through the flexible interconnected web, characterized in that each of the plurality of vertices is defined by a transitional element that varies a thickness of an associated web element along at least a portion of a length of the web element, and wherein the transitional element is defined by a radius (R 2) that is 400% to 800% of a mean element thickness. a generally annular inner ring having an axis of rotation; a deformable generally annular outer ring; and a flexible interconnected web extending between the inner ring and the outer ring, the interconnected web including at least two radially adjacent layers of web elements at every radial cross-section of the tire, the web elements defining a plurality of generally polygonal openings and including a plurality of radial web elements that are angled relative to a plane that extends radially through the axis of rotation and a plurality of distinct tangential web elements that are generally transverse to the radial plane, wherein each generally polygonal opening is defined by a plurality of vertices, wherein when load is applied, a substantial amount of the load is supported by a plurality of the web elements working in tension, and wherein a plurality of the radial web elements in a region above the axis of rotation are subjected to a tensile force while at least some of the radial web elements in a region between the load and a footprint region buckle and a plurality of the tangential web elements distribute the load through the flexible interconnected web, characterized in that each of the plurality of vertices is defined by a transitional element that varies a thickness of an associated web element along at least a portion of a length of the web element, and wherein the transitional element is defined by a radius (R 2) that is 400% to 800% of a mean element thickness. wherein each generally polygonal opening is defined by a plurality of vertices, wherein when load is applied, a substantial amount of the load is supported by a plurality of the web elements working in tension, and wherein a plurality of the radial web elements in a region above the axis of rotation are subjected to a tensile force while at least some of the radial web elements in a region between the load and a footprint region buckle and a plurality of the tangential web elements distribute the load through the flexible interconnected web, characterized in that each of the plurality of vertices is defined by a transitional element that varies a thickness of an associated web element along at least a portion of a length of the web element, and wherein the transitional element is defined by a radius (R 2) that is 400% to 800% of a mean element thickness.