A new type of planar array geometry is proposed which specifically exploits rotationally symmetry for determining the arrangement of antenna elements. Application of symmetry in the design of arrays is often attractive since it aids in manufacturability. Common translational symmetry, most often seen in periodic arrays, leads to grating lobes in the array factor when electrical spacing between elements becomes large. Grating lobes do not occur in designs which exploit rotational symmetry, and as such are an attractive property for the design of ultra-wideband planar arrays. Two ultra-wideband array design techniques are proposed that use rotational symmetry for positioning the elements and for fast calculation of their associated array factors.