The trirectangular tetrahedron array provides nearly constant gain over a hemisphere, by adaptively combining signals from elements, having substantially cosine-squared power patterns, on orthogonal faces. By using a deterministic aperiodic lattice, the array can use higher gain elements rather than lower gain elements for traditional wide-scan phased arrays. Thus, the number of elements needed can be reduced by more than a factor of two. Importantly, element spacing is increased with this design, thus lowering mutual coupling and the associated potential for scan blindness. Higher gain elements require spacing exceeding ½ wavelength can have grating lobes. This is addressed with an aperiodic lattice designed to ensure that no grating lobe can form. By connecting two trirectangular tetrahedrons by their bases and mounting on an air/space-based platform, nearly spherical coverage with constant gain results.