A phased array antenna (PAA) that is particularly adapted to accommodate communications with low earth orbiting (LEO) satellites includes three antenna faces which comprise a phased array of radiating elements, each antenna face is triangular and the three faces form a triangular pyramid. Each triangular face has a height h and a base length B. B and h are chosen to optimize the antenna's gain variation with beam elevation angle to compensate for the path losses dependent on beam elevation angle. At low elevation, increased free space loss in incurred due to longer range to a low earth orbiting satellite, and more rain and atmospheric loss is incurred due to longer path through the atmosphere compared with the losses at higher elevations or at zenith. Since the intrinsic shape compensates for the elevation dependent losses, the PAA design minimizes total array area compared with other known geometries and thus exhibits lower cost.