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We address the optimization of the geometric design of two classes of multifaceted antenna arrays, namely, pyramids and pyramidal frusta. The optimization involves choosing the face elevation and the number of arrays. The optimal face elevation minimizes the maximum scan angle encountered by the arrays, given a general hemispherical coverage requirement. Firstly, an approach is presented to compute the face elevation of the pyramidal frustum, based on equalizing the maximum scan angles. It is demonstrated that the equalization-based approach is not always optimal. Secondly, a new optimal approach based on minimax optimization is presented and used for both pyramids and pyramidal frusta, along with a comparison of the two approaches. Finally, the choice of the number of arrays is addressed using different cost functions including scan angles, scan losses, antenna dimensions, geometric directivity, and total number of antenna elements. Quantitative guidelines on how to choose among planar, pyramidal, and pyramidal frustum antenna systems are outlined.