We report the analysis, design, fabrication and experimental characterization of novel subwavelength computer-generated holograms that produce uniform symmetric spot array. We distinguish between a polarization-sensitive and polarization-insensitive far-field reconstruction and show that a linearly polarized incident illumination is required in the former case in order to generate a symmetric reconstruction. The polarization-insensitive case generates a symmetric response independent of the illumination polarization. We show that this response is equivalent to that of a scalar-based computer-generated hologram but with an additional, independent, term that describes the undiffracted zeroth order. These findings simplify the design and optimization of form birefringent computer-generated holograms (F-BCGH) significantly. We present experimental results that verify our analysis and highlight the advantage of these novel elements over scalar-designed elements.