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We present a systematic and comprehensive analysis of photonic crystal fibers with a general Bravais lattice and one hole per unit cell. We show how the lack of a proper separation of lattice shape effects from volume rescaling can lead to an incorrect assessment of the impact of lattice shape. We study and compare the endlessly single-mode, waveguide dispersion, and birefringence properties of the fundamental mode across all lattice shapes. For example, we show that the triangular and square lattice shapes offer the largest critical air-hole radius for the endlessly single-mode operation. We identify a general class of PCFs with large birefringence and show that the total birefringence of the fundamental mode is the result of the competition between two opposing effects: the cladding lattice shape and the asymmetry of the core and can vanish for some PCFs with even very nonsymmetric lattices. We show designs for which the birefringence vanishes even with nonsymmetric lattices and cores.