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We study the propagation of electromagnetic waves through arrays of perfectly conducting cylinders for both fundamental polarization cases s and p. We use a generalized Rayleigh identity method and show that for p polarization the fundamental band defines an effective refractive index not in keeping with electrostatics. We exhibit the photonic band structures for very dilute arrays, where they tend towards the expected free-propagation form. We also study them for arrays approaching touching, where very interesting differences between s and p polarization behavior are manifest.