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The electrostatic fields and potentials associated with neutral periodic crystals are defined by sums that are not absolutely convergent. The sums depend on the order of summation. The mean-zero periodic solution φ of Poisson's equation provides a natural potential and electric field. This sum is inconsistent with the electric field in ferroelectric materials. We introduce summation methods based on the concept of neutral charge groups, a notion common in computational chemistry. If a charge group has moments of order < κ vanishing, then the sum for ∂α φ defined by summing first by charge groups is absolutely convergent for |α| ≥ 3 - κ. In the borderline case |α| ≥ 2 - κ, consider charge groups coming from primitive unit cells. For a macroscopic shape Ω, the unit-cell RΩ algorithm sums over unit cells in RΩ and then takes the limit R → ∞. This yields an answer for ∂α φ that depends on Ω and the unit cell. The limits differ from ∂α φ by a constant given as an easily approximable integral. For quadrupolar primitive unit cells, κ = 2. The unit-cell RΩ algorithm gives a potential φ that differs from φ by a constant. This constant enters additively in the energy content per unit volume. If one could grow or cut crystals respecting these unit cells, this shape-dependent energy effect could be verified experimentally. For dipolar primitive unit cells, κ = 1. Given a shape Ω and unit cell, the algorithm yields a well-defined electric field that differs from the mean-zero periodic field by a constant vector. If one could grow or cut crystals respecting these dipolar unit cells, this shape-dependent ferroelectric effect [C. Kittel, Introduction to Solid State Physics, 8th ed., Wiley, New York, 2004] could be verified experimentally. [ABSTRACT FROM AUTHOR]