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Homogeneous prismatic targets, commonly used in geophysical modelling, are special cases of general polyhedral target bodies. In this article, advances made in the polyhedral formulation of the gravimagnetic anomalies are incorporated into the prismatic treatment, which has hitherto maintained reliance on historical pre-polyhedral formulation. By this approach we derive a single compact scheme incorporating all the prismatic anomalies. The benefits are faster algorithms that are easier to maintain and allowance for variants that are numerically more stable.