  The current density and field distributions in polygonally arranged thin
superconducting tapes carrying AC current are derived under the assumption of
the critical state model. Starting from the generic Biot-Savart law for a
general polygonal geometry, we derive a suitable integral equation for the
calculation of the current density and magnetic field in each tape. The model
works for any transport current below $I_c$, which makes it attractive for
studying cases of practical interest, particularly the dependence of AC losses
on parameters such as the number of tapes, their distance from the center, and
their separation.
