The hysteretic ac loss of a current-carrying conductor in which multiple superconducting strips are polygonally arranged around a cylindrical former is theoretically investigated as a model of superconducting cables. Using the critical state model, we analytically derive the ac loss Qn of a total of n strips. The normalized loss Qn/Q1 is determined by the number of strips n and the ratio of the strip width 2w to the diameter 2R of the cylindrical former. When n ≫ 1 and w/R ≪ 1, the behavior of Qn is similar to that of an infinite array of coplanar strips.