For fibers whose cross-section is an n-sided regular polygon, torsion constant, maximum stress, and torsion shape factor have been obtained in closed form. The solution is expressed in terms of the coefficients of the mapping function which maps the interior of a unit circle into the interior of an n-sided regular polygon. Conformal mapping function in a power series form is derived using the Schwarz-Christoffel formula. Complex variable techniques were used to solve the torsion problem.
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