The optical performance of CPCs having n-sided polygonal inlet and outlet apertures is investigated by Monte-Carlo ray-tracing. The polygonal CPCs are formed by circumscribing regular polygons about the circular apertures of an underlying revolved CPC. The resulting side walls are extruded 2D CPC profiles with 1-dimensional curvature thus profiting from improved manufacturability compared to the revolved CPC. Furthermore, these designs may be uniformly tiled on fiat or curved planes with minimal gap loss for applications requiring multiple absorbers: The principal property of interest is the optical efficiency defined as the fraction of radiant power incident on the inlet aperture which reaches the outlet aperture. The effect of geometry, reflectivity, and surface errors on the optical efficiency is presented. In analyzing these effects, a new approach for calculating the average number of reflections is derived and utilized. Additionally, the flux distributions at the outlet of the concentrators are examined. Especially for large acceptance angles, the performance of polygonal CPCs with reasonable numbers of sides is found to approach that of the revolved CPC, which may be considered a limiting case of the polygonal CPC for n -> infinity. It is found that the square CPC (n = 4) has some favorable anomalous behavior, with performance surpassing that of designs with 5 and 6 sides for small acceptance angles. Polygonal CPCs show promise as less expensive alternatives to the revolved CPC for applications including stationary solar concentrators, and secondary concentrators for dish, tower, and trough primaries. (C) 2013 Elsevier Ltd. All rights reserved.