This is the accepted version of the journal article: Cobos, Fernando; Fernández-Cabrera, Luz M.; Martín i Pedret, Joaquim. «Some reiteration results for interpolation methods defined by means of polygons». Proceedings of the Royal Society of Edinburgh Section A: Mathematics, Vol. 138, issue 6 (Dec. 2008), p. 1179-1195. DOI 10.1017/S0308210507000315 This version is available at https://ddd.uab.cat/record/271421 under the terms of the license