The use of skeletons or stick figures for binary image shape analysis, object classification and coding has been widely reported in the literature. Tools using the nomenclature of mathematical morphology for defining skeletons and analysing algorithms based on the iterative deletion of pixels have recently been developed and are extended here to examine the processing of binary images sampled on a hexagonal grid of points. The properties of a skeleton in a hexagonal grid are defined and thinning templates designed. It is shown that even when simple templates are used, some parallel application can be achieved. The analysis leads to the development of a new algorithm in which pairs of templates are applied in parallel, resulting in accurate and efficient processing. Finally, the new algorithm is compared experimentally to a similar parallel algorithm designed for a conventional rectangular sampling grid. The hexagonal skeleton exhibited more accurate corner representation, limbs that enable the area of a rectangular shape to be estimated form the skeleton, noise immunity without preprocessing and a processing time of 55% of that required to process the rectangular scheme skeleton.