Sentiment analysis and opinion mining is an area that has experienced considerable growth over the last decade. This area of research attempts to determine the feelings, opinions, emotions, among other things, of people on something or someone. To do this, techniques from natural language processing and machine learning algorithms are mainly used. This article discusses the problem of determining the polarity of reviews using a novel ordinal classification technique called Barycentric Coordinates for Ordinal Classification (BCOC). The aim of this analysis is to explore the viability of application of BCOC on the field of sentiment analysis. This new method is based on the hypothesis that the ordinal classes can be represented geometrically inside a convex polygon on the real plane by using barycentric coordinates. A set of experiments were conducted to evaluate the capability and performance of the proposed approach relative to a baseline, using accuracy as the general measure of performance. The experiments include testing on generic ordinal classification data sets and on multi-class sentiment analysis data sets. In general the method is competitive with the state of the art. The results show no significant difference over the baseline in the case of generic ordinal classification and sentiment analysis with three classes. However, in the case of sentiment analysis with four classes the results show improvements in the overall accuracy.