The introduction of mathematical sculpture in advanced education needs a taxonomy to classify all the different types of sculpture. From our point of view, this classification has never been arranged deeply. This paper is a first attempt to that classification. We expect to receive suggestions from the Art and Mathematics community in order to start a work that we will take away during the next two years and whose first step is given with this paper. As a preliminary starting point we have suggested the following nine categories for mathematical sculpture: I. Polyhedral and classic geometry, II. Non-oriented surfaces, III. Topological knots, IV. Quadrics and ruled surfaces, V. Symmetric and modular structures, VI. Boolean operations, VII. Minimal surfaces, VIII. Transformations IX. Others.