This paper summarises my research on mathematical sculpture and offers the latest version of my proposed classification. The introduction to the study of this kind of sculpture in higher education requires a taxonomy to classify mathematically all its different types. From our point of view, this taxonomy had never been arranged in depth. The first version of the classification (with Professor Javier Barrallo) was shown at ISAMA BRIDGES 2003 Meeting Alhambra . It was a preliminary starting point in which we suggested nine categories, based on mathematical concepts. Since then, I have improved taxonomy structure until it has adapted to a mathematical classification. The best way for categorising mathematical sculpture consists in establishing general groups for the different areas of Mathematics and then subdividing these groups according to the main mathematical concepts used in the sculpture design. As it has happened in the past, I would be pleased to receive suggestions from the art and mathematics community in order to improve this taxonomy.