| Summary: | The objective of this paper is to study fullerene geometry properties and attempt to stablish a dialogue between the teaching of mathematics and chemistry concepts using hands-on cardboard geometric models, in classroom, in order to facilitate the understanding of fullerene structures. This approach to the study of such molecules represents a unique opportunity to explore a complex and rich array of concepts that are essential to the teaching of chemistry at university level and have to be applied by the students along their course. At the same time the study of fullerenes can also profit from a mathematics approach to it, especially from a geometry perspective as argued here. In our research, the use of paper-made geometric models has proven to help the students to visualize and understand such molecular structures, their chemical bonds and their physical-chemical properties. These models have also contributed to overcome representational constraints of such tiny structures, which often come close to a "quasi-abstract' dimension, in a scale that can be manually handled by the students and at the same time played into multiple possible variations that allow them to test concepts and compare different molecular structures and arrangements.
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