3D Printing Mathematical Objects

Date started: September 2019
Leads: Rémi Coulon


The goal of this project was to learn how produce 3D objects from generating the files to using the 3D printers. The following objects were produced:

– The group of symmetry of the dodecahedron is known to be the alternated group A_5. However it is not easy to see what are the 5 “objects” which are permuted. They turn out to be 5 cubes embedded in the dodecahedron. This first models represent these five cubes.

– A solid is said to have constant width if any two parallel planes touching it are at fix distance. The sphere is such a solid. But there exists many others. In the second series of prints we have a sphere, the two Meissner bodies and a surface of revolution of the Reuleaux pentagon.


The five cubes in the dodecahedron
The five cubes in a dodecahedron (printed models)
Constant width solids