In spite of their elementary definition, polytopes are very interesting objects, in particular since the combinatorial structure given by their faces can be used to encode diverse families of mathematical objects.

In this talk I will mainly focus on the classical and beautiful examples of the permutahedron and the associahedron (related to permutations and Catalan objects). Then, I plan to present recent work about the s-permutahedron, obtained in collaboration with Rafael S. González D’León, Alejandro H. Morales, Daniel Tamayo Jiménez, Yannic Vargas, Marha Yip.