I will talk about operads and their connection to polytopes such as associahedra, multiplihedra, also freehedra (as explained in arXiv:2011.11607)... I will explain how cellular approximations of polytopal diagonals allow for tensor products of various algebraic structures. I will give several existing formulas for polytopal diagonals ("magic" formula for associahedral diagonal, Saneblidze-Umble formula for permutahedral diagonal with a recent reinterpretation by Laplante-Anfossi), and will pose some open questions.