Platonic Bell inequalities for all dimensions

In this paper we study the Platonic Bell inequalities for all possible dimensions. There are five solids in three dimensions, but there also with properties (also known as regular polyhedra) four and higher The concept of three-dimensional Euclidean space was introduced by Tavakoli Gisin [Quantum 4, 293 (2020)]. For any solid, an arrangement projective measurements is associated where measurement directions point toward vertices solids. dimensional polyhedra, use correspondence to abstract Tsirelson space. We give a remarkably simple formula quantum violation inequalities, which prove attain maximum i.e. bound. To construct large number settings, it crucial compute local bound efficiently. general, computation time required grows exponentially settings. find method exactly bipartite two-outcome inequality, dependence becomes polynomial whose degree rank matrix. show that algorithm can be used practice, 300-setting inequality based on halved dodecaplex. addition, diagonal modification original matrix increase ratio way, obtain four-dimensional 60-setting tetraplex exceeds $\sqrt 2$ ratio.