Group synchronization asks to recover group elements from their pairwise measurements. It has found numerous applications across various scientific disciplines. In this work, we focus on orthogonal and permutation which are widely used in computer vision such as object matching structure motion. Among many available approaches, the spectral methods have enjoyed great popularity due efficiency c...

Any Coxeter group Γ, with string diagram, is the symmetry group of a (possibly infinite) regular polytope P. When Γ is crystallographic, we may reduce its standard real representation modulo an odd prime p, thereby obtaining a finite representation in some orthogonal space over Zp. In many cases, the latter group will be the symmetry group of a finite regular polytope. In this paper, we investi...