We investigate the automorphism groups of graded algebras defined by lattice polyhedral complexes and of the corresponding projective varieties, which form arrangements of projective toric varieties. These groups are polyhedral versions of the general and projective linear groups. It is shown that for wide classes of complexes they are generated by toric actions, elementary transformations and symmetries of the underlying complex. The main results extend our previous work for single polytopes [BG].