Orthoisomorphisms between lattices of geometric tripotents in dual spaces of facially symmetric spaces

In this paper we consider properties of bijection between lattices of geometric tripotents in dual spaces of two facially symmetric spaces. More precisely, we will prove that if a bijection is an order isomorphism and preserves orthogonality in one direction, then it is an orthoisomorphism, and vice versa. We will also define order isomorphisms and orthoisomorphisms between some classes of lattices of geometric tripotents in the dual space of a facially symmetric space