The exact values of the complexity for a 2-parameter family of Paoluzzi-Zimmermann Manifolds are found. The invariant of 3-manifolds and a special spine of a compact manifold is considered. Identifications defining the equivalence relations on the sets of faces, edges, and vertices of the bipyramid, are described. The space can be obtained by gluing the tetrahedra via affine homeomorphisms of their faces and this gluing determines a pseudotriangulation and induces a gluing of polyhedra. The spline is found to have two 2-components, and each of them corresponds to an edge of the pseudotriangulation.