Some of the combinations of shape and vertex are disabled
This is because certain combinations do not result in a hyperbolic tesselation (namely, those where (number of side of polygon - 2) * (number of polygons that meet at a vertex) ≤ 4). A simple example is four squares meeting at each vertex - that is just a checkerboard which produces a flat tiling. Three triangles meeting at each vertex is actually a tetrahedron, which makes for a very boring tiling.
Other flipping/mirroring are disabled sometimes
This is because being able to mirror the basic shape requires that the shape have an even number of sides, while flipping over the vertex requires that there is an even number of shapes meeting at each vertex. If either are odd, then that option is disabled.