def _find_mirror(self, axis):
        """
        Looks for mirror symmetry of specified type about axis.  Possible
        types are "h" or "vd".  Horizontal (h) mirrors are perpendicular to
        the axis while vertical (v) or diagonal (d) mirrors are parallel.  v
        mirrors has atoms lying on the mirror plane while d mirrors do
        not.
        """
        mirror_type = ""

        # First test whether the axis itself is the normal to a mirror plane.
        if self.is_valid_op(SymmOp.reflection(axis)):
            self.symmops.append(SymmOp.reflection(axis))
            mirror_type = "h"
        else:
            # Iterate through all pairs of atoms to find mirror
            for s1, s2 in itertools.combinations(self.centered_mol, 2):
                if s1.species == s2.species:
                    normal = s1.coords - s2.coords
                    if np.dot(normal, axis) < self.tol:
                        op = SymmOp.reflection(normal)
                        if self.is_valid_op(op):
                            self.symmops.append(op)
                            if len(self.rot_sym) > 1:
                                mirror_type = "d"
                                for v, r in self.rot_sym:
                                    if not np.linalg.norm(v - axis) < self.tol:
                                        if np.dot(v, normal) < self.tol:
                                            mirror_type = "v"
                                            break
                            else:
                                mirror_type = "v"
                            break

        return mirror_type