diff --git a/qpms/qpms_c.pyx b/qpms/qpms_c.pyx
index ab76c97..7ea3b9c 100644
--- a/qpms/qpms_c.pyx
+++ b/qpms/qpms_c.pyx
@@ -535,6 +535,11 @@ cdef class ScatteringSystem:
             r.append(self.s[0].p[pi])
         return r
 
+    property particle_count:
+        """Number of particles in the system (or unit cell)"""
+        def __get__(self):
+            self.check_s()
+            return self.s[0].p_count
     property fecv_size: 
         """Length of the full excitation coefficient vector"""
         def __get__(self): 
@@ -561,6 +566,44 @@ cdef class ScatteringSystem:
         def __get__(self):
             return self.s[0].lattice_dimension
 
+    property lattice_basis:
+        """Direct lattice basis vectors for periodic system in 3D cartesian coordinates"""
+        def __get__(self):
+            cdef int d = self.lattice_dimension
+            if d == 0:
+                return None
+            else:
+                return np.array([[self.s[0].per.lattice_basis[i].x,
+                                  self.s[0].per.lattice_basis[i].y,
+                                  self.s[0].per.lattice_basis[i].z,
+                    ] for i in range(d)])
+
+    property reciprocal_basis:
+        """Reciprocal lattice basis vectors for periodic system in 3D cartesian coordinates"""
+        def __get__(self):
+            cdef int d = self.lattice_dimension
+            if d == 0:
+                return None
+            else:
+                return np.array([[self.s[0].per.reciprocal_basis[i].x,
+                                  self.s[0].per.reciprocal_basis[i].y,
+                                  self.s[0].per.reciprocal_basis[i].z,
+                    ] for i in range(d)])
+
+    def bspec_pi(self, qpms_ss_pi_t pi):
+            """Gives the BaseSpec of a particle defined by an index in the internal particles' order, in the form of an array that can be fed to BaseSpec constructor"""
+            self.check_s()
+            cdef qpms_ss_pi_t pcount = self.s[0].p_count
+            if pi >= pcount or pi < 0:  raise IndexError("Invalid particle index")
+            cdef const qpms_vswf_set_spec_t *bspec = qpms_ss_bspec_pi(self.s, pi)
+            return np.array([ bspec[0].ilist[i] for i in range(bspec[0].n)])
+    property bspecs:
+        """Gives the BaseSpecs of all particles in the internal particles' order, in the form of arrays that can be fed to BaseSpec constructor"""
+        def __get__(self):
+            self.check_s()
+            cdef qpms_ss_pi_t pi, pcount = self.s[0].p_count
+            return [self.bspec_pi(pi) for pi in range(pcount)]
+
     property unitcell_volume:
         def __get__(self):
             self.check_s()
@@ -792,7 +835,7 @@ cdef class ScatteringSystem:
         cdef np.ndarray[int32_t, ndim=1] ar = np.empty((self.s[0].p_count,), dtype=np.int32)
         cdef int32_t[::1] ar_view = ar
         for pi in range(self.s[0].p_count):
-            ar_view[pi] = self.s[0].tm[self.s[0].p[pi].tmatrix_id].spec[0].n
+            ar_view[pi] = qpms_ss_bspec_pi(self.s, pi)[0].n
         return ar
 
 
diff --git a/qpms/qpms_cdefs.pxd b/qpms/qpms_cdefs.pxd
index 4a3c174..8d43538 100644
--- a/qpms/qpms_cdefs.pxd
+++ b/qpms/qpms_cdefs.pxd
@@ -602,6 +602,7 @@ cdef extern from "scatsystem.h":
         qpms_tmatrix_operation_t op
     struct qpms_scatsys_periodic_info_t:
         cart3_t lattice_basis[3]
+        cart3_t reciprocal_basis[3]
         double unitcell_volume
         double eta
         #etc.