The structure described by Th9CeO20 is Fluorite-derived structured and crystallizes in the triclinic P-1 space group. There are five inequivalent Th sites. In the first Th site, Th(1) is bonded in a body-centered cubic geometry to one O(1), one O(5), one O(6), one O(7), two equivalent O(2), and two equivalent O(4) atoms. In the second Th site, Th(2) is bonded in a body-centered cubic geometry to one O(2), one O(5), one O(7), one O(8), two equivalent O(1), and two equivalent O(3) atoms. In the third Th site, Th(3) is bonded in a body-centered cubic geometry to one O(10), one O(2), one O(3), one O(4), one O(5), one O(6), and two equivalent O(9) atoms. In the fourth Th site, Th(4) is bonded in a body-centered cubic geometry to one O(1), one O(3), one O(4), one O(7), one O(8), one O(9), and two equivalent O(10) atoms. In the fifth Th site, Th(5) is bonded in a body-centered cubic geometry to two equivalent O(10), two equivalent O(6), two equivalent O(7), and two equivalent O(8) atoms. Ce(1) is bonded in a body-centered cubic geometry to two equivalent O(5), two equivalent O(6), two equivalent O(8), and two equivalent O(9) atoms. There are ten inequivalent O sites. In the first O site, O(1) is bonded to one Th(1), one Th(4), and two equivalent Th(2) atoms to form OTh4 tetrahedra that share  a cornercorner with one O(5)CeTh3 tetrahedra,  a cornercorner with one O(6)CeTh3 tetrahedra,  a cornercorner with one O(8)CeTh3 tetrahedra,  a cornercorner with one O(9)CeTh3 tetrahedra,  a cornercorner with one O(4)Th4 tetrahedra, corners with two equivalent O(10)Th4 tetrahedra, corners with two equivalent O(2)Th4 tetrahedra, corners with three equivalent O(3)Th4 tetrahedra, corners with four equivalent O(7)Th4 tetrahedra,  an edgeedge with one O(5)CeTh3 tetrahedra,  an edgeedge with one O(8)CeTh3 tetrahedra,  an edgeedge with one O(1)Th4 tetrahedra,  an edgeedge with one O(2)Th4 tetrahedra,  an edgeedge with one O(3)Th4 tetrahedra, and  an edgeedge with one O(4)Th4 tetrahedra. In the second O site, O(2) is bonded to one Th(2), one Th(3), and two equivalent Th(1) atoms to form OTh4 tetrahedra that share  a cornercorner with one O(6)CeTh3 tetrahedra,  a cornercorner with one O(8)CeTh3 tetrahedra,  a cornercorner with one O(10)Th4 tetrahedra,  a cornercorner with one O(3)Th4 tetrahedra,  a cornercorner with one O(7)Th4 tetrahedra, corners with two equivalent O(9)CeTh3 tetrahedra, corners with two equivalent O(1)Th4 tetrahedra, corners with three equivalent O(4)Th4 tetrahedra, corners with four equivalent O(5)CeTh3 tetrahedra,  an edgeedge with one O(6)CeTh3 tetrahedra,  an edgeedge with one O(1)Th4 tetrahedra,  an edgeedge with one O(2)Th4 tetrahedra,  an edgeedge with one O(3)Th4 tetrahedra,  an edgeedge with one O(4)Th4 tetrahedra, and  an edgeedge with one O(7)Th4 tetrahedra. In the third O site, O(3) is bonded to one Th(3), one Th(4), and two equivalent Th(2) atoms to form OTh4 tetrahedra that share  a cornercorner with one O(5)CeTh3 tetrahedra,  a cornercorner with one O(6)CeTh3 tetrahedra,  a cornercorner with one O(9)CeTh3 tetrahedra,  a cornercorner with one O(2)Th4 tetrahedra,  a cornercorner with one O(7)Th4 tetrahedra, corners with two equivalent O(4)Th4 tetrahedra, corners with three equivalent O(8)CeTh3 tetrahedra, corners with three equivalent O(1)Th4 tetrahedra, corners with three equivalent O(10)Th4 tetrahedra,  an edgeedge with one O(5)CeTh3 tetrahedra,  an edgeedge with one O(9)CeTh3 tetrahedra,  an edgeedge with one O(1)Th4 tetrahedra,  an edgeedge with one O(2)Th4 tetrahedra,  an edgeedge with one O(3)Th4 tetrahedra, and  an edgeedge with one O(7)Th4 tetrahedra. In the fourth O site, O(4) is bonded to one Th(3), one Th(4), and two equivalent Th(1) atoms to form OTh4 tetrahedra that share  a cornercorner with one O(5)CeTh3 tetrahedra,  a cornercorner with one O(8)CeTh3 tetrahedra,  a cornercorner with one O(1)Th4 tetrahedra,  a cornercorner with one O(10)Th4 tetrahedra,  a cornercorner with one O(7)Th4 tetrahedra, corners with two equivalent O(3)Th4 tetrahedra, corners with three equivalent O(6)CeTh3 tetrahedra, corners with three equivalent O(9)CeTh3 tetrahedra, corners with three equivalent O(2)Th4 tetrahedra,  an edgeedge with one O(5)CeTh3 tetrahedra,  an edgeedge with one O(1)Th4 tetrahedra,  an edgeedge with one O(10)Th4 tetrahedra,  an edgeedge with one O(2)Th4 tetrahedra,  an edgeedge with one O(4)Th4 tetrahedra, and  an edgeedge with one O(7)Th4 tetrahedra. In the fifth O site, O(5) is bonded to one Th(1), one Th(2), one Th(3), and one Ce(1) atom to form OCeTh3 tetrahedra that share  a cornercorner with one O(5)CeTh3 tetrahedra,  a cornercorner with one O(8)CeTh3 tetrahedra,  a cornercorner with one O(1)Th4 tetrahedra,  a cornercorner with one O(10)Th4 tetrahedra,  a cornercorner with one O(3)Th4 tetrahedra,  a cornercorner with one O(4)Th4 tetrahedra, corners with two equivalent O(6)CeTh3 tetrahedra, corners with two equivalent O(9)CeTh3 tetrahedra, corners with two equivalent O(7)Th4 tetrahedra, corners with four equivalent O(2)Th4 tetrahedra,  an edgeedge with one O(6)CeTh3 tetrahedra,  an edgeedge with one O(8)CeTh3 tetrahedra,  an edgeedge with one O(9)CeTh3 tetrahedra,  an edgeedge with one O(1)Th4 tetrahedra,  an edgeedge with one O(3)Th4 tetrahedra, and  an edgeedge with one O(4)Th4 tetrahedra. In the sixth O site, O(6) is bonded to one Th(1), one Th(3), one Th(5), and one Ce(1) atom to form OCeTh3 tetrahedra that share  a cornercorner with one O(1)Th4 tetrahedra,  a cornercorner with one O(10)Th4 tetrahedra,  a cornercorner with one O(2)Th4 tetrahedra,  a cornercorner with one O(3)Th4 tetrahedra,  a cornercorner with one O(7)Th4 tetrahedra, corners with two equivalent O(5)CeTh3 tetrahedra, corners with two equivalent O(6)CeTh3 tetrahedra, corners with two equivalent O(8)CeTh3 tetrahedra, corners with two equivalent O(9)CeTh3 tetrahedra, corners with three equivalent O(4)Th4 tetrahedra,  an edgeedge with one O(5)CeTh3 tetrahedra,  an edgeedge with one O(8)CeTh3 tetrahedra,  an edgeedge with one O(9)CeTh3 tetrahedra,  an edgeedge with one O(10)Th4 tetrahedra,  an edgeedge with one O(2)Th4 tetrahedra, and  an edgeedge with one O(7)Th4 tetrahedra. In the seventh O site, O(7) is bonded to one Th(1), one Th(2), one Th(4), and one Th(5) atom to form OTh4 tetrahedra that share  a cornercorner with one O(6)CeTh3 tetrahedra,  a cornercorner with one O(9)CeTh3 tetrahedra,  a cornercorner with one O(2)Th4 tetrahedra,  a cornercorner with one O(3)Th4 tetrahedra,  a cornercorner with one O(4)Th4 tetrahedra,  a cornercorner with one O(7)Th4 tetrahedra, corners with two equivalent O(5)CeTh3 tetrahedra, corners with two equivalent O(8)CeTh3 tetrahedra, corners with two equivalent O(10)Th4 tetrahedra, corners with four equivalent O(1)Th4 tetrahedra,  an edgeedge with one O(6)CeTh3 tetrahedra,  an edgeedge with one O(8)CeTh3 tetrahedra,  an edgeedge with one O(10)Th4 tetrahedra,  an edgeedge with one O(2)Th4 tetrahedra,  an edgeedge with one O(3)Th4 tetrahedra, and  an edgeedge with one O(4)Th4 tetrahedra. In the eighth O site, O(8) is bonded to one Th(2), one Th(4), one Th(5), and one Ce(1) atom to form OCeTh3 tetrahedra that share  a cornercorner with one O(5)CeTh3 tetrahedra,  a cornercorner with one O(9)CeTh3 tetrahedra,  a cornercorner with one O(1)Th4 tetrahedra,  a cornercorner with one O(2)Th4 tetrahedra,  a cornercorner with one O(4)Th4 tetrahedra, corners with two equivalent O(6)CeTh3 tetrahedra, corners with two equivalent O(8)CeTh3 tetrahedra, corners with two equivalent O(10)Th4 tetrahedra, corners with two equivalent O(7)Th4 tetrahedra, corners with three equivalent O(3)Th4 tetrahedra,  an edgeedge with one O(5)CeTh3 tetrahedra,  an edgeedge with one O(6)CeTh3 tetrahedra,  an edgeedge with one O(9)CeTh3 tetrahedra,  an edgeedge with one O(1)Th4 tetrahedra,  an edgeedge with one O(10)Th4 tetrahedra, and  an edgeedge with one O(7)Th4 tetrahedra. In the ninth O site, O(9) is bonded to one Th(4), two equivalent Th(3), and one Ce(1) atom to form OCeTh3 tetrahedra that share  a cornercorner with one O(8)CeTh3 tetrahedra,  a cornercorner with one O(9)CeTh3 tetrahedra,  a cornercorner with one O(1)Th4 tetrahedra,  a cornercorner with one O(3)Th4 tetrahedra,  a cornercorner with one O(7)Th4 tetrahedra, corners with two equivalent O(5)CeTh3 tetrahedra, corners with two equivalent O(6)CeTh3 tetrahedra, corners with two equivalent O(10)Th4 tetrahedra, corners with two equivalent O(2)Th4 tetrahedra, corners with three equivalent O(4)Th4 tetrahedra,  an edgeedge with one O(5)CeTh3 tetrahedra,  an edgeedge with one O(6)CeTh3 tetrahedra,  an edgeedge with one O(8)CeTh3 tetrahedra,  an edgeedge with one O(9)CeTh3 tetrahedra,  an edgeedge with one O(10)Th4 tetrahedra, and  an edgeedge with one O(3)Th4 tetrahedra. In the tenth O site, O(10) is bonded to one Th(3), one Th(5), and two equivalent Th(4) atoms to form OTh4 tetrahedra that share  a cornercorner with one O(5)CeTh3 tetrahedra,  a cornercorner with one O(6)CeTh3 tetrahedra,  a cornercorner with one O(10)Th4 tetrahedra,  a cornercorner with one O(2)Th4 tetrahedra,  a cornercorner with one O(4)Th4 tetrahedra, corners with two equivalent O(8)CeTh3 tetrahedra, corners with two equivalent O(9)CeTh3 tetrahedra, corners with two equivalent O(1)Th4 tetrahedra, corners with two equivalent O(7)Th4 tetrahedra, corners with three equivalent O(3)Th4 tetrahedra,  an edgeedge with one O(6)CeTh3 tetrahedra,  an edgeedge with one O(8)CeTh3 tetrahedra,  an edgeedge with one O(9)CeTh3 tetrahedra,  an edgeedge with one O(10)Th4 tetrahedra,  an edgeedge with one O(4)Th4 tetrahedra, and  an edgeedge with one O(7)Th4 tetrahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_CeTh9O20
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.841
_cell_length_b   7.899
_cell_length_c   8.831
_cell_angle_alpha   102.924
_cell_angle_beta   97.420
_cell_angle_gamma   106.778
_symmetry_Int_Tables_number   1
_cell_volume   435.624
_cell_formula_units_Z   1
loop_
 _symmetry_equiv_pos_site_id
 _symmetry_equiv_pos_as_xyz
  1  'x, y, z'
loop_
 _atom_site_type_symbol
 _atom_site_label
 _atom_site_symmetry_multiplicity
 _atom_site_fract_x
 _atom_site_fract_y
 _atom_site_fract_z
 _atom_site_occupancy
  Ce  Ce0  1  0.000  0.500  0.000  1.0
  Th  Th1  1  0.199  0.899  0.399  1.0
  Th  Th2  1  0.199  0.400  0.399  1.0
  Th  Th3  1  0.600  0.699  0.199  1.0
  Th  Th4  1  0.601  0.201  0.200  1.0
  Th  Th5  1  0.000  0.000  0.000  1.0
  Th  Th6  1  0.801  0.101  0.601  1.0
  Th  Th7  1  0.801  0.600  0.601  1.0
  Th  Th8  1  0.400  0.301  0.801  1.0
  Th  Th9  1  0.399  0.799  0.800  1.0
  O  O10  1  0.850  0.325  0.450  1.0
  O  O11  1  0.150  0.675  0.550  1.0
  O  O12  1  0.150  0.175  0.550  1.0
  O  O13  1  0.850  0.825  0.450  1.0
  O  O14  1  0.550  0.475  0.350  1.0
  O  O15  1  0.550  0.975  0.350  1.0
  O  O16  1  0.247  0.623  0.247  1.0
  O  O17  1  0.950  0.772  0.148  1.0
  O  O18  1  0.249  0.125  0.250  1.0
  O  O19  1  0.950  0.277  0.148  1.0
  O  O20  1  0.346  0.574  0.951  1.0
  O  O21  1  0.350  0.075  0.950  1.0
  O  O22  1  0.050  0.228  0.852  1.0
  O  O23  1  0.650  0.925  0.050  1.0
  O  O24  1  0.654  0.426  0.049  1.0
  O  O25  1  0.050  0.723  0.852  1.0
  O  O26  1  0.450  0.525  0.650  1.0
  O  O27  1  0.450  0.025  0.650  1.0
  O  O28  1  0.751  0.875  0.750  1.0
  O  O29  1  0.753  0.377  0.753  1.0
[/CIF]
.
The structure described by Th9CeO20 is Fluorite-derived structured and crystallizes in the triclinic P-1 space group. There are five inequivalent Th sites. In the first Th site, Th(1) is bonded in a body-centered cubic geometry to one O(1), one O(5), one O(6), one O(7), two equivalent O(2), and two equivalent O(4) atoms. In the second Th site, Th(2) is bonded in a body-centered cubic geometry to one O(2), one O(5), one O(7), one O(8), two equivalent O(1), and two equivalent O(3) atoms. In the third Th site, Th(3) is bonded in a body-centered cubic geometry to one O(10), one O(2), one O(3), one O(4), one O(5), one O(6), and two equivalent O(9) atoms. In the fourth Th site, Th(4) is bonded in a body-centered cubic geometry to one O(1), one O(3), one O(4), one O(7), one O(8), one O(9), and two equivalent O(10) atoms. In the fifth Th site, Th(5) is bonded in a body-centered cubic geometry to two equivalent O(10), two equivalent O(6), two equivalent O(7), and two equivalent O(8) atoms. Ce(1) is bonded in a body-centered cubic geometry to two equivalent O(5), two equivalent O(6), two equivalent O(8), and two equivalent O(9) atoms. There are ten inequivalent O sites. In the first O site, O(1) is bonded to one Th(1), one Th(4), and two equivalent Th(2) atoms to form OTh4 tetrahedra that share  a cornercorner with one O(5)CeTh3 tetrahedra,  a cornercorner with one O(6)CeTh3 tetrahedra,  a cornercorner with one O(8)CeTh3 tetrahedra,  a cornercorner with one O(9)CeTh3 tetrahedra,  a cornercorner with one O(4)Th4 tetrahedra, corners with two equivalent O(10)Th4 tetrahedra, corners with two equivalent O(2)Th4 tetrahedra, corners with three equivalent O(3)Th4 tetrahedra, corners with four equivalent O(7)Th4 tetrahedra,  an edgeedge with one O(5)CeTh3 tetrahedra,  an edgeedge with one O(8)CeTh3 tetrahedra,  an edgeedge with one O(1)Th4 tetrahedra,  an edgeedge with one O(2)Th4 tetrahedra,  an edgeedge with one O(3)Th4 tetrahedra, and  an edgeedge with one O(4)Th4 tetrahedra. In the second O site, O(2) is bonded to one Th(2), one Th(3), and two equivalent Th(1) atoms to form OTh4 tetrahedra that share  a cornercorner with one O(6)CeTh3 tetrahedra,  a cornercorner with one O(8)CeTh3 tetrahedra,  a cornercorner with one O(10)Th4 tetrahedra,  a cornercorner with one O(3)Th4 tetrahedra,  a cornercorner with one O(7)Th4 tetrahedra, corners with two equivalent O(9)CeTh3 tetrahedra, corners with two equivalent O(1)Th4 tetrahedra, corners with three equivalent O(4)Th4 tetrahedra, corners with four equivalent O(5)CeTh3 tetrahedra,  an edgeedge with one O(6)CeTh3 tetrahedra,  an edgeedge with one O(1)Th4 tetrahedra,  an edgeedge with one O(2)Th4 tetrahedra,  an edgeedge with one O(3)Th4 tetrahedra,  an edgeedge with one O(4)Th4 tetrahedra, and  an edgeedge with one O(7)Th4 tetrahedra. In the third O site, O(3) is bonded to one Th(3), one Th(4), and two equivalent Th(2) atoms to form OTh4 tetrahedra that share  a cornercorner with one O(5)CeTh3 tetrahedra,  a cornercorner with one O(6)CeTh3 tetrahedra,  a cornercorner with one O(9)CeTh3 tetrahedra,  a cornercorner with one O(2)Th4 tetrahedra,  a cornercorner with one O(7)Th4 tetrahedra, corners with two equivalent O(4)Th4 tetrahedra, corners with three equivalent O(8)CeTh3 tetrahedra, corners with three equivalent O(1)Th4 tetrahedra, corners with three equivalent O(10)Th4 tetrahedra,  an edgeedge with one O(5)CeTh3 tetrahedra,  an edgeedge with one O(9)CeTh3 tetrahedra,  an edgeedge with one O(1)Th4 tetrahedra,  an edgeedge with one O(2)Th4 tetrahedra,  an edgeedge with one O(3)Th4 tetrahedra, and  an edgeedge with one O(7)Th4 tetrahedra. In the fourth O site, O(4) is bonded to one Th(3), one Th(4), and two equivalent Th(1) atoms to form OTh4 tetrahedra that share  a cornercorner with one O(5)CeTh3 tetrahedra,  a cornercorner with one O(8)CeTh3 tetrahedra,  a cornercorner with one O(1)Th4 tetrahedra,  a cornercorner with one O(10)Th4 tetrahedra,  a cornercorner with one O(7)Th4 tetrahedra, corners with two equivalent O(3)Th4 tetrahedra, corners with three equivalent O(6)CeTh3 tetrahedra, corners with three equivalent O(9)CeTh3 tetrahedra, corners with three equivalent O(2)Th4 tetrahedra,  an edgeedge with one O(5)CeTh3 tetrahedra,  an edgeedge with one O(1)Th4 tetrahedra,  an edgeedge with one O(10)Th4 tetrahedra,  an edgeedge with one O(2)Th4 tetrahedra,  an edgeedge with one O(4)Th4 tetrahedra, and  an edgeedge with one O(7)Th4 tetrahedra. In the fifth O site, O(5) is bonded to one Th(1), one Th(2), one Th(3), and one Ce(1) atom to form OCeTh3 tetrahedra that share  a cornercorner with one O(5)CeTh3 tetrahedra,  a cornercorner with one O(8)CeTh3 tetrahedra,  a cornercorner with one O(1)Th4 tetrahedra,  a cornercorner with one O(10)Th4 tetrahedra,  a cornercorner with one O(3)Th4 tetrahedra,  a cornercorner with one O(4)Th4 tetrahedra, corners with two equivalent O(6)CeTh3 tetrahedra, corners with two equivalent O(9)CeTh3 tetrahedra, corners with two equivalent O(7)Th4 tetrahedra, corners with four equivalent O(2)Th4 tetrahedra,  an edgeedge with one O(6)CeTh3 tetrahedra,  an edgeedge with one O(8)CeTh3 tetrahedra,  an edgeedge with one O(9)CeTh3 tetrahedra,  an edgeedge with one O(1)Th4 tetrahedra,  an edgeedge with one O(3)Th4 tetrahedra, and  an edgeedge with one O(4)Th4 tetrahedra. In the sixth O site, O(6) is bonded to one Th(1), one Th(3), one Th(5), and one Ce(1) atom to form OCeTh3 tetrahedra that share  a cornercorner with one O(1)Th4 tetrahedra,  a cornercorner with one O(10)Th4 tetrahedra,  a cornercorner with one O(2)Th4 tetrahedra,  a cornercorner with one O(3)Th4 tetrahedra,  a cornercorner with one O(7)Th4 tetrahedra, corners with two equivalent O(5)CeTh3 tetrahedra, corners with two equivalent O(6)CeTh3 tetrahedra, corners with two equivalent O(8)CeTh3 tetrahedra, corners with two equivalent O(9)CeTh3 tetrahedra, corners with three equivalent O(4)Th4 tetrahedra,  an edgeedge with one O(5)CeTh3 tetrahedra,  an edgeedge with one O(8)CeTh3 tetrahedra,  an edgeedge with one O(9)CeTh3 tetrahedra,  an edgeedge with one O(10)Th4 tetrahedra,  an edgeedge with one O(2)Th4 tetrahedra, and  an edgeedge with one O(7)Th4 tetrahedra. In the seventh O site, O(7) is bonded to one Th(1), one Th(2), one Th(4), and one Th(5) atom to form OTh4 tetrahedra that share  a cornercorner with one O(6)CeTh3 tetrahedra,  a cornercorner with one O(9)CeTh3 tetrahedra,  a cornercorner with one O(2)Th4 tetrahedra,  a cornercorner with one O(3)Th4 tetrahedra,  a cornercorner with one O(4)Th4 tetrahedra,  a cornercorner with one O(7)Th4 tetrahedra, corners with two equivalent O(5)CeTh3 tetrahedra, corners with two equivalent O(8)CeTh3 tetrahedra, corners with two equivalent O(10)Th4 tetrahedra, corners with four equivalent O(1)Th4 tetrahedra,  an edgeedge with one O(6)CeTh3 tetrahedra,  an edgeedge with one O(8)CeTh3 tetrahedra,  an edgeedge with one O(10)Th4 tetrahedra,  an edgeedge with one O(2)Th4 tetrahedra,  an edgeedge with one O(3)Th4 tetrahedra, and  an edgeedge with one O(4)Th4 tetrahedra. In the eighth O site, O(8) is bonded to one Th(2), one Th(4), one Th(5), and one Ce(1) atom to form OCeTh3 tetrahedra that share  a cornercorner with one O(5)CeTh3 tetrahedra,  a cornercorner with one O(9)CeTh3 tetrahedra,  a cornercorner with one O(1)Th4 tetrahedra,  a cornercorner with one O(2)Th4 tetrahedra,  a cornercorner with one O(4)Th4 tetrahedra, corners with two equivalent O(6)CeTh3 tetrahedra, corners with two equivalent O(8)CeTh3 tetrahedra, corners with two equivalent O(10)Th4 tetrahedra, corners with two equivalent O(7)Th4 tetrahedra, corners with three equivalent O(3)Th4 tetrahedra,  an edgeedge with one O(5)CeTh3 tetrahedra,  an edgeedge with one O(6)CeTh3 tetrahedra,  an edgeedge with one O(9)CeTh3 tetrahedra,  an edgeedge with one O(1)Th4 tetrahedra,  an edgeedge with one O(10)Th4 tetrahedra, and  an edgeedge with one O(7)Th4 tetrahedra. In the ninth O site, O(9) is bonded to one Th(4), two equivalent Th(3), and one Ce(1) atom to form OCeTh3 tetrahedra that share  a cornercorner with one O(8)CeTh3 tetrahedra,  a cornercorner with one O(9)CeTh3 tetrahedra,  a cornercorner with one O(1)Th4 tetrahedra,  a cornercorner with one O(3)Th4 tetrahedra,  a cornercorner with one O(7)Th4 tetrahedra, corners with two equivalent O(5)CeTh3 tetrahedra, corners with two equivalent O(6)CeTh3 tetrahedra, corners with two equivalent O(10)Th4 tetrahedra, corners with two equivalent O(2)Th4 tetrahedra, corners with three equivalent O(4)Th4 tetrahedra,  an edgeedge with one O(5)CeTh3 tetrahedra,  an edgeedge with one O(6)CeTh3 tetrahedra,  an edgeedge with one O(8)CeTh3 tetrahedra,  an edgeedge with one O(9)CeTh3 tetrahedra,  an edgeedge with one O(10)Th4 tetrahedra, and  an edgeedge with one O(3)Th4 tetrahedra. In the tenth O site, O(10) is bonded to one Th(3), one Th(5), and two equivalent Th(4) atoms to form OTh4 tetrahedra that share  a cornercorner with one O(5)CeTh3 tetrahedra,  a cornercorner with one O(6)CeTh3 tetrahedra,  a cornercorner with one O(10)Th4 tetrahedra,  a cornercorner with one O(2)Th4 tetrahedra,  a cornercorner with one O(4)Th4 tetrahedra, corners with two equivalent O(8)CeTh3 tetrahedra, corners with two equivalent O(9)CeTh3 tetrahedra, corners with two equivalent O(1)Th4 tetrahedra, corners with two equivalent O(7)Th4 tetrahedra, corners with three equivalent O(3)Th4 tetrahedra,  an edgeedge with one O(6)CeTh3 tetrahedra,  an edgeedge with one O(8)CeTh3 tetrahedra,  an edgeedge with one O(9)CeTh3 tetrahedra,  an edgeedge with one O(10)Th4 tetrahedra,  an edgeedge with one O(4)Th4 tetrahedra, and  an edgeedge with one O(7)Th4 tetrahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_CeTh9O20
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.841
_cell_length_b   7.899
_cell_length_c   8.831
_cell_angle_alpha   102.924
_cell_angle_beta   97.420
_cell_angle_gamma   106.778
_symmetry_Int_Tables_number   1
_cell_volume   435.624
_cell_formula_units_Z   1
loop_
 _symmetry_equiv_pos_site_id
 _symmetry_equiv_pos_as_xyz
  1  'x, y, z'
loop_
 _atom_site_type_symbol
 _atom_site_label
 _atom_site_symmetry_multiplicity
 _atom_site_fract_x
 _atom_site_fract_y
 _atom_site_fract_z
 _atom_site_occupancy
  Ce  Ce0  1  0.000  0.500  0.000  1.0
  Th  Th1  1  0.199  0.899  0.399  1.0
  Th  Th2  1  0.199  0.400  0.399  1.0
  Th  Th3  1  0.600  0.699  0.199  1.0
  Th  Th4  1  0.601  0.201  0.200  1.0
  Th  Th5  1  0.000  0.000  0.000  1.0
  Th  Th6  1  0.801  0.101  0.601  1.0
  Th  Th7  1  0.801  0.600  0.601  1.0
  Th  Th8  1  0.400  0.301  0.801  1.0
  Th  Th9  1  0.399  0.799  0.800  1.0
  O  O10  1  0.850  0.325  0.450  1.0
  O  O11  1  0.150  0.675  0.550  1.0
  O  O12  1  0.150  0.175  0.550  1.0
  O  O13  1  0.850  0.825  0.450  1.0
  O  O14  1  0.550  0.475  0.350  1.0
  O  O15  1  0.550  0.975  0.350  1.0
  O  O16  1  0.247  0.623  0.247  1.0
  O  O17  1  0.950  0.772  0.148  1.0
  O  O18  1  0.249  0.125  0.250  1.0
  O  O19  1  0.950  0.277  0.148  1.0
  O  O20  1  0.346  0.574  0.951  1.0
  O  O21  1  0.350  0.075  0.950  1.0
  O  O22  1  0.050  0.228  0.852  1.0
  O  O23  1  0.650  0.925  0.050  1.0
  O  O24  1  0.654  0.426  0.049  1.0
  O  O25  1  0.050  0.723  0.852  1.0
  O  O26  1  0.450  0.525  0.650  1.0
  O  O27  1  0.450  0.025  0.650  1.0
  O  O28  1  0.751  0.875  0.750  1.0
  O  O29  1  0.753  0.377  0.753  1.0
[/CIF]
.