The compound described by U3ThRe8 is Frank-Kasper $\mu$ Phase-derived structured and crystallizes in the monoclinic Cm space group. There are three inequivalent U sites. In the first U site, U(1) is bonded in a 16-coordinate geometry to one U(3), three equivalent Th(1), one Re(3), two equivalent Re(4), two equivalent Re(5), three equivalent Re(1), and four equivalent Re(6) atoms. In the second U site, U(2) is bonded in a 14-coordinate geometry to one U(3), one Th(1), one Re(4), two equivalent Re(3), two equivalent Re(6), three equivalent Re(2), and four equivalent Re(5) atoms. In the third U site, U(3) is bonded in a 14-coordinate geometry to one U(1), one U(2), one Re(3), two equivalent Re(4), two equivalent Re(5), three equivalent Re(2), and four equivalent Re(6) atoms. Th(1) is bonded in a 16-coordinate geometry to one U(2), three equivalent U(1), one Re(4), two equivalent Re(3), two equivalent Re(6), three equivalent Re(1), and four equivalent Re(5) atoms. There are six inequivalent Re sites. In the first Re site, Re(1) is bonded to three equivalent U(1), three equivalent Th(1), one Re(3), one Re(4), two equivalent Re(5), and two equivalent Re(6) atoms to form distorted ReTh3U3Re6 cuboctahedra that share corners with two equivalent Re(3)Th2U4Re6 cuboctahedra, corners with two equivalent Re(4)ThU5Re6 cuboctahedra, corners with four equivalent Re(5)Th2U4Re6 cuboctahedra, corners with four equivalent Re(6)ThU5Re6 cuboctahedra, edges with six equivalent Re(1)Th3U3Re6 cuboctahedra, faces with two equivalent Re(2)U6Re6 cuboctahedra, faces with three equivalent Re(3)Th2U4Re6 cuboctahedra, faces with three equivalent Re(4)ThU5Re6 cuboctahedra, faces with six equivalent Re(5)Th2U4Re6 cuboctahedra, and faces with six equivalent Re(6)ThU5Re6 cuboctahedra. In the second Re site, Re(2) is bonded to three equivalent U(2), three equivalent U(3), one Re(3), one Re(4), two equivalent Re(5), and two equivalent Re(6) atoms to form ReU6Re6 cuboctahedra that share corners with two equivalent Re(3)Th2U4Re6 cuboctahedra, corners with two equivalent Re(4)ThU5Re6 cuboctahedra, corners with four equivalent Re(5)Th2U4Re6 cuboctahedra, corners with four equivalent Re(6)ThU5Re6 cuboctahedra, edges with six equivalent Re(2)U6Re6 cuboctahedra, faces with two equivalent Re(1)Th3U3Re6 cuboctahedra, faces with three equivalent Re(3)Th2U4Re6 cuboctahedra, faces with three equivalent Re(4)ThU5Re6 cuboctahedra, faces with six equivalent Re(5)Th2U4Re6 cuboctahedra, and faces with six equivalent Re(6)ThU5Re6 cuboctahedra. In the third Re site, Re(3) is bonded to one U(1), one U(3), two equivalent U(2), two equivalent Th(1), one Re(1), one Re(2), and four equivalent Re(5) atoms to form ReTh2U4Re6 cuboctahedra that share corners with two equivalent Re(1)Th3U3Re6 cuboctahedra, corners with two equivalent Re(4)ThU5Re6 cuboctahedra, corners with two equivalent Re(2)U6Re6 cuboctahedra, corners with four equivalent Re(3)Th2U4Re6 cuboctahedra, corners with eight equivalent Re(6)ThU5Re6 cuboctahedra, edges with two equivalent Re(3)Th2U4Re6 cuboctahedra, edges with four equivalent Re(4)ThU5Re6 cuboctahedra, faces with three equivalent Re(1)Th3U3Re6 cuboctahedra, faces with three equivalent Re(2)U6Re6 cuboctahedra, faces with four equivalent Re(6)ThU5Re6 cuboctahedra, and faces with eight equivalent Re(5)Th2U4Re6 cuboctahedra. In the fourth Re site, Re(4) is bonded to one U(2), two equivalent U(1), two equivalent U(3), one Th(1), one Re(1), one Re(2), and four equivalent Re(6) atoms to form ReThU5Re6 cuboctahedra that share corners with two equivalent Re(3)Th2U4Re6 cuboctahedra, corners with two equivalent Re(1)Th3U3Re6 cuboctahedra, corners with two equivalent Re(2)U6Re6 cuboctahedra, corners with four equivalent Re(4)ThU5Re6 cuboctahedra, corners with eight equivalent Re(5)Th2U4Re6 cuboctahedra, edges with two equivalent Re(4)ThU5Re6 cuboctahedra, edges with four equivalent Re(3)Th2U4Re6 cuboctahedra, faces with three equivalent Re(1)Th3U3Re6 cuboctahedra, faces with three equivalent Re(2)U6Re6 cuboctahedra, faces with four equivalent Re(5)Th2U4Re6 cuboctahedra, and faces with eight equivalent Re(6)ThU5Re6 cuboctahedra. In the fifth Re site, Re(5) is bonded to one U(1), one U(3), two equivalent U(2), two equivalent Th(1), one Re(1), one Re(2), two equivalent Re(3), and two equivalent Re(5) atoms to form distorted ReTh2U4Re6 cuboctahedra that share corners with two equivalent Re(1)Th3U3Re6 cuboctahedra, corners with two equivalent Re(2)U6Re6 cuboctahedra, corners with four equivalent Re(5)Th2U4Re6 cuboctahedra, corners with four equivalent Re(4)ThU5Re6 cuboctahedra, corners with six equivalent Re(6)ThU5Re6 cuboctahedra, edges with two equivalent Re(5)Th2U4Re6 cuboctahedra, edges with four equivalent Re(6)ThU5Re6 cuboctahedra, faces with two equivalent Re(4)ThU5Re6 cuboctahedra, faces with two equivalent Re(6)ThU5Re6 cuboctahedra, faces with three equivalent Re(1)Th3U3Re6 cuboctahedra, faces with three equivalent Re(2)U6Re6 cuboctahedra, faces with four equivalent Re(3)Th2U4Re6 cuboctahedra, and faces with four equivalent Re(5)Th2U4Re6 cuboctahedra. In the sixth Re site, Re(6) is bonded to one U(2), two equivalent U(1), two equivalent U(3), one Th(1), one Re(1), one Re(2), two equivalent Re(4), and two equivalent Re(6) atoms to form distorted ReThU5Re6 cuboctahedra that share corners with two equivalent Re(1)Th3U3Re6 cuboctahedra, corners with two equivalent Re(2)U6Re6 cuboctahedra, corners with four equivalent Re(3)Th2U4Re6 cuboctahedra, corners with four equivalent Re(6)ThU5Re6 cuboctahedra, corners with six equivalent Re(5)Th2U4Re6 cuboctahedra, edges with two equivalent Re(6)ThU5Re6 cuboctahedra, edges with four equivalent Re(5)Th2U4Re6 cuboctahedra, faces with two equivalent Re(3)Th2U4Re6 cuboctahedra, faces with two equivalent Re(5)Th2U4Re6 cuboctahedra, faces with three equivalent Re(1)Th3U3Re6 cuboctahedra, faces with three equivalent Re(2)U6Re6 cuboctahedra, faces with four equivalent Re(4)ThU5Re6 cuboctahedra, and faces with four equivalent Re(6)ThU5Re6 cuboctahedra. is represented by the CIF card [CIF]
data_ThU3Re8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.289
_cell_length_b   5.289
_cell_length_c   8.633
_cell_angle_alpha   89.761
_cell_angle_beta   89.761
_cell_angle_gamma   67.588
_symmetry_Int_Tables_number   1
_cell_volume   223.264
_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
  Th  Th0  1  0.335  0.335  0.434  1.0
  U  U1  1  0.671  0.671  0.584  1.0
  U  U2  1  0.339  0.339  0.065  1.0
  U  U3  1  0.662  0.662  0.925  1.0
  Re  Re4  1  0.995  0.995  0.500  1.0
  Re  Re5  1  1.000  1.000  0.999  1.0
  Re  Re6  1  0.826  0.826  0.249  1.0
  Re  Re7  1  0.171  0.171  0.752  1.0
  Re  Re8  1  0.340  0.831  0.243  1.0
  Re  Re9  1  0.169  0.661  0.754  1.0
  Re  Re10  1  0.661  0.169  0.754  1.0
  Re  Re11  1  0.831  0.340  0.243  1.0
[/CIF]
.
The compound described by U3ThRe8 is Frank-Kasper $\mu$ Phase-derived structured and crystallizes in the monoclinic Cm space group. There are three inequivalent U sites. In the first U site, U(1) is bonded in a 16-coordinate geometry to one U(3), three equivalent Th(1), one Re(3), two equivalent Re(4), two equivalent Re(5), three equivalent Re(1), and four equivalent Re(6) atoms. In the second U site, U(2) is bonded in a 14-coordinate geometry to one U(3), one Th(1), one Re(4), two equivalent Re(3), two equivalent Re(6), three equivalent Re(2), and four equivalent Re(5) atoms. In the third U site, U(3) is bonded in a 14-coordinate geometry to one U(1), one U(2), one Re(3), two equivalent Re(4), two equivalent Re(5), three equivalent Re(2), and four equivalent Re(6) atoms. Th(1) is bonded in a 16-coordinate geometry to one U(2), three equivalent U(1), one Re(4), two equivalent Re(3), two equivalent Re(6), three equivalent Re(1), and four equivalent Re(5) atoms. There are six inequivalent Re sites. In the first Re site, Re(1) is bonded to three equivalent U(1), three equivalent Th(1), one Re(3), one Re(4), two equivalent Re(5), and two equivalent Re(6) atoms to form distorted ReTh3U3Re6 cuboctahedra that share corners with two equivalent Re(3)Th2U4Re6 cuboctahedra, corners with two equivalent Re(4)ThU5Re6 cuboctahedra, corners with four equivalent Re(5)Th2U4Re6 cuboctahedra, corners with four equivalent Re(6)ThU5Re6 cuboctahedra, edges with six equivalent Re(1)Th3U3Re6 cuboctahedra, faces with two equivalent Re(2)U6Re6 cuboctahedra, faces with three equivalent Re(3)Th2U4Re6 cuboctahedra, faces with three equivalent Re(4)ThU5Re6 cuboctahedra, faces with six equivalent Re(5)Th2U4Re6 cuboctahedra, and faces with six equivalent Re(6)ThU5Re6 cuboctahedra. In the second Re site, Re(2) is bonded to three equivalent U(2), three equivalent U(3), one Re(3), one Re(4), two equivalent Re(5), and two equivalent Re(6) atoms to form ReU6Re6 cuboctahedra that share corners with two equivalent Re(3)Th2U4Re6 cuboctahedra, corners with two equivalent Re(4)ThU5Re6 cuboctahedra, corners with four equivalent Re(5)Th2U4Re6 cuboctahedra, corners with four equivalent Re(6)ThU5Re6 cuboctahedra, edges with six equivalent Re(2)U6Re6 cuboctahedra, faces with two equivalent Re(1)Th3U3Re6 cuboctahedra, faces with three equivalent Re(3)Th2U4Re6 cuboctahedra, faces with three equivalent Re(4)ThU5Re6 cuboctahedra, faces with six equivalent Re(5)Th2U4Re6 cuboctahedra, and faces with six equivalent Re(6)ThU5Re6 cuboctahedra. In the third Re site, Re(3) is bonded to one U(1), one U(3), two equivalent U(2), two equivalent Th(1), one Re(1), one Re(2), and four equivalent Re(5) atoms to form ReTh2U4Re6 cuboctahedra that share corners with two equivalent Re(1)Th3U3Re6 cuboctahedra, corners with two equivalent Re(4)ThU5Re6 cuboctahedra, corners with two equivalent Re(2)U6Re6 cuboctahedra, corners with four equivalent Re(3)Th2U4Re6 cuboctahedra, corners with eight equivalent Re(6)ThU5Re6 cuboctahedra, edges with two equivalent Re(3)Th2U4Re6 cuboctahedra, edges with four equivalent Re(4)ThU5Re6 cuboctahedra, faces with three equivalent Re(1)Th3U3Re6 cuboctahedra, faces with three equivalent Re(2)U6Re6 cuboctahedra, faces with four equivalent Re(6)ThU5Re6 cuboctahedra, and faces with eight equivalent Re(5)Th2U4Re6 cuboctahedra. In the fourth Re site, Re(4) is bonded to one U(2), two equivalent U(1), two equivalent U(3), one Th(1), one Re(1), one Re(2), and four equivalent Re(6) atoms to form ReThU5Re6 cuboctahedra that share corners with two equivalent Re(3)Th2U4Re6 cuboctahedra, corners with two equivalent Re(1)Th3U3Re6 cuboctahedra, corners with two equivalent Re(2)U6Re6 cuboctahedra, corners with four equivalent Re(4)ThU5Re6 cuboctahedra, corners with eight equivalent Re(5)Th2U4Re6 cuboctahedra, edges with two equivalent Re(4)ThU5Re6 cuboctahedra, edges with four equivalent Re(3)Th2U4Re6 cuboctahedra, faces with three equivalent Re(1)Th3U3Re6 cuboctahedra, faces with three equivalent Re(2)U6Re6 cuboctahedra, faces with four equivalent Re(5)Th2U4Re6 cuboctahedra, and faces with eight equivalent Re(6)ThU5Re6 cuboctahedra. In the fifth Re site, Re(5) is bonded to one U(1), one U(3), two equivalent U(2), two equivalent Th(1), one Re(1), one Re(2), two equivalent Re(3), and two equivalent Re(5) atoms to form distorted ReTh2U4Re6 cuboctahedra that share corners with two equivalent Re(1)Th3U3Re6 cuboctahedra, corners with two equivalent Re(2)U6Re6 cuboctahedra, corners with four equivalent Re(5)Th2U4Re6 cuboctahedra, corners with four equivalent Re(4)ThU5Re6 cuboctahedra, corners with six equivalent Re(6)ThU5Re6 cuboctahedra, edges with two equivalent Re(5)Th2U4Re6 cuboctahedra, edges with four equivalent Re(6)ThU5Re6 cuboctahedra, faces with two equivalent Re(4)ThU5Re6 cuboctahedra, faces with two equivalent Re(6)ThU5Re6 cuboctahedra, faces with three equivalent Re(1)Th3U3Re6 cuboctahedra, faces with three equivalent Re(2)U6Re6 cuboctahedra, faces with four equivalent Re(3)Th2U4Re6 cuboctahedra, and faces with four equivalent Re(5)Th2U4Re6 cuboctahedra. In the sixth Re site, Re(6) is bonded to one U(2), two equivalent U(1), two equivalent U(3), one Th(1), one Re(1), one Re(2), two equivalent Re(4), and two equivalent Re(6) atoms to form distorted ReThU5Re6 cuboctahedra that share corners with two equivalent Re(1)Th3U3Re6 cuboctahedra, corners with two equivalent Re(2)U6Re6 cuboctahedra, corners with four equivalent Re(3)Th2U4Re6 cuboctahedra, corners with four equivalent Re(6)ThU5Re6 cuboctahedra, corners with six equivalent Re(5)Th2U4Re6 cuboctahedra, edges with two equivalent Re(6)ThU5Re6 cuboctahedra, edges with four equivalent Re(5)Th2U4Re6 cuboctahedra, faces with two equivalent Re(3)Th2U4Re6 cuboctahedra, faces with two equivalent Re(5)Th2U4Re6 cuboctahedra, faces with three equivalent Re(1)Th3U3Re6 cuboctahedra, faces with three equivalent Re(2)U6Re6 cuboctahedra, faces with four equivalent Re(4)ThU5Re6 cuboctahedra, and faces with four equivalent Re(6)ThU5Re6 cuboctahedra. is represented by the CIF card [CIF]
data_ThU3Re8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.289
_cell_length_b   5.289
_cell_length_c   8.633
_cell_angle_alpha   89.761
_cell_angle_beta   89.761
_cell_angle_gamma   67.588
_symmetry_Int_Tables_number   1
_cell_volume   223.264
_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
  Th  Th0  1  0.335  0.335  0.434  1.0
  U  U1  1  0.671  0.671  0.584  1.0
  U  U2  1  0.339  0.339  0.065  1.0
  U  U3  1  0.662  0.662  0.925  1.0
  Re  Re4  1  0.995  0.995  0.500  1.0
  Re  Re5  1  1.000  1.000  0.999  1.0
  Re  Re6  1  0.826  0.826  0.249  1.0
  Re  Re7  1  0.171  0.171  0.752  1.0
  Re  Re8  1  0.340  0.831  0.243  1.0
  Re  Re9  1  0.169  0.661  0.754  1.0
  Re  Re10  1  0.661  0.169  0.754  1.0
  Re  Re11  1  0.831  0.340  0.243  1.0
[/CIF]
.