The crystal structure described by Ba4MgTl8O16 crystallizes in the monoclinic Pm space group. There are four inequivalent Ba sites. In the first Ba site, Ba(1) is bonded in a 8-coordinate geometry to one O(16), one O(8), two equivalent O(3), two equivalent O(4), and two equivalent O(7) atoms. In the second Ba site, Ba(2) is bonded in a 8-coordinate geometry to one O(1), one O(9), two equivalent O(2), two equivalent O(5), and two equivalent O(6) atoms. In the third Ba site, Ba(3) is bonded in a 8-coordinate geometry to one O(16), one O(8), two equivalent O(11), two equivalent O(12), and two equivalent O(15) atoms. In the fourth Ba site, Ba(4) is bonded in a 8-coordinate geometry to one O(1), one O(9), two equivalent O(10), two equivalent O(13), and two equivalent O(14) atoms. Mg(1) is bonded to one O(10), one O(5), and two equivalent O(9) atoms to form MgO4 tetrahedra that share  a cornercorner with one Tl(1)O6 octahedra,  a cornercorner with one Tl(6)O6 octahedra, corners with two equivalent Tl(5)O6 octahedra, corners with two equivalent Mg(1)O4 tetrahedra, corners with two equivalent Tl(3)O4 trigonal pyramids, and  an edgeedge with one Tl(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 17-36°. There are eight inequivalent Tl sites. In the first Tl site, Tl(1) is bonded to one O(14), one O(5), two equivalent O(1), and two equivalent O(3) atoms to form TlO6 octahedra that share corners with two equivalent Tl(7)O6 octahedra,  a cornercorner with one Mg(1)O4 tetrahedra, edges with two equivalent Tl(1)O6 octahedra, edges with two equivalent Tl(8)O6 octahedra, and edges with two equivalent Tl(3)O4 trigonal pyramids. The corner-sharing octahedral tilt angles are 52°. In the second Tl site, Tl(2) is bonded to one O(16), one O(2), two equivalent O(15), and two equivalent O(4) atoms to form a mixture of edge and corner-sharing TlO6 octahedra. The corner-sharing octahedral tilt angles range from 50-57°. In the third Tl site, Tl(3) is bonded to one O(3), one O(7), and two equivalent O(5) atoms to form TlO4 trigonal pyramids that share  a cornercorner with one Tl(8)O6 octahedra, corners with two equivalent Tl(6)O6 octahedra, corners with two equivalent Mg(1)O4 tetrahedra, corners with two equivalent Tl(3)O4 trigonal pyramids, and edges with two equivalent Tl(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 5-75°. In the fourth Tl site, Tl(4) is bonded to one O(11), one O(4), two equivalent O(6), and two equivalent O(8) atoms to form a mixture of edge and corner-sharing TlO6 octahedra. The corner-sharing octahedral tilt angles range from 52-57°. In the fifth Tl site, Tl(5) is bonded to one O(13), one O(6), two equivalent O(11), and two equivalent O(9) atoms to form distorted TlO6 octahedra that share corners with two equivalent Tl(7)O6 octahedra, corners with two equivalent Mg(1)O4 tetrahedra, edges with two equivalent Tl(4)O6 octahedra, edges with two equivalent Tl(5)O6 octahedra, and  an edgeedge with one Mg(1)O4 tetrahedra. The corner-sharing octahedral tilt angles are 66°. In the sixth Tl site, Tl(6) is bonded to one O(10), one O(8), two equivalent O(12), and two equivalent O(7) atoms to form distorted TlO6 octahedra that share corners with two equivalent Tl(4)O6 octahedra, corners with two equivalent Tl(8)O6 octahedra,  a cornercorner with one Mg(1)O4 tetrahedra, corners with two equivalent Tl(3)O4 trigonal pyramids, and edges with two equivalent Tl(6)O6 octahedra. The corner-sharing octahedral tilt angles range from 52-59°. In the seventh Tl site, Tl(7) is bonded to one O(1), one O(15), two equivalent O(13), and two equivalent O(2) atoms to form a mixture of edge and corner-sharing TlO6 octahedra. The corner-sharing octahedral tilt angles range from 52-66°. In the eighth Tl site, Tl(8) is bonded to one O(12), one O(3), two equivalent O(14), and two equivalent O(16) atoms to form TlO6 octahedra that share corners with two equivalent Tl(2)O6 octahedra, corners with two equivalent Tl(6)O6 octahedra,  a cornercorner with one Tl(3)O4 trigonal pyramid, edges with two equivalent Tl(1)O6 octahedra, and edges with two equivalent Tl(8)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-59°. There are sixteen inequivalent O sites. In the first O site, O(1) is bonded to one Ba(2), one Ba(4), one Tl(7), and two equivalent Tl(1) atoms to form distorted OBa2Tl3 trigonal bipyramids that share corners with two equivalent O(3)Ba2Tl4 octahedra,  a cornercorner with one O(15)Ba2Tl3 trigonal bipyramid, corners with two equivalent O(1)Ba2Tl3 trigonal bipyramids, corners with two equivalent O(6)Ba2Tl3 trigonal bipyramids,  an edgeedge with one O(3)Ba2Tl4 octahedra, edges with two equivalent O(5)Ba2MgTl3 octahedra, edges with two equivalent O(14)Ba2Tl3 square pyramids, and edges with two equivalent O(2)Ba2Tl3 trigonal bipyramids. The corner-sharing octahedral tilt angles are 6°. In the second O site, O(2) is bonded to two equivalent Ba(2), one Tl(2), and two equivalent Tl(7) atoms to form distorted OBa2Tl3 trigonal bipyramids that share corners with two equivalent O(5)Ba2MgTl3 octahedra,  a cornercorner with one O(16)Ba2Tl3 trigonal bipyramid, corners with two equivalent O(6)Ba2Tl3 trigonal bipyramids,  an edgeedge with one O(5)Ba2MgTl3 octahedra,  an edgeedge with one O(6)Ba2Tl3 trigonal bipyramid, edges with two equivalent O(1)Ba2Tl3 trigonal bipyramids, edges with two equivalent O(15)Ba2Tl3 trigonal bipyramids, and edges with two equivalent O(2)Ba2Tl3 trigonal bipyramids. The corner-sharing octahedral tilt angles are 42°. In the third O site, O(3) is bonded to two equivalent Ba(1), one Tl(3), one Tl(8), and two equivalent Tl(1) atoms to form OBa2Tl4 octahedra that share corners with two equivalent O(7)Ba2Tl3 square pyramids, corners with two equivalent O(1)Ba2Tl3 trigonal bipyramids, corners with two equivalent O(8)Ba2Tl3 trigonal bipyramids, edges with two equivalent O(5)Ba2MgTl3 octahedra, edges with two equivalent O(3)Ba2Tl4 octahedra, edges with two equivalent O(14)Ba2Tl3 square pyramids,  an edgeedge with one O(1)Ba2Tl3 trigonal bipyramid, edges with two equivalent O(16)Ba2Tl3 trigonal bipyramids, and  a faceface with one O(7)Ba2Tl3 square pyramid. In the fourth O site, O(4) is bonded in a 5-coordinate geometry to two equivalent Ba(1), one Tl(4), and two equivalent Tl(2) atoms. In the fifth O site, O(5) is bonded to two equivalent Ba(2), one Mg(1), one Tl(1), and two equivalent Tl(3) atoms to form distorted OBa2MgTl3 octahedra that share  a cornercorner with one O(14)Ba2Tl3 square pyramid, corners with two equivalent O(7)Ba2Tl3 square pyramids, corners with two equivalent O(2)Ba2Tl3 trigonal bipyramids, corners with two equivalent O(6)Ba2Tl3 trigonal bipyramids, edges with two equivalent O(5)Ba2MgTl3 octahedra, edges with two equivalent O(3)Ba2Tl4 octahedra,  an edgeedge with one O(2)Ba2Tl3 trigonal bipyramid,  an edgeedge with one O(6)Ba2Tl3 trigonal bipyramid, and edges with two equivalent O(1)Ba2Tl3 trigonal bipyramids. In the sixth O site, O(6) is bonded to two equivalent Ba(2), one Tl(5), and two equivalent Tl(4) atoms to form distorted OBa2Tl3 trigonal bipyramids that share corners with two equivalent O(5)Ba2MgTl3 octahedra, corners with two equivalent O(1)Ba2Tl3 trigonal bipyramids, corners with two equivalent O(2)Ba2Tl3 trigonal bipyramids, corners with two equivalent O(8)Ba2Tl3 trigonal bipyramids,  an edgeedge with one O(5)Ba2MgTl3 octahedra, edges with two equivalent O(11)Ba2Tl3 square pyramids,  an edgeedge with one O(2)Ba2Tl3 trigonal bipyramid,  an edgeedge with one O(8)Ba2Tl3 trigonal bipyramid, and edges with two equivalent O(6)Ba2Tl3 trigonal bipyramids. The corner-sharing octahedral tilt angles are 44°. In the seventh O site, O(7) is bonded to two equivalent Ba(1), one Tl(3), and two equivalent Tl(6) atoms to form distorted OBa2Tl3 square pyramids that share corners with two equivalent O(5)Ba2MgTl3 octahedra, corners with two equivalent O(3)Ba2Tl4 octahedra, corners with two equivalent O(16)Ba2Tl3 trigonal bipyramids, edges with two equivalent O(7)Ba2Tl3 square pyramids, edges with two equivalent O(8)Ba2Tl3 trigonal bipyramids, and  a faceface with one O(3)Ba2Tl4 octahedra. The corner-sharing octahedral tilt angles range from 48-64°. In the eighth O site, O(8) is bonded to one Ba(1), one Ba(3), one Tl(6), and two equivalent Tl(4) atoms to form distorted OBa2Tl3 trigonal bipyramids that share corners with two equivalent O(3)Ba2Tl4 octahedra, corners with two equivalent O(15)Ba2Tl3 trigonal bipyramids, corners with two equivalent O(16)Ba2Tl3 trigonal bipyramids, corners with two equivalent O(6)Ba2Tl3 trigonal bipyramids, corners with two equivalent O(8)Ba2Tl3 trigonal bipyramids, edges with two equivalent O(11)Ba2Tl3 square pyramids, edges with two equivalent O(7)Ba2Tl3 square pyramids, and  an edgeedge with one O(6)Ba2Tl3 trigonal bipyramid. The corner-sharing octahedral tilt angles are 47°. In the ninth O site, O(9) is bonded in a distorted bent 120 degrees geometry to one Ba(2), one Ba(4), two equivalent Mg(1), and two equivalent Tl(5) atoms. In the tenth O site, O(10) is bonded in a distorted rectangular see-saw-like geometry to two equivalent Ba(4), one Mg(1), and one Tl(6) atom. In the eleventh O site, O(11) is bonded to two equivalent Ba(3), one Tl(4), and two equivalent Tl(5) atoms to form a mixture of edge and corner-sharing OBa2Tl3 square pyramids. In the twelfth O site, O(12) is bonded in a 5-coordinate geometry to two equivalent Ba(3), one Tl(8), and two equivalent Tl(6) atoms. In the thirteenth O site, O(13) is bonded in a 5-coordinate geometry to two equivalent Ba(4), one Tl(5), and two equivalent Tl(7) atoms. In the fourteenth O site, O(14) is bonded to two equivalent Ba(4), one Tl(1), and two equivalent Tl(8) atoms to form distorted OBa2Tl3 square pyramids that share  a cornercorner with one O(5)Ba2MgTl3 octahedra, corners with two equivalent O(16)Ba2Tl3 trigonal bipyramids, edges with two equivalent O(3)Ba2Tl4 octahedra, edges with two equivalent O(14)Ba2Tl3 square pyramids,  an edgeedge with one O(16)Ba2Tl3 trigonal bipyramid, and edges with two equivalent O(1)Ba2Tl3 trigonal bipyramids. The corner-sharing octahedral tilt angles are 11°. In the fifteenth O site, O(15) is bonded to two equivalent Ba(3), one Tl(7), and two equivalent Tl(2) atoms to form a mixture of distorted edge and corner-sharing OBa2Tl3 trigonal bipyramids. In the sixteenth O site, O(16) is bonded to one Ba(1), one Ba(3), one Tl(2), and two equivalent Tl(8) atoms to form distorted OBa2Tl3 trigonal bipyramids that share corners with two equivalent O(11)Ba2Tl3 square pyramids, corners with two equivalent O(14)Ba2Tl3 square pyramids, corners with two equivalent O(7)Ba2Tl3 square pyramids,  a cornercorner with one O(2)Ba2Tl3 trigonal bipyramid, corners with two equivalent O(16)Ba2Tl3 trigonal bipyramids, corners with two equivalent O(8)Ba2Tl3 trigonal bipyramids, edges with two equivalent O(3)Ba2Tl4 octahedra,  an edgeedge with one O(14)Ba2Tl3 square pyramid, and edges with two equivalent O(15)Ba2Tl3 trigonal bipyramids. is represented by the Crystallographic Information File (CIF) [CIF]
data_Ba4MgTl8O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   10.599
_cell_length_b   12.551
_cell_length_c   3.582
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   89.530
_symmetry_Int_Tables_number   1
_cell_volume   476.485
_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
  Ba  Ba0  1  0.244  0.328  0.750  1.0
  Ba  Ba1  1  0.255  0.861  0.250  1.0
  Ba  Ba2  1  0.751  0.168  0.750  1.0
  Ba  Ba3  1  0.751  0.643  0.250  1.0
  Mg  Mg4  1  0.486  0.708  0.750  1.0
  Tl  Tl5  1  0.066  0.616  0.750  1.0
  Tl  Tl6  1  0.069  0.103  0.750  1.0
  Tl  Tl7  1  0.338  0.568  0.250  1.0
  Tl  Tl8  1  0.429  0.112  0.250  1.0
  Tl  Tl9  1  0.600  0.918  0.750  1.0
  Tl  Tl10  1  0.571  0.397  0.750  1.0
  Tl  Tl11  1  0.924  0.892  0.250  1.0
  Tl  Tl12  1  0.925  0.394  0.250  1.0
  O  O13  1  0.015  0.720  0.250  1.0
  O  O14  1  0.075  0.924  0.750  1.0
  O  O15  1  0.131  0.490  0.250  1.0
  O  O16  1  0.211  0.154  0.250  1.0
  O  O17  1  0.296  0.694  0.750  1.0
  O  O18  1  0.400  0.977  0.750  1.0
  O  O19  1  0.421  0.400  0.250  1.0
  O  O20  1  0.482  0.215  0.750  1.0
  O  O21  1  0.526  0.777  0.250  1.0
  O  O22  1  0.585  0.575  0.750  1.0
  O  O23  1  0.632  0.035  0.250  1.0
  O  O24  1  0.710  0.344  0.250  1.0
  O  O25  1  0.787  0.838  0.750  1.0
  O  O26  1  0.886  0.517  0.750  1.0
  O  O27  1  0.922  0.075  0.250  1.0
  O  O28  1  0.985  0.283  0.750  1.0
[/CIF]
.
The crystal structure described by Ba4MgTl8O16 crystallizes in the monoclinic Pm space group. There are four inequivalent Ba sites. In the first Ba site, Ba(1) is bonded in a 8-coordinate geometry to one O(16), one O(8), two equivalent O(3), two equivalent O(4), and two equivalent O(7) atoms. In the second Ba site, Ba(2) is bonded in a 8-coordinate geometry to one O(1), one O(9), two equivalent O(2), two equivalent O(5), and two equivalent O(6) atoms. In the third Ba site, Ba(3) is bonded in a 8-coordinate geometry to one O(16), one O(8), two equivalent O(11), two equivalent O(12), and two equivalent O(15) atoms. In the fourth Ba site, Ba(4) is bonded in a 8-coordinate geometry to one O(1), one O(9), two equivalent O(10), two equivalent O(13), and two equivalent O(14) atoms. Mg(1) is bonded to one O(10), one O(5), and two equivalent O(9) atoms to form MgO4 tetrahedra that share  a cornercorner with one Tl(1)O6 octahedra,  a cornercorner with one Tl(6)O6 octahedra, corners with two equivalent Tl(5)O6 octahedra, corners with two equivalent Mg(1)O4 tetrahedra, corners with two equivalent Tl(3)O4 trigonal pyramids, and  an edgeedge with one Tl(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 17-36°. There are eight inequivalent Tl sites. In the first Tl site, Tl(1) is bonded to one O(14), one O(5), two equivalent O(1), and two equivalent O(3) atoms to form TlO6 octahedra that share corners with two equivalent Tl(7)O6 octahedra,  a cornercorner with one Mg(1)O4 tetrahedra, edges with two equivalent Tl(1)O6 octahedra, edges with two equivalent Tl(8)O6 octahedra, and edges with two equivalent Tl(3)O4 trigonal pyramids. The corner-sharing octahedral tilt angles are 52°. In the second Tl site, Tl(2) is bonded to one O(16), one O(2), two equivalent O(15), and two equivalent O(4) atoms to form a mixture of edge and corner-sharing TlO6 octahedra. The corner-sharing octahedral tilt angles range from 50-57°. In the third Tl site, Tl(3) is bonded to one O(3), one O(7), and two equivalent O(5) atoms to form TlO4 trigonal pyramids that share  a cornercorner with one Tl(8)O6 octahedra, corners with two equivalent Tl(6)O6 octahedra, corners with two equivalent Mg(1)O4 tetrahedra, corners with two equivalent Tl(3)O4 trigonal pyramids, and edges with two equivalent Tl(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 5-75°. In the fourth Tl site, Tl(4) is bonded to one O(11), one O(4), two equivalent O(6), and two equivalent O(8) atoms to form a mixture of edge and corner-sharing TlO6 octahedra. The corner-sharing octahedral tilt angles range from 52-57°. In the fifth Tl site, Tl(5) is bonded to one O(13), one O(6), two equivalent O(11), and two equivalent O(9) atoms to form distorted TlO6 octahedra that share corners with two equivalent Tl(7)O6 octahedra, corners with two equivalent Mg(1)O4 tetrahedra, edges with two equivalent Tl(4)O6 octahedra, edges with two equivalent Tl(5)O6 octahedra, and  an edgeedge with one Mg(1)O4 tetrahedra. The corner-sharing octahedral tilt angles are 66°. In the sixth Tl site, Tl(6) is bonded to one O(10), one O(8), two equivalent O(12), and two equivalent O(7) atoms to form distorted TlO6 octahedra that share corners with two equivalent Tl(4)O6 octahedra, corners with two equivalent Tl(8)O6 octahedra,  a cornercorner with one Mg(1)O4 tetrahedra, corners with two equivalent Tl(3)O4 trigonal pyramids, and edges with two equivalent Tl(6)O6 octahedra. The corner-sharing octahedral tilt angles range from 52-59°. In the seventh Tl site, Tl(7) is bonded to one O(1), one O(15), two equivalent O(13), and two equivalent O(2) atoms to form a mixture of edge and corner-sharing TlO6 octahedra. The corner-sharing octahedral tilt angles range from 52-66°. In the eighth Tl site, Tl(8) is bonded to one O(12), one O(3), two equivalent O(14), and two equivalent O(16) atoms to form TlO6 octahedra that share corners with two equivalent Tl(2)O6 octahedra, corners with two equivalent Tl(6)O6 octahedra,  a cornercorner with one Tl(3)O4 trigonal pyramid, edges with two equivalent Tl(1)O6 octahedra, and edges with two equivalent Tl(8)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-59°. There are sixteen inequivalent O sites. In the first O site, O(1) is bonded to one Ba(2), one Ba(4), one Tl(7), and two equivalent Tl(1) atoms to form distorted OBa2Tl3 trigonal bipyramids that share corners with two equivalent O(3)Ba2Tl4 octahedra,  a cornercorner with one O(15)Ba2Tl3 trigonal bipyramid, corners with two equivalent O(1)Ba2Tl3 trigonal bipyramids, corners with two equivalent O(6)Ba2Tl3 trigonal bipyramids,  an edgeedge with one O(3)Ba2Tl4 octahedra, edges with two equivalent O(5)Ba2MgTl3 octahedra, edges with two equivalent O(14)Ba2Tl3 square pyramids, and edges with two equivalent O(2)Ba2Tl3 trigonal bipyramids. The corner-sharing octahedral tilt angles are 6°. In the second O site, O(2) is bonded to two equivalent Ba(2), one Tl(2), and two equivalent Tl(7) atoms to form distorted OBa2Tl3 trigonal bipyramids that share corners with two equivalent O(5)Ba2MgTl3 octahedra,  a cornercorner with one O(16)Ba2Tl3 trigonal bipyramid, corners with two equivalent O(6)Ba2Tl3 trigonal bipyramids,  an edgeedge with one O(5)Ba2MgTl3 octahedra,  an edgeedge with one O(6)Ba2Tl3 trigonal bipyramid, edges with two equivalent O(1)Ba2Tl3 trigonal bipyramids, edges with two equivalent O(15)Ba2Tl3 trigonal bipyramids, and edges with two equivalent O(2)Ba2Tl3 trigonal bipyramids. The corner-sharing octahedral tilt angles are 42°. In the third O site, O(3) is bonded to two equivalent Ba(1), one Tl(3), one Tl(8), and two equivalent Tl(1) atoms to form OBa2Tl4 octahedra that share corners with two equivalent O(7)Ba2Tl3 square pyramids, corners with two equivalent O(1)Ba2Tl3 trigonal bipyramids, corners with two equivalent O(8)Ba2Tl3 trigonal bipyramids, edges with two equivalent O(5)Ba2MgTl3 octahedra, edges with two equivalent O(3)Ba2Tl4 octahedra, edges with two equivalent O(14)Ba2Tl3 square pyramids,  an edgeedge with one O(1)Ba2Tl3 trigonal bipyramid, edges with two equivalent O(16)Ba2Tl3 trigonal bipyramids, and  a faceface with one O(7)Ba2Tl3 square pyramid. In the fourth O site, O(4) is bonded in a 5-coordinate geometry to two equivalent Ba(1), one Tl(4), and two equivalent Tl(2) atoms. In the fifth O site, O(5) is bonded to two equivalent Ba(2), one Mg(1), one Tl(1), and two equivalent Tl(3) atoms to form distorted OBa2MgTl3 octahedra that share  a cornercorner with one O(14)Ba2Tl3 square pyramid, corners with two equivalent O(7)Ba2Tl3 square pyramids, corners with two equivalent O(2)Ba2Tl3 trigonal bipyramids, corners with two equivalent O(6)Ba2Tl3 trigonal bipyramids, edges with two equivalent O(5)Ba2MgTl3 octahedra, edges with two equivalent O(3)Ba2Tl4 octahedra,  an edgeedge with one O(2)Ba2Tl3 trigonal bipyramid,  an edgeedge with one O(6)Ba2Tl3 trigonal bipyramid, and edges with two equivalent O(1)Ba2Tl3 trigonal bipyramids. In the sixth O site, O(6) is bonded to two equivalent Ba(2), one Tl(5), and two equivalent Tl(4) atoms to form distorted OBa2Tl3 trigonal bipyramids that share corners with two equivalent O(5)Ba2MgTl3 octahedra, corners with two equivalent O(1)Ba2Tl3 trigonal bipyramids, corners with two equivalent O(2)Ba2Tl3 trigonal bipyramids, corners with two equivalent O(8)Ba2Tl3 trigonal bipyramids,  an edgeedge with one O(5)Ba2MgTl3 octahedra, edges with two equivalent O(11)Ba2Tl3 square pyramids,  an edgeedge with one O(2)Ba2Tl3 trigonal bipyramid,  an edgeedge with one O(8)Ba2Tl3 trigonal bipyramid, and edges with two equivalent O(6)Ba2Tl3 trigonal bipyramids. The corner-sharing octahedral tilt angles are 44°. In the seventh O site, O(7) is bonded to two equivalent Ba(1), one Tl(3), and two equivalent Tl(6) atoms to form distorted OBa2Tl3 square pyramids that share corners with two equivalent O(5)Ba2MgTl3 octahedra, corners with two equivalent O(3)Ba2Tl4 octahedra, corners with two equivalent O(16)Ba2Tl3 trigonal bipyramids, edges with two equivalent O(7)Ba2Tl3 square pyramids, edges with two equivalent O(8)Ba2Tl3 trigonal bipyramids, and  a faceface with one O(3)Ba2Tl4 octahedra. The corner-sharing octahedral tilt angles range from 48-64°. In the eighth O site, O(8) is bonded to one Ba(1), one Ba(3), one Tl(6), and two equivalent Tl(4) atoms to form distorted OBa2Tl3 trigonal bipyramids that share corners with two equivalent O(3)Ba2Tl4 octahedra, corners with two equivalent O(15)Ba2Tl3 trigonal bipyramids, corners with two equivalent O(16)Ba2Tl3 trigonal bipyramids, corners with two equivalent O(6)Ba2Tl3 trigonal bipyramids, corners with two equivalent O(8)Ba2Tl3 trigonal bipyramids, edges with two equivalent O(11)Ba2Tl3 square pyramids, edges with two equivalent O(7)Ba2Tl3 square pyramids, and  an edgeedge with one O(6)Ba2Tl3 trigonal bipyramid. The corner-sharing octahedral tilt angles are 47°. In the ninth O site, O(9) is bonded in a distorted bent 120 degrees geometry to one Ba(2), one Ba(4), two equivalent Mg(1), and two equivalent Tl(5) atoms. In the tenth O site, O(10) is bonded in a distorted rectangular see-saw-like geometry to two equivalent Ba(4), one Mg(1), and one Tl(6) atom. In the eleventh O site, O(11) is bonded to two equivalent Ba(3), one Tl(4), and two equivalent Tl(5) atoms to form a mixture of edge and corner-sharing OBa2Tl3 square pyramids. In the twelfth O site, O(12) is bonded in a 5-coordinate geometry to two equivalent Ba(3), one Tl(8), and two equivalent Tl(6) atoms. In the thirteenth O site, O(13) is bonded in a 5-coordinate geometry to two equivalent Ba(4), one Tl(5), and two equivalent Tl(7) atoms. In the fourteenth O site, O(14) is bonded to two equivalent Ba(4), one Tl(1), and two equivalent Tl(8) atoms to form distorted OBa2Tl3 square pyramids that share  a cornercorner with one O(5)Ba2MgTl3 octahedra, corners with two equivalent O(16)Ba2Tl3 trigonal bipyramids, edges with two equivalent O(3)Ba2Tl4 octahedra, edges with two equivalent O(14)Ba2Tl3 square pyramids,  an edgeedge with one O(16)Ba2Tl3 trigonal bipyramid, and edges with two equivalent O(1)Ba2Tl3 trigonal bipyramids. The corner-sharing octahedral tilt angles are 11°. In the fifteenth O site, O(15) is bonded to two equivalent Ba(3), one Tl(7), and two equivalent Tl(2) atoms to form a mixture of distorted edge and corner-sharing OBa2Tl3 trigonal bipyramids. In the sixteenth O site, O(16) is bonded to one Ba(1), one Ba(3), one Tl(2), and two equivalent Tl(8) atoms to form distorted OBa2Tl3 trigonal bipyramids that share corners with two equivalent O(11)Ba2Tl3 square pyramids, corners with two equivalent O(14)Ba2Tl3 square pyramids, corners with two equivalent O(7)Ba2Tl3 square pyramids,  a cornercorner with one O(2)Ba2Tl3 trigonal bipyramid, corners with two equivalent O(16)Ba2Tl3 trigonal bipyramids, corners with two equivalent O(8)Ba2Tl3 trigonal bipyramids, edges with two equivalent O(3)Ba2Tl4 octahedra,  an edgeedge with one O(14)Ba2Tl3 square pyramid, and edges with two equivalent O(15)Ba2Tl3 trigonal bipyramids. is represented by the Crystallographic Information File (CIF) [CIF]
data_Ba4MgTl8O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   10.599
_cell_length_b   12.551
_cell_length_c   3.582
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   89.530
_symmetry_Int_Tables_number   1
_cell_volume   476.485
_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
  Ba  Ba0  1  0.244  0.328  0.750  1.0
  Ba  Ba1  1  0.255  0.861  0.250  1.0
  Ba  Ba2  1  0.751  0.168  0.750  1.0
  Ba  Ba3  1  0.751  0.643  0.250  1.0
  Mg  Mg4  1  0.486  0.708  0.750  1.0
  Tl  Tl5  1  0.066  0.616  0.750  1.0
  Tl  Tl6  1  0.069  0.103  0.750  1.0
  Tl  Tl7  1  0.338  0.568  0.250  1.0
  Tl  Tl8  1  0.429  0.112  0.250  1.0
  Tl  Tl9  1  0.600  0.918  0.750  1.0
  Tl  Tl10  1  0.571  0.397  0.750  1.0
  Tl  Tl11  1  0.924  0.892  0.250  1.0
  Tl  Tl12  1  0.925  0.394  0.250  1.0
  O  O13  1  0.015  0.720  0.250  1.0
  O  O14  1  0.075  0.924  0.750  1.0
  O  O15  1  0.131  0.490  0.250  1.0
  O  O16  1  0.211  0.154  0.250  1.0
  O  O17  1  0.296  0.694  0.750  1.0
  O  O18  1  0.400  0.977  0.750  1.0
  O  O19  1  0.421  0.400  0.250  1.0
  O  O20  1  0.482  0.215  0.750  1.0
  O  O21  1  0.526  0.777  0.250  1.0
  O  O22  1  0.585  0.575  0.750  1.0
  O  O23  1  0.632  0.035  0.250  1.0
  O  O24  1  0.710  0.344  0.250  1.0
  O  O25  1  0.787  0.838  0.750  1.0
  O  O26  1  0.886  0.517  0.750  1.0
  O  O27  1  0.922  0.075  0.250  1.0
  O  O28  1  0.985  0.283  0.750  1.0
[/CIF]
.