The crystal structure described by Ba3MgSi2O8 crystallizes in the trigonal P-3 space group. There are three inequivalent Ba sites. In the first Ba site, Ba(1) is bonded in a 10-coordinate geometry to one O(3), three equivalent O(1), three equivalent O(2), and three equivalent O(4) atoms. In the second Ba site, Ba(2) is bonded in a distorted q6 geometry to three equivalent O(2), three equivalent O(3), and three equivalent O(4) atoms. In the third Ba site, Ba(3) is bonded to six equivalent O(1) and six equivalent O(3) atoms to form BaO12 cuboctahedra that share edges with six equivalent Si(1)O4 tetrahedra and faces with two equivalent Mg(2)O6 octahedra. There are two inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to three equivalent O(2) and three equivalent O(4) atoms to form MgO6 octahedra that share corners with six equivalent Si(1)O4 tetrahedra. In the second Mg site, Mg(2) is bonded to six equivalent O(1) atoms to form MgO6 octahedra that share corners with six equivalent Si(1)O4 tetrahedra and faces with two equivalent Ba(3)O12 cuboctahedra. Si(1) is bonded to one O(1), one O(2), one O(3), and one O(4) atom to form SiO4 tetrahedra that share  a cornercorner with one Mg(2)O6 octahedra, corners with two equivalent Mg(1)O6 octahedra, and  an edgeedge with one Ba(3)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 8-22°. There are four inequivalent O sites. In the first O site, O(4) is bonded in a 2-coordinate geometry to one Ba(2), three equivalent Ba(1), one Mg(1), and one Si(1) atom. In the second O site, O(1) is bonded in a 2-coordinate geometry to one Ba(3), three equivalent Ba(1), one Mg(2), and one Si(1) atom. In the third O site, O(2) is bonded in a 2-coordinate geometry to one Ba(2), three equivalent Ba(1), one Mg(1), and one Si(1) atom. In the fourth O site, O(3) is bonded in a 1-coordinate geometry to one Ba(1), one Ba(2), one Ba(3), and one Si(1) atom. is represented by the CIF file [CIF]
data_Ba3Mg(SiO4)2
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   9.850
_cell_length_b   9.850
_cell_length_c   7.373
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   619.506
_cell_formula_units_Z   3
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  0.668  0.002  0.178  1.0
  Ba  Ba1  1  0.998  0.665  0.178  1.0
  Ba  Ba2  1  0.335  0.332  0.178  1.0
  Ba  Ba3  1  0.332  0.998  0.822  1.0
  Ba  Ba4  1  0.002  0.335  0.822  1.0
  Ba  Ba5  1  0.665  0.668  0.822  1.0
  Ba  Ba6  1  0.667  0.333  0.504  1.0
  Ba  Ba7  1  0.333  0.667  0.496  1.0
  Ba  Ba8  1  0.000  0.000  0.500  1.0
  Mg  Mg9  1  0.667  0.333  0.011  1.0
  Mg  Mg10  1  0.333  0.667  0.989  1.0
  Mg  Mg11  1  0.000  0.000  0.000  1.0
  Si  Si12  1  0.663  0.671  0.259  1.0
  Si  Si13  1  0.329  0.992  0.259  1.0
  Si  Si14  1  0.008  0.337  0.259  1.0
  Si  Si15  1  0.337  0.329  0.741  1.0
  Si  Si16  1  0.671  0.008  0.741  1.0
  Si  Si17  1  0.992  0.663  0.741  1.0
  O  O18  1  1.000  0.175  0.177  1.0
  O  O19  1  0.825  0.825  0.177  1.0
  O  O20  1  0.175  0.000  0.177  1.0
  O  O21  1  0.000  0.825  0.823  1.0
  O  O22  1  0.175  0.175  0.823  1.0
  O  O23  1  0.825  1.000  0.823  1.0
  O  O24  1  0.844  0.334  0.196  1.0
  O  O25  1  0.666  0.511  0.196  1.0
  O  O26  1  0.489  0.156  0.196  1.0
  O  O27  1  0.156  0.666  0.804  1.0
  O  O28  1  0.334  0.489  0.804  1.0
  O  O29  1  0.511  0.844  0.804  1.0
  O  O30  1  0.645  0.688  0.475  1.0
  O  O31  1  0.312  0.957  0.475  1.0
  O  O32  1  0.043  0.355  0.475  1.0
  O  O33  1  0.355  0.312  0.525  1.0
  O  O34  1  0.688  0.043  0.525  1.0
  O  O35  1  0.957  0.645  0.525  1.0
  O  O36  1  0.510  0.667  0.155  1.0
  O  O37  1  0.333  0.843  0.155  1.0
  O  O38  1  0.157  0.490  0.155  1.0
  O  O39  1  0.490  0.333  0.845  1.0
  O  O40  1  0.667  0.157  0.845  1.0
  O  O41  1  0.843  0.510  0.845  1.0
[/CIF]
.
The crystal structure described by Ba3MgSi2O8 crystallizes in the trigonal P-3 space group. There are three inequivalent Ba sites. In the first Ba site, Ba(1) is bonded in a 10-coordinate geometry to one O(3), three equivalent O(1), three equivalent O(2), and three equivalent O(4) atoms. In the second Ba site, Ba(2) is bonded in a distorted q6 geometry to three equivalent O(2), three equivalent O(3), and three equivalent O(4) atoms. In the third Ba site, Ba(3) is bonded to six equivalent O(1) and six equivalent O(3) atoms to form BaO12 cuboctahedra that share edges with six equivalent Si(1)O4 tetrahedra and faces with two equivalent Mg(2)O6 octahedra. There are two inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to three equivalent O(2) and three equivalent O(4) atoms to form MgO6 octahedra that share corners with six equivalent Si(1)O4 tetrahedra. In the second Mg site, Mg(2) is bonded to six equivalent O(1) atoms to form MgO6 octahedra that share corners with six equivalent Si(1)O4 tetrahedra and faces with two equivalent Ba(3)O12 cuboctahedra. Si(1) is bonded to one O(1), one O(2), one O(3), and one O(4) atom to form SiO4 tetrahedra that share  a cornercorner with one Mg(2)O6 octahedra, corners with two equivalent Mg(1)O6 octahedra, and  an edgeedge with one Ba(3)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 8-22°. There are four inequivalent O sites. In the first O site, O(4) is bonded in a 2-coordinate geometry to one Ba(2), three equivalent Ba(1), one Mg(1), and one Si(1) atom. In the second O site, O(1) is bonded in a 2-coordinate geometry to one Ba(3), three equivalent Ba(1), one Mg(2), and one Si(1) atom. In the third O site, O(2) is bonded in a 2-coordinate geometry to one Ba(2), three equivalent Ba(1), one Mg(1), and one Si(1) atom. In the fourth O site, O(3) is bonded in a 1-coordinate geometry to one Ba(1), one Ba(2), one Ba(3), and one Si(1) atom. is represented by the CIF file [CIF]
data_Ba3Mg(SiO4)2
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   9.850
_cell_length_b   9.850
_cell_length_c   7.373
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   619.506
_cell_formula_units_Z   3
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  0.668  0.002  0.178  1.0
  Ba  Ba1  1  0.998  0.665  0.178  1.0
  Ba  Ba2  1  0.335  0.332  0.178  1.0
  Ba  Ba3  1  0.332  0.998  0.822  1.0
  Ba  Ba4  1  0.002  0.335  0.822  1.0
  Ba  Ba5  1  0.665  0.668  0.822  1.0
  Ba  Ba6  1  0.667  0.333  0.504  1.0
  Ba  Ba7  1  0.333  0.667  0.496  1.0
  Ba  Ba8  1  0.000  0.000  0.500  1.0
  Mg  Mg9  1  0.667  0.333  0.011  1.0
  Mg  Mg10  1  0.333  0.667  0.989  1.0
  Mg  Mg11  1  0.000  0.000  0.000  1.0
  Si  Si12  1  0.663  0.671  0.259  1.0
  Si  Si13  1  0.329  0.992  0.259  1.0
  Si  Si14  1  0.008  0.337  0.259  1.0
  Si  Si15  1  0.337  0.329  0.741  1.0
  Si  Si16  1  0.671  0.008  0.741  1.0
  Si  Si17  1  0.992  0.663  0.741  1.0
  O  O18  1  1.000  0.175  0.177  1.0
  O  O19  1  0.825  0.825  0.177  1.0
  O  O20  1  0.175  0.000  0.177  1.0
  O  O21  1  0.000  0.825  0.823  1.0
  O  O22  1  0.175  0.175  0.823  1.0
  O  O23  1  0.825  1.000  0.823  1.0
  O  O24  1  0.844  0.334  0.196  1.0
  O  O25  1  0.666  0.511  0.196  1.0
  O  O26  1  0.489  0.156  0.196  1.0
  O  O27  1  0.156  0.666  0.804  1.0
  O  O28  1  0.334  0.489  0.804  1.0
  O  O29  1  0.511  0.844  0.804  1.0
  O  O30  1  0.645  0.688  0.475  1.0
  O  O31  1  0.312  0.957  0.475  1.0
  O  O32  1  0.043  0.355  0.475  1.0
  O  O33  1  0.355  0.312  0.525  1.0
  O  O34  1  0.688  0.043  0.525  1.0
  O  O35  1  0.957  0.645  0.525  1.0
  O  O36  1  0.510  0.667  0.155  1.0
  O  O37  1  0.333  0.843  0.155  1.0
  O  O38  1  0.157  0.490  0.155  1.0
  O  O39  1  0.490  0.333  0.845  1.0
  O  O40  1  0.667  0.157  0.845  1.0
  O  O41  1  0.843  0.510  0.845  1.0
[/CIF]
.