The structure described by MgCr3(SO4)6 crystallizes in the trigonal R3 space group. Mg(1) is bonded to three equivalent O(6) and three equivalent O(8) atoms to form MgO6 octahedra that share corners with three equivalent S(1)O4 tetrahedra and corners with three equivalent S(2)O4 tetrahedra. There are three inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to three equivalent O(1) and three equivalent O(3) atoms to form CrO6 octahedra that share corners with three equivalent S(1)O4 tetrahedra and corners with three equivalent S(2)O4 tetrahedra. In the second Cr site, Cr(2) is bonded to three equivalent O(5) and three equivalent O(7) atoms to form CrO6 octahedra that share corners with three equivalent S(1)O4 tetrahedra and corners with three equivalent S(2)O4 tetrahedra. In the third Cr site, Cr(3) is bonded to three equivalent O(2) and three equivalent O(4) atoms to form CrO6 octahedra that share corners with three equivalent S(1)O4 tetrahedra and corners with three equivalent S(2)O4 tetrahedra. There are two inequivalent S sites. In the first S site, S(1) is bonded to one O(1), one O(2), one O(5), and one O(6) atom to form SO4 tetrahedra that share  a cornercorner with one Mg(1)O6 octahedra,  a cornercorner with one Cr(1)O6 octahedra,  a cornercorner with one Cr(2)O6 octahedra, and  a cornercorner with one Cr(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 26-43°. In the second S site, S(2) is bonded to one O(3), one O(4), one O(7), and one O(8) atom to form SO4 tetrahedra that share  a cornercorner with one Mg(1)O6 octahedra,  a cornercorner with one Cr(1)O6 octahedra,  a cornercorner with one Cr(2)O6 octahedra, and  a cornercorner with one Cr(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 26-45°. There are eight inequivalent O sites. In the first O site, O(3) is bonded in a bent 150 degrees geometry to one Cr(1) and one S(2) atom. In the second O site, O(4) is bonded in a bent 150 degrees geometry to one Cr(3) and one S(2) atom. In the third O site, O(5) is bonded in a bent 150 degrees geometry to one Cr(2) and one S(1) atom. In the fourth O site, O(6) is bonded in a distorted bent 150 degrees geometry to one Mg(1) and one S(1) atom. In the fifth O site, O(7) is bonded in a distorted bent 150 degrees geometry to one Cr(2) and one S(2) atom. In the sixth O site, O(8) is bonded in a bent 150 degrees geometry to one Mg(1) and one S(2) atom. In the seventh O site, O(1) is bonded in a bent 150 degrees geometry to one Cr(1) and one S(1) atom. In the eighth O site, O(2) is bonded in a bent 150 degrees geometry to one Cr(3) and one S(1) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_MgCr3(SO4)6
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.857
_cell_length_b   8.857
_cell_length_c   8.857
_cell_angle_alpha   55.910
_cell_angle_beta   55.910
_cell_angle_gamma   55.910
_symmetry_Int_Tables_number   1
_cell_volume   444.749
_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
  Mg  Mg0  1  0.642  0.642  0.642  1.0
  Cr  Cr1  1  0.849  0.849  0.849  1.0
  Cr  Cr2  1  0.356  0.356  0.356  1.0
  Cr  Cr3  1  0.150  0.150  0.150  1.0
  S  S4  1  0.540  0.961  0.246  1.0
  S  S5  1  0.747  0.461  0.044  1.0
  S  S6  1  0.044  0.747  0.461  1.0
  S  S7  1  0.961  0.246  0.540  1.0
  S  S8  1  0.246  0.540  0.961  1.0
  S  S9  1  0.461  0.044  0.747  1.0
  O  O10  1  0.671  0.993  0.038  1.0
  O  O11  1  0.343  0.982  0.278  1.0
  O  O12  1  0.720  0.651  0.028  1.0
  O  O13  1  0.023  0.955  0.324  1.0
  O  O14  1  0.295  0.511  0.112  1.0
  O  O15  1  0.619  0.766  0.375  1.0
  O  O16  1  0.955  0.324  0.023  1.0
  O  O17  1  0.243  0.616  0.378  1.0
  O  O18  1  0.893  0.706  0.485  1.0
  O  O19  1  0.485  0.893  0.706  1.0
  O  O20  1  0.616  0.378  0.243  1.0
  O  O21  1  0.028  0.720  0.651  1.0
  O  O22  1  0.982  0.278  0.343  1.0
  O  O23  1  0.375  0.619  0.766  1.0
  O  O24  1  0.511  0.112  0.295  1.0
  O  O25  1  0.112  0.295  0.511  1.0
  O  O26  1  0.766  0.375  0.619  1.0
  O  O27  1  0.038  0.671  0.993  1.0
  O  O28  1  0.378  0.243  0.616  1.0
  O  O29  1  0.706  0.485  0.893  1.0
  O  O30  1  0.993  0.038  0.671  1.0
  O  O31  1  0.278  0.343  0.982  1.0
  O  O32  1  0.651  0.028  0.720  1.0
  O  O33  1  0.324  0.023  0.955  1.0
[/CIF]
.
The structure described by MgCr3(SO4)6 crystallizes in the trigonal R3 space group. Mg(1) is bonded to three equivalent O(6) and three equivalent O(8) atoms to form MgO6 octahedra that share corners with three equivalent S(1)O4 tetrahedra and corners with three equivalent S(2)O4 tetrahedra. There are three inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to three equivalent O(1) and three equivalent O(3) atoms to form CrO6 octahedra that share corners with three equivalent S(1)O4 tetrahedra and corners with three equivalent S(2)O4 tetrahedra. In the second Cr site, Cr(2) is bonded to three equivalent O(5) and three equivalent O(7) atoms to form CrO6 octahedra that share corners with three equivalent S(1)O4 tetrahedra and corners with three equivalent S(2)O4 tetrahedra. In the third Cr site, Cr(3) is bonded to three equivalent O(2) and three equivalent O(4) atoms to form CrO6 octahedra that share corners with three equivalent S(1)O4 tetrahedra and corners with three equivalent S(2)O4 tetrahedra. There are two inequivalent S sites. In the first S site, S(1) is bonded to one O(1), one O(2), one O(5), and one O(6) atom to form SO4 tetrahedra that share  a cornercorner with one Mg(1)O6 octahedra,  a cornercorner with one Cr(1)O6 octahedra,  a cornercorner with one Cr(2)O6 octahedra, and  a cornercorner with one Cr(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 26-43°. In the second S site, S(2) is bonded to one O(3), one O(4), one O(7), and one O(8) atom to form SO4 tetrahedra that share  a cornercorner with one Mg(1)O6 octahedra,  a cornercorner with one Cr(1)O6 octahedra,  a cornercorner with one Cr(2)O6 octahedra, and  a cornercorner with one Cr(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 26-45°. There are eight inequivalent O sites. In the first O site, O(3) is bonded in a bent 150 degrees geometry to one Cr(1) and one S(2) atom. In the second O site, O(4) is bonded in a bent 150 degrees geometry to one Cr(3) and one S(2) atom. In the third O site, O(5) is bonded in a bent 150 degrees geometry to one Cr(2) and one S(1) atom. In the fourth O site, O(6) is bonded in a distorted bent 150 degrees geometry to one Mg(1) and one S(1) atom. In the fifth O site, O(7) is bonded in a distorted bent 150 degrees geometry to one Cr(2) and one S(2) atom. In the sixth O site, O(8) is bonded in a bent 150 degrees geometry to one Mg(1) and one S(2) atom. In the seventh O site, O(1) is bonded in a bent 150 degrees geometry to one Cr(1) and one S(1) atom. In the eighth O site, O(2) is bonded in a bent 150 degrees geometry to one Cr(3) and one S(1) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_MgCr3(SO4)6
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.857
_cell_length_b   8.857
_cell_length_c   8.857
_cell_angle_alpha   55.910
_cell_angle_beta   55.910
_cell_angle_gamma   55.910
_symmetry_Int_Tables_number   1
_cell_volume   444.749
_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
  Mg  Mg0  1  0.642  0.642  0.642  1.0
  Cr  Cr1  1  0.849  0.849  0.849  1.0
  Cr  Cr2  1  0.356  0.356  0.356  1.0
  Cr  Cr3  1  0.150  0.150  0.150  1.0
  S  S4  1  0.540  0.961  0.246  1.0
  S  S5  1  0.747  0.461  0.044  1.0
  S  S6  1  0.044  0.747  0.461  1.0
  S  S7  1  0.961  0.246  0.540  1.0
  S  S8  1  0.246  0.540  0.961  1.0
  S  S9  1  0.461  0.044  0.747  1.0
  O  O10  1  0.671  0.993  0.038  1.0
  O  O11  1  0.343  0.982  0.278  1.0
  O  O12  1  0.720  0.651  0.028  1.0
  O  O13  1  0.023  0.955  0.324  1.0
  O  O14  1  0.295  0.511  0.112  1.0
  O  O15  1  0.619  0.766  0.375  1.0
  O  O16  1  0.955  0.324  0.023  1.0
  O  O17  1  0.243  0.616  0.378  1.0
  O  O18  1  0.893  0.706  0.485  1.0
  O  O19  1  0.485  0.893  0.706  1.0
  O  O20  1  0.616  0.378  0.243  1.0
  O  O21  1  0.028  0.720  0.651  1.0
  O  O22  1  0.982  0.278  0.343  1.0
  O  O23  1  0.375  0.619  0.766  1.0
  O  O24  1  0.511  0.112  0.295  1.0
  O  O25  1  0.112  0.295  0.511  1.0
  O  O26  1  0.766  0.375  0.619  1.0
  O  O27  1  0.038  0.671  0.993  1.0
  O  O28  1  0.378  0.243  0.616  1.0
  O  O29  1  0.706  0.485  0.893  1.0
  O  O30  1  0.993  0.038  0.671  1.0
  O  O31  1  0.278  0.343  0.982  1.0
  O  O32  1  0.651  0.028  0.720  1.0
  O  O33  1  0.324  0.023  0.955  1.0
[/CIF]
.