The structure described by MgCr3(SO4)6 crystallizes in the trigonal R3 space group. Mg(1) is bonded in a 6-coordinate geometry to three equivalent O(2) and three equivalent O(5) atoms. There are three inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to three equivalent O(2) and three equivalent O(6) atoms to form distorted 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(7) and three equivalent O(8) 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(3) and three equivalent O(5) 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(2), one O(3), one O(4), and one O(8) atom to form SO4 tetrahedra that share  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 23-51°. In the second S site, S(2) is bonded to one O(1), one O(5), one O(6), and one O(7) atom to form SO4 tetrahedra that share  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 29-46°. There are eight inequivalent O sites. In the first O site, O(2) is bonded in a 3-coordinate geometry to one Mg(1), one Cr(1), and one S(1) atom. In the second O site, O(3) is bonded in a bent 150 degrees geometry to one Cr(3) and one S(1) atom. In the third O site, O(4) is bonded in a single-bond geometry to one S(1) atom. In the fourth O site, O(5) is bonded in a 3-coordinate geometry to one Mg(1), one Cr(3), and one S(2) atom. In the fifth O site, O(6) is bonded in a bent 150 degrees geometry to one Cr(1) and one S(2) atom. In the sixth O site, O(7) is bonded in a distorted bent 120 degrees geometry to one Cr(2) and one S(2) atom. In the seventh O site, O(8) is bonded in a bent 150 degrees geometry to one Cr(2) and one S(1) atom. In the eighth O site, O(1) is bonded in a single-bond geometry to one S(2) 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   8.529
_cell_length_b   8.527
_cell_length_c   8.528
_cell_angle_alpha   60.405
_cell_angle_beta   60.398
_cell_angle_gamma   60.407
_symmetry_Int_Tables_number   1
_cell_volume   442.587
_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  0.999  0.999  0.999  1.0
  Cr  Cr1  1  0.146  0.146  0.146  1.0
  Cr  Cr2  1  0.639  0.639  0.639  1.0
  Cr  Cr3  1  0.855  0.855  0.855  1.0
  S  S4  1  0.041  0.754  0.449  1.0
  S  S5  1  0.449  0.041  0.754  1.0
  S  S6  1  0.754  0.449  0.041  1.0
  S  S7  1  0.254  0.548  0.960  1.0
  S  S8  1  0.548  0.960  0.254  1.0
  S  S9  1  0.960  0.254  0.548  1.0
  O  O10  1  0.107  0.314  0.513  1.0
  O  O11  1  0.314  0.513  0.107  1.0
  O  O12  1  0.026  0.935  0.268  1.0
  O  O13  1  0.513  0.107  0.314  1.0
  O  O14  1  0.996  0.820  0.604  1.0
  O  O15  1  0.230  0.620  0.412  1.0
  O  O16  1  0.413  0.230  0.620  1.0
  O  O17  1  0.268  0.026  0.934  1.0
  O  O18  1  0.620  0.412  0.230  1.0
  O  O19  1  0.078  0.735  0.953  1.0
  O  O20  1  0.196  0.395  0.988  1.0
  O  O21  1  0.395  0.987  0.196  1.0
  O  O22  1  0.604  0.996  0.820  1.0
  O  O23  1  0.819  0.604  0.996  1.0
  O  O24  1  0.935  0.268  0.026  1.0
  O  O25  1  0.394  0.585  0.761  1.0
  O  O26  1  0.735  0.953  0.078  1.0
  O  O27  1  0.585  0.761  0.394  1.0
  O  O28  1  0.761  0.394  0.585  1.0
  O  O29  1  0.988  0.196  0.395  1.0
  O  O30  1  0.491  0.887  0.691  1.0
  O  O31  1  0.952  0.078  0.735  1.0
  O  O32  1  0.692  0.490  0.887  1.0
  O  O33  1  0.887  0.692  0.491  1.0
[/CIF]
.
The structure described by MgCr3(SO4)6 crystallizes in the trigonal R3 space group. Mg(1) is bonded in a 6-coordinate geometry to three equivalent O(2) and three equivalent O(5) atoms. There are three inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to three equivalent O(2) and three equivalent O(6) atoms to form distorted 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(7) and three equivalent O(8) 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(3) and three equivalent O(5) 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(2), one O(3), one O(4), and one O(8) atom to form SO4 tetrahedra that share  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 23-51°. In the second S site, S(2) is bonded to one O(1), one O(5), one O(6), and one O(7) atom to form SO4 tetrahedra that share  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 29-46°. There are eight inequivalent O sites. In the first O site, O(2) is bonded in a 3-coordinate geometry to one Mg(1), one Cr(1), and one S(1) atom. In the second O site, O(3) is bonded in a bent 150 degrees geometry to one Cr(3) and one S(1) atom. In the third O site, O(4) is bonded in a single-bond geometry to one S(1) atom. In the fourth O site, O(5) is bonded in a 3-coordinate geometry to one Mg(1), one Cr(3), and one S(2) atom. In the fifth O site, O(6) is bonded in a bent 150 degrees geometry to one Cr(1) and one S(2) atom. In the sixth O site, O(7) is bonded in a distorted bent 120 degrees geometry to one Cr(2) and one S(2) atom. In the seventh O site, O(8) is bonded in a bent 150 degrees geometry to one Cr(2) and one S(1) atom. In the eighth O site, O(1) is bonded in a single-bond geometry to one S(2) 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   8.529
_cell_length_b   8.527
_cell_length_c   8.528
_cell_angle_alpha   60.405
_cell_angle_beta   60.398
_cell_angle_gamma   60.407
_symmetry_Int_Tables_number   1
_cell_volume   442.587
_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  0.999  0.999  0.999  1.0
  Cr  Cr1  1  0.146  0.146  0.146  1.0
  Cr  Cr2  1  0.639  0.639  0.639  1.0
  Cr  Cr3  1  0.855  0.855  0.855  1.0
  S  S4  1  0.041  0.754  0.449  1.0
  S  S5  1  0.449  0.041  0.754  1.0
  S  S6  1  0.754  0.449  0.041  1.0
  S  S7  1  0.254  0.548  0.960  1.0
  S  S8  1  0.548  0.960  0.254  1.0
  S  S9  1  0.960  0.254  0.548  1.0
  O  O10  1  0.107  0.314  0.513  1.0
  O  O11  1  0.314  0.513  0.107  1.0
  O  O12  1  0.026  0.935  0.268  1.0
  O  O13  1  0.513  0.107  0.314  1.0
  O  O14  1  0.996  0.820  0.604  1.0
  O  O15  1  0.230  0.620  0.412  1.0
  O  O16  1  0.413  0.230  0.620  1.0
  O  O17  1  0.268  0.026  0.934  1.0
  O  O18  1  0.620  0.412  0.230  1.0
  O  O19  1  0.078  0.735  0.953  1.0
  O  O20  1  0.196  0.395  0.988  1.0
  O  O21  1  0.395  0.987  0.196  1.0
  O  O22  1  0.604  0.996  0.820  1.0
  O  O23  1  0.819  0.604  0.996  1.0
  O  O24  1  0.935  0.268  0.026  1.0
  O  O25  1  0.394  0.585  0.761  1.0
  O  O26  1  0.735  0.953  0.078  1.0
  O  O27  1  0.585  0.761  0.394  1.0
  O  O28  1  0.761  0.394  0.585  1.0
  O  O29  1  0.988  0.196  0.395  1.0
  O  O30  1  0.491  0.887  0.691  1.0
  O  O31  1  0.952  0.078  0.735  1.0
  O  O32  1  0.692  0.490  0.887  1.0
  O  O33  1  0.887  0.692  0.491  1.0
[/CIF]
.