The compound described by MgBi12AsO20 crystallizes in the trigonal R3 space group. Mg(1) is bonded to one O(7), one O(8), and three equivalent O(6) atoms to form MgO5 trigonal bipyramids that share  a cornercorner with one As(1)O4 tetrahedra and edges with three equivalent Bi(3)O5 square pyramids. There are four inequivalent Bi sites. In the first Bi site, Bi(1) is bonded in a rectangular see-saw-like geometry to one O(1), one O(4), and two equivalent O(5) atoms. In the second Bi site, Bi(2) is bonded in a rectangular see-saw-like geometry to one O(1), one O(3), and two equivalent O(2) atoms. In the third Bi site, Bi(3) is bonded to one O(2), one O(3), one O(4), one O(6), and one O(7) atom to form distorted BiO5 square pyramids that share corners with two equivalent Bi(3)O5 square pyramids,  a cornercorner with one As(1)O4 tetrahedra, and  an edgeedge with one Mg(1)O5 trigonal bipyramid. In the fourth Bi site, Bi(4) is bonded in a 5-coordinate geometry to one O(1), one O(4), one O(6), and two equivalent O(5) atoms. As(1) is bonded to one O(8) and three equivalent O(3) atoms to form AsO4 tetrahedra that share corners with three equivalent Bi(3)O5 square pyramids and  a cornercorner with one Mg(1)O5 trigonal bipyramid. There are eight inequivalent O sites. In the first O site, O(1) is bonded in a trigonal non-coplanar geometry to one Bi(1), one Bi(2), and one Bi(4) atom. In the second O site, O(2) is bonded in a trigonal non-coplanar geometry to one Bi(3) and two equivalent Bi(2) atoms. In the third O site, O(3) is bonded in a distorted single-bond geometry to one Bi(2), one Bi(3), and one As(1) atom. In the fourth O site, O(4) is bonded in a distorted trigonal non-coplanar geometry to one Bi(1), one Bi(3), and one Bi(4) atom. In the fifth O site, O(5) is bonded to two equivalent Bi(1) and two equivalent Bi(4) atoms to form distorted edge-sharing OBi4 tetrahedra. In the sixth O site, O(6) is bonded in a distorted T-shaped geometry to one Mg(1), one Bi(3), and one Bi(4) atom. In the seventh O site, O(7) is bonded in a trigonal pyramidal geometry to one Mg(1) and three equivalent Bi(3) atoms. In the eighth O site, O(8) is bonded in a linear geometry to one Mg(1) and one As(1) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_MgBi12AsO20
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   9.202
_cell_length_b   9.202
_cell_length_c   9.202
_cell_angle_alpha   109.980
_cell_angle_beta   109.980
_cell_angle_gamma   109.980
_symmetry_Int_Tables_number   1
_cell_volume   588.224
_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  0.595  0.595  0.595  1.0
  Bi  Bi1  1  0.804  0.156  0.303  1.0
  Bi  Bi2  1  0.867  0.661  0.153  1.0
  Bi  Bi3  1  0.503  0.344  0.196  1.0
  Bi  Bi4  1  0.661  0.153  0.867  1.0
  Bi  Bi5  1  0.344  0.196  0.503  1.0
  Bi  Bi6  1  0.876  0.486  0.698  1.0
  Bi  Bi7  1  0.196  0.503  0.344  1.0
  Bi  Bi8  1  0.303  0.804  0.156  1.0
  Bi  Bi9  1  0.698  0.876  0.486  1.0
  Bi  Bi10  1  0.156  0.303  0.804  1.0
  Bi  Bi11  1  0.486  0.698  0.876  1.0
  Bi  Bi12  1  0.153  0.867  0.661  1.0
  As  As13  1  0.007  0.007  0.007  1.0
  O  O14  1  0.602  0.005  0.998  1.0
  O  O15  1  0.754  0.388  0.118  1.0
  O  O16  1  0.193  0.012  0.994  1.0
  O  O17  1  0.627  0.246  0.357  1.0
  O  O18  1  0.875  0.230  0.620  1.0
  O  O19  1  0.994  0.193  0.012  1.0
  O  O20  1  0.012  0.994  0.193  1.0
  O  O21  1  0.700  0.618  0.435  1.0
  O  O22  1  0.364  0.364  0.364  1.0
  O  O23  1  0.618  0.435  0.700  1.0
  O  O24  1  0.388  0.118  0.754  1.0
  O  O25  1  0.357  0.627  0.246  1.0
  O  O26  1  0.620  0.875  0.230  1.0
  O  O27  1  0.005  0.998  0.602  1.0
  O  O28  1  0.998  0.602  0.005  1.0
  O  O29  1  0.246  0.357  0.627  1.0
  O  O30  1  0.816  0.816  0.816  1.0
  O  O31  1  0.435  0.700  0.618  1.0
  O  O32  1  0.118  0.754  0.388  1.0
  O  O33  1  0.230  0.620  0.875  1.0
[/CIF]
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The compound described by MgBi12AsO20 crystallizes in the trigonal R3 space group. Mg(1) is bonded to one O(7), one O(8), and three equivalent O(6) atoms to form MgO5 trigonal bipyramids that share  a cornercorner with one As(1)O4 tetrahedra and edges with three equivalent Bi(3)O5 square pyramids. There are four inequivalent Bi sites. In the first Bi site, Bi(1) is bonded in a rectangular see-saw-like geometry to one O(1), one O(4), and two equivalent O(5) atoms. In the second Bi site, Bi(2) is bonded in a rectangular see-saw-like geometry to one O(1), one O(3), and two equivalent O(2) atoms. In the third Bi site, Bi(3) is bonded to one O(2), one O(3), one O(4), one O(6), and one O(7) atom to form distorted BiO5 square pyramids that share corners with two equivalent Bi(3)O5 square pyramids,  a cornercorner with one As(1)O4 tetrahedra, and  an edgeedge with one Mg(1)O5 trigonal bipyramid. In the fourth Bi site, Bi(4) is bonded in a 5-coordinate geometry to one O(1), one O(4), one O(6), and two equivalent O(5) atoms. As(1) is bonded to one O(8) and three equivalent O(3) atoms to form AsO4 tetrahedra that share corners with three equivalent Bi(3)O5 square pyramids and  a cornercorner with one Mg(1)O5 trigonal bipyramid. There are eight inequivalent O sites. In the first O site, O(1) is bonded in a trigonal non-coplanar geometry to one Bi(1), one Bi(2), and one Bi(4) atom. In the second O site, O(2) is bonded in a trigonal non-coplanar geometry to one Bi(3) and two equivalent Bi(2) atoms. In the third O site, O(3) is bonded in a distorted single-bond geometry to one Bi(2), one Bi(3), and one As(1) atom. In the fourth O site, O(4) is bonded in a distorted trigonal non-coplanar geometry to one Bi(1), one Bi(3), and one Bi(4) atom. In the fifth O site, O(5) is bonded to two equivalent Bi(1) and two equivalent Bi(4) atoms to form distorted edge-sharing OBi4 tetrahedra. In the sixth O site, O(6) is bonded in a distorted T-shaped geometry to one Mg(1), one Bi(3), and one Bi(4) atom. In the seventh O site, O(7) is bonded in a trigonal pyramidal geometry to one Mg(1) and three equivalent Bi(3) atoms. In the eighth O site, O(8) is bonded in a linear geometry to one Mg(1) and one As(1) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_MgBi12AsO20
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   9.202
_cell_length_b   9.202
_cell_length_c   9.202
_cell_angle_alpha   109.980
_cell_angle_beta   109.980
_cell_angle_gamma   109.980
_symmetry_Int_Tables_number   1
_cell_volume   588.224
_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  0.595  0.595  0.595  1.0
  Bi  Bi1  1  0.804  0.156  0.303  1.0
  Bi  Bi2  1  0.867  0.661  0.153  1.0
  Bi  Bi3  1  0.503  0.344  0.196  1.0
  Bi  Bi4  1  0.661  0.153  0.867  1.0
  Bi  Bi5  1  0.344  0.196  0.503  1.0
  Bi  Bi6  1  0.876  0.486  0.698  1.0
  Bi  Bi7  1  0.196  0.503  0.344  1.0
  Bi  Bi8  1  0.303  0.804  0.156  1.0
  Bi  Bi9  1  0.698  0.876  0.486  1.0
  Bi  Bi10  1  0.156  0.303  0.804  1.0
  Bi  Bi11  1  0.486  0.698  0.876  1.0
  Bi  Bi12  1  0.153  0.867  0.661  1.0
  As  As13  1  0.007  0.007  0.007  1.0
  O  O14  1  0.602  0.005  0.998  1.0
  O  O15  1  0.754  0.388  0.118  1.0
  O  O16  1  0.193  0.012  0.994  1.0
  O  O17  1  0.627  0.246  0.357  1.0
  O  O18  1  0.875  0.230  0.620  1.0
  O  O19  1  0.994  0.193  0.012  1.0
  O  O20  1  0.012  0.994  0.193  1.0
  O  O21  1  0.700  0.618  0.435  1.0
  O  O22  1  0.364  0.364  0.364  1.0
  O  O23  1  0.618  0.435  0.700  1.0
  O  O24  1  0.388  0.118  0.754  1.0
  O  O25  1  0.357  0.627  0.246  1.0
  O  O26  1  0.620  0.875  0.230  1.0
  O  O27  1  0.005  0.998  0.602  1.0
  O  O28  1  0.998  0.602  0.005  1.0
  O  O29  1  0.246  0.357  0.627  1.0
  O  O30  1  0.816  0.816  0.816  1.0
  O  O31  1  0.435  0.700  0.618  1.0
  O  O32  1  0.118  0.754  0.388  1.0
  O  O33  1  0.230  0.620  0.875  1.0
[/CIF]
.