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.
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. The Mg(1)-O(7) bond length is 2.06 Å. The Mg(1)-O(8) bond length is 1.99 Å. All Mg(1)-O(6) bond lengths are 2.05 Å. 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. The Bi(1)-O(1) bond length is 2.29 Å. The Bi(1)-O(4) bond length is 2.18 Å. There is one shorter (2.25 Å) and one longer (2.54 Å) Bi(1)-O(5) bond length. 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. The Bi(2)-O(1) bond length is 2.17 Å. The Bi(2)-O(3) bond length is 2.72 Å. There is one shorter (2.17 Å) and one longer (2.22 Å) Bi(2)-O(2) bond length. 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. The Bi(3)-O(2) bond length is 2.59 Å. The Bi(3)-O(3) bond length is 2.73 Å. The Bi(3)-O(4) bond length is 2.19 Å. The Bi(3)-O(6) bond length is 2.20 Å. The Bi(3)-O(7) bond length is 2.31 Å. 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. The Bi(4)-O(1) bond length is 2.31 Å. The Bi(4)-O(4) bond length is 2.62 Å. The Bi(4)-O(6) bond length is 2.26 Å. There is one shorter (2.21 Å) and one longer (2.66 Å) Bi(4)-O(5) bond length. 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. The As(1)-O(8) bond length is 1.72 Å. All As(1)-O(3) bond lengths are 1.74 Å. 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.