MgCr2(BiO4)2 crystallizes in the monoclinic C2 space group. Mg(1) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(4) atoms to form distorted MgO6 octahedra that share corners with two equivalent Cr(1)O4 tetrahedra and edges with two equivalent Cr(1)O4 tetrahedra. Cr(1) is bonded to one O(1), one O(2), one O(3), and one O(4) atom to form CrO4 tetrahedra that share  a cornercorner with one Mg(1)O6 octahedra and  an edgeedge with one Mg(1)O6 octahedra. The corner-sharing octahedral tilt angles are 56°. Bi(1) is bonded in a 5-coordinate geometry to one O(1), one O(2), one O(4), and two equivalent O(3) atoms. There are four inequivalent O sites. In the first O site, O(1) is bonded in a 3-coordinate geometry to one Mg(1), one Cr(1), and one Bi(1) atom. In the second O site, O(2) is bonded in a 3-coordinate geometry to one Mg(1), one Cr(1), and one Bi(1) atom. In the third O site, O(3) is bonded in a 3-coordinate geometry to one Cr(1) and two equivalent Bi(1) atoms. In the fourth O site, O(4) is bonded in a distorted T-shaped geometry to one Mg(1), one Cr(1), and one Bi(1) atom.
MgCr2(BiO4)2 crystallizes in the monoclinic C2 space group. Mg(1) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(4) atoms to form distorted MgO6 octahedra that share corners with two equivalent Cr(1)O4 tetrahedra and edges with two equivalent Cr(1)O4 tetrahedra. Both Mg(1)-O(1) bond lengths are 2.07 Å. Both Mg(1)-O(2) bond lengths are 2.11 Å. Both Mg(1)-O(4) bond lengths are 2.21 Å. Cr(1) is bonded to one O(1), one O(2), one O(3), and one O(4) atom to form CrO4 tetrahedra that share  a cornercorner with one Mg(1)O6 octahedra and  an edgeedge with one Mg(1)O6 octahedra. The corner-sharing octahedral tilt angles are 56°. The Cr(1)-O(1) bond length is 1.90 Å. The Cr(1)-O(2) bond length is 1.77 Å. The Cr(1)-O(3) bond length is 1.80 Å. The Cr(1)-O(4) bond length is 1.80 Å. Bi(1) is bonded in a 5-coordinate geometry to one O(1), one O(2), one O(4), and two equivalent O(3) atoms. The Bi(1)-O(1) bond length is 2.22 Å. The Bi(1)-O(2) bond length is 2.40 Å. The Bi(1)-O(4) bond length is 2.37 Å. Both Bi(1)-O(3) bond lengths are 2.35 Å. There are four inequivalent O sites. In the first O site, O(1) is bonded in a 3-coordinate geometry to one Mg(1), one Cr(1), and one Bi(1) atom. In the second O site, O(2) is bonded in a 3-coordinate geometry to one Mg(1), one Cr(1), and one Bi(1) atom. In the third O site, O(3) is bonded in a 3-coordinate geometry to one Cr(1) and two equivalent Bi(1) atoms. In the fourth O site, O(4) is bonded in a distorted T-shaped geometry to one Mg(1), one Cr(1), and one Bi(1) atom.