MgCr3CuO8 crystallizes in the monoclinic Cm space group. Mg(1) is bonded to one O(3), one O(6), and two equivalent O(4) atoms to form distorted MgO4 tetrahedra that share corners with three equivalent Cr(3)O6 octahedra, corners with three equivalent Cu(1)O6 octahedra, corners with two equivalent Cr(2)O4 tetrahedra, and  an edgeedge with one Cr(1)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 60-73°. There are three inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(2), one O(5), and two equivalent O(4) atoms to form CrO4 tetrahedra that share corners with three equivalent Cr(3)O6 octahedra, corners with three equivalent Cu(1)O6 octahedra, and  an edgeedge with one Mg(1)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 46-59°. In the second Cr site, Cr(2) is bonded to one O(3), one O(6), and two equivalent O(1) atoms to form CrO4 tetrahedra that share corners with three equivalent Cr(3)O6 octahedra, corners with three equivalent Cu(1)O6 octahedra, and corners with two equivalent Mg(1)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 50-54°. In the third Cr site, Cr(3) is bonded to one O(3), one O(5), two equivalent O(1), and two equivalent O(4) atoms to form CrO6 octahedra that share corners with three equivalent Mg(1)O4 tetrahedra, corners with three equivalent Cr(1)O4 tetrahedra, corners with three equivalent Cr(2)O4 tetrahedra, and edges with two equivalent Cu(1)O6 octahedra. Cu(1) is bonded to one O(2), one O(6), two equivalent O(1), and two equivalent O(4) atoms to form CuO6 octahedra that share corners with three equivalent Mg(1)O4 tetrahedra, corners with three equivalent Cr(1)O4 tetrahedra, corners with three equivalent Cr(2)O4 tetrahedra, and edges with two equivalent Cr(3)O6 octahedra. There are six inequivalent O sites. In the first O site, O(1) is bonded in a distorted trigonal planar geometry to one Cr(2), one Cr(3), and one Cu(1) atom. In the second O site, O(2) is bonded in a distorted bent 120 degrees geometry to one Cr(1) and one Cu(1) atom. In the third O site, O(3) is bonded in a trigonal planar geometry to one Mg(1), one Cr(2), and one Cr(3) atom. In the fourth O site, O(4) is bonded in a 4-coordinate geometry to one Mg(1), one Cr(1), one Cr(3), and one Cu(1) atom. In the fifth O site, O(5) is bonded in a bent 120 degrees geometry to one Cr(1) and one Cr(3) atom. In the sixth O site, O(6) is bonded in a trigonal planar geometry to one Mg(1), one Cr(2), and one Cu(1) atom.
MgCr3CuO8 crystallizes in the monoclinic Cm space group. Mg(1) is bonded to one O(3), one O(6), and two equivalent O(4) atoms to form distorted MgO4 tetrahedra that share corners with three equivalent Cr(3)O6 octahedra, corners with three equivalent Cu(1)O6 octahedra, corners with two equivalent Cr(2)O4 tetrahedra, and  an edgeedge with one Cr(1)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 60-73°. The Mg(1)-O(3) bond length is 1.96 Å. The Mg(1)-O(6) bond length is 1.97 Å. Both Mg(1)-O(4) bond lengths are 2.06 Å. There are three inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(2), one O(5), and two equivalent O(4) atoms to form CrO4 tetrahedra that share corners with three equivalent Cr(3)O6 octahedra, corners with three equivalent Cu(1)O6 octahedra, and  an edgeedge with one Mg(1)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 46-59°. The Cr(1)-O(2) bond length is 1.67 Å. The Cr(1)-O(5) bond length is 1.67 Å. Both Cr(1)-O(4) bond lengths are 1.84 Å. In the second Cr site, Cr(2) is bonded to one O(3), one O(6), and two equivalent O(1) atoms to form CrO4 tetrahedra that share corners with three equivalent Cr(3)O6 octahedra, corners with three equivalent Cu(1)O6 octahedra, and corners with two equivalent Mg(1)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 50-54°. The Cr(2)-O(3) bond length is 1.83 Å. The Cr(2)-O(6) bond length is 1.79 Å. Both Cr(2)-O(1) bond lengths are 1.77 Å. In the third Cr site, Cr(3) is bonded to one O(3), one O(5), two equivalent O(1), and two equivalent O(4) atoms to form CrO6 octahedra that share corners with three equivalent Mg(1)O4 tetrahedra, corners with three equivalent Cr(1)O4 tetrahedra, corners with three equivalent Cr(2)O4 tetrahedra, and edges with two equivalent Cu(1)O6 octahedra. The Cr(3)-O(3) bond length is 1.96 Å. The Cr(3)-O(5) bond length is 2.01 Å. Both Cr(3)-O(1) bond lengths are 1.99 Å. Both Cr(3)-O(4) bond lengths are 2.12 Å. Cu(1) is bonded to one O(2), one O(6), two equivalent O(1), and two equivalent O(4) atoms to form CuO6 octahedra that share corners with three equivalent Mg(1)O4 tetrahedra, corners with three equivalent Cr(1)O4 tetrahedra, corners with three equivalent Cr(2)O4 tetrahedra, and edges with two equivalent Cr(3)O6 octahedra. The Cu(1)-O(2) bond length is 1.97 Å. The Cu(1)-O(6) bond length is 1.93 Å. Both Cu(1)-O(1) bond lengths are 2.17 Å. Both Cu(1)-O(4) bond lengths are 2.34 Å. There are six inequivalent O sites. In the first O site, O(1) is bonded in a distorted trigonal planar geometry to one Cr(2), one Cr(3), and one Cu(1) atom. In the second O site, O(2) is bonded in a distorted bent 120 degrees geometry to one Cr(1) and one Cu(1) atom. In the third O site, O(3) is bonded in a trigonal planar geometry to one Mg(1), one Cr(2), and one Cr(3) atom. In the fourth O site, O(4) is bonded in a 4-coordinate geometry to one Mg(1), one Cr(1), one Cr(3), and one Cu(1) atom. In the fifth O site, O(5) is bonded in a bent 120 degrees geometry to one Cr(1) and one Cr(3) atom. In the sixth O site, O(6) is bonded in a trigonal planar geometry to one Mg(1), one Cr(2), and one Cu(1) atom.