MgCr3AgO8 crystallizes in the monoclinic Cm space group. Mg(1) is bonded to one O(2), one O(3), and two equivalent O(1) atoms to form distorted MgO4 tetrahedra that share corners with three equivalent Cr(1)O6 octahedra, corners with three equivalent Ag(1)O6 octahedra, corners with two equivalent Cr(3)O4 tetrahedra, and  an edgeedge with one Cr(2)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 59-77°. There are three inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(3), one O(4), two equivalent O(1), and two equivalent O(6) atoms to form CrO6 octahedra that share corners with three equivalent Mg(1)O4 tetrahedra, corners with three equivalent Cr(2)O4 tetrahedra, corners with three equivalent Cr(3)O4 tetrahedra, and edges with two equivalent Ag(1)O6 octahedra. In the second Cr site, Cr(2) is bonded to one O(4), one O(5), and two equivalent O(1) atoms to form CrO4 tetrahedra that share corners with three equivalent Cr(1)O6 octahedra, corners with three equivalent Ag(1)O6 octahedra, and  an edgeedge with one Mg(1)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 49-63°. In the third Cr site, Cr(3) is bonded to one O(2), one O(3), and two equivalent O(6) atoms to form CrO4 tetrahedra that share corners with three equivalent Cr(1)O6 octahedra, corners with three equivalent Ag(1)O6 octahedra, and corners with two equivalent Mg(1)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 45-60°. Ag(1) is bonded to one O(2), one O(5), two equivalent O(1), and two equivalent O(6) atoms to form AgO6 octahedra that share corners with three equivalent Mg(1)O4 tetrahedra, corners with three equivalent Cr(2)O4 tetrahedra, corners with three equivalent Cr(3)O4 tetrahedra, and edges with two equivalent Cr(1)O6 octahedra. There are six inequivalent O sites. In the first O site, O(1) is bonded to one Mg(1), one Cr(1), one Cr(2), and one Ag(1) atom to form distorted edge-sharing OMgCr2Ag tetrahedra. In the second O site, O(2) is bonded in a distorted trigonal planar geometry to one Mg(1), one Cr(3), and one Ag(1) atom. In the third O site, O(3) is bonded in a trigonal planar geometry to one Mg(1), one Cr(1), and one Cr(3) atom. In the fourth O site, O(4) is bonded in a distorted bent 120 degrees geometry to one Cr(1) and one Cr(2) atom. In the fifth O site, O(5) is bonded in a distorted bent 120 degrees geometry to one Cr(2) and one Ag(1) atom. In the sixth O site, O(6) is bonded in a 3-coordinate geometry to one Cr(1), one Cr(3), and one Ag(1) atom.
MgCr3AgO8 crystallizes in the monoclinic Cm space group. Mg(1) is bonded to one O(2), one O(3), and two equivalent O(1) atoms to form distorted MgO4 tetrahedra that share corners with three equivalent Cr(1)O6 octahedra, corners with three equivalent Ag(1)O6 octahedra, corners with two equivalent Cr(3)O4 tetrahedra, and  an edgeedge with one Cr(2)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 59-77°. The Mg(1)-O(2) bond length is 2.01 Å. The Mg(1)-O(3) bond length is 2.02 Å. Both Mg(1)-O(1) bond lengths are 2.05 Å. There are three inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(3), one O(4), two equivalent O(1), and two equivalent O(6) atoms to form CrO6 octahedra that share corners with three equivalent Mg(1)O4 tetrahedra, corners with three equivalent Cr(2)O4 tetrahedra, corners with three equivalent Cr(3)O4 tetrahedra, and edges with two equivalent Ag(1)O6 octahedra. The Cr(1)-O(3) bond length is 2.03 Å. The Cr(1)-O(4) bond length is 2.00 Å. Both Cr(1)-O(1) bond lengths are 2.07 Å. Both Cr(1)-O(6) bond lengths are 2.02 Å. In the second Cr site, Cr(2) is bonded to one O(4), one O(5), and two equivalent O(1) atoms to form CrO4 tetrahedra that share corners with three equivalent Cr(1)O6 octahedra, corners with three equivalent Ag(1)O6 octahedra, and  an edgeedge with one Mg(1)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 49-63°. The Cr(2)-O(4) bond length is 1.68 Å. The Cr(2)-O(5) bond length is 1.64 Å. Both Cr(2)-O(1) bond lengths are 1.84 Å. In the third Cr site, Cr(3) is bonded to one O(2), one O(3), and two equivalent O(6) atoms to form CrO4 tetrahedra that share corners with three equivalent Cr(1)O6 octahedra, corners with three equivalent Ag(1)O6 octahedra, and corners with two equivalent Mg(1)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 45-60°. The Cr(3)-O(2) bond length is 1.72 Å. The Cr(3)-O(3) bond length is 1.82 Å. Both Cr(3)-O(6) bond lengths are 1.73 Å. Ag(1) is bonded to one O(2), one O(5), two equivalent O(1), and two equivalent O(6) atoms to form AgO6 octahedra that share corners with three equivalent Mg(1)O4 tetrahedra, corners with three equivalent Cr(2)O4 tetrahedra, corners with three equivalent Cr(3)O4 tetrahedra, and edges with two equivalent Cr(1)O6 octahedra. The Ag(1)-O(2) bond length is 2.33 Å. The Ag(1)-O(5) bond length is 2.36 Å. Both Ag(1)-O(1) bond lengths are 2.48 Å. Both Ag(1)-O(6) bond lengths are 2.38 Å. There are six inequivalent O sites. In the first O site, O(1) is bonded to one Mg(1), one Cr(1), one Cr(2), and one Ag(1) atom to form distorted edge-sharing OMgCr2Ag tetrahedra. In the second O site, O(2) is bonded in a distorted trigonal planar geometry to one Mg(1), one Cr(3), and one Ag(1) atom. In the third O site, O(3) is bonded in a trigonal planar geometry to one Mg(1), one Cr(1), and one Cr(3) atom. In the fourth O site, O(4) is bonded in a distorted bent 120 degrees geometry to one Cr(1) and one Cr(2) atom. In the fifth O site, O(5) is bonded in a distorted bent 120 degrees geometry to one Cr(2) and one Ag(1) atom. In the sixth O site, O(6) is bonded in a 3-coordinate geometry to one Cr(1), one Cr(3), and one Ag(1) atom.