BaMg(AgO2)4 crystallizes in the trigonal P-31m space group. Ba(1) is bonded to six equivalent O(1) and six equivalent O(2) atoms to form BaO12 cuboctahedra that share edges with six equivalent Ba(1)O12 cuboctahedra, edges with twelve equivalent Ag(1)O4 trigonal pyramids, and faces with two equivalent Mg(1)O6 octahedra. Mg(1) is bonded to six equivalent O(1) atoms to form MgO6 octahedra that share corners with twelve equivalent Ag(1)O4 trigonal pyramids and faces with two equivalent Ba(1)O12 cuboctahedra. Ag(1) is bonded to one O(2) and three equivalent O(1) atoms to form AgO4 trigonal pyramids that share corners with three equivalent Mg(1)O6 octahedra, corners with four equivalent Ag(1)O4 trigonal pyramids, and edges with three equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 58°. There are two inequivalent O sites. In the first O site, O(1) is bonded to one Ba(1), one Mg(1), and two equivalent Ag(1) atoms to form a mixture of distorted edge and corner-sharing OBaMgAg2 tetrahedra. In the second O site, O(2) is bonded in a linear geometry to three equivalent Ba(1) and two equivalent Ag(1) atoms.
BaMg(AgO2)4 crystallizes in the trigonal P-31m space group. Ba(1) is bonded to six equivalent O(1) and six equivalent O(2) atoms to form BaO12 cuboctahedra that share edges with six equivalent Ba(1)O12 cuboctahedra, edges with twelve equivalent Ag(1)O4 trigonal pyramids, and faces with two equivalent Mg(1)O6 octahedra. All Ba(1)-O(1) bond lengths are 2.81 Å. All Ba(1)-O(2) bond lengths are 3.32 Å. Mg(1) is bonded to six equivalent O(1) atoms to form MgO6 octahedra that share corners with twelve equivalent Ag(1)O4 trigonal pyramids and faces with two equivalent Ba(1)O12 cuboctahedra. All Mg(1)-O(1) bond lengths are 2.10 Å. Ag(1) is bonded to one O(2) and three equivalent O(1) atoms to form AgO4 trigonal pyramids that share corners with three equivalent Mg(1)O6 octahedra, corners with four equivalent Ag(1)O4 trigonal pyramids, and edges with three equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 58°. The Ag(1)-O(2) bond length is 2.09 Å. All Ag(1)-O(1) bond lengths are 2.10 Å. There are two inequivalent O sites. In the first O site, O(1) is bonded to one Ba(1), one Mg(1), and two equivalent Ag(1) atoms to form a mixture of distorted edge and corner-sharing OBaMgAg2 tetrahedra. In the second O site, O(2) is bonded in a linear geometry to three equivalent Ba(1) and two equivalent Ag(1) atoms.