Ba4Co(ReO6)2 crystallizes in the trigonal R-3m space group. There are two inequivalent Ba sites. In the first Ba site, Ba(1) is bonded to three equivalent O(2) and nine equivalent O(1) atoms to form BaO12 cuboctahedra that share corners with three equivalent Ba(2)O12 cuboctahedra, corners with six equivalent Ba(1)O12 cuboctahedra, faces with three equivalent Ba(1)O12 cuboctahedra, faces with four equivalent Ba(2)O12 cuboctahedra, faces with three equivalent Co(1)O6 octahedra, and faces with four equivalent Re(1)O6 octahedra. In the second Ba site, Ba(2) is bonded to three equivalent O(1) and nine equivalent O(2) atoms to form distorted BaO12 cuboctahedra that share corners with three equivalent Ba(1)O12 cuboctahedra, corners with six equivalent Ba(2)O12 cuboctahedra, corners with three equivalent Re(1)O6 octahedra, faces with three equivalent Ba(2)O12 cuboctahedra, faces with four equivalent Ba(1)O12 cuboctahedra,  a faceface with one Co(1)O6 octahedra, and faces with three equivalent Re(1)O6 octahedra. The corner-sharing octahedral tilt angles are 20°. Re(1) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form ReO6 octahedra that share corners with three equivalent Ba(2)O12 cuboctahedra, corners with three equivalent Co(1)O6 octahedra, faces with three equivalent Ba(2)O12 cuboctahedra, and faces with four equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 2°. Co(1) is bonded to six equivalent O(1) atoms to form CoO6 octahedra that share corners with six equivalent Re(1)O6 octahedra, faces with two equivalent Ba(2)O12 cuboctahedra, and faces with six equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 2°. There are two inequivalent O sites. In the first O site, O(1) is bonded in a distorted linear geometry to one Ba(2), three equivalent Ba(1), one Re(1), and one Co(1) atom. In the second O site, O(2) is bonded in a distorted single-bond geometry to one Ba(1), three equivalent Ba(2), and one Re(1) atom.
Ba4Co(ReO6)2 crystallizes in the trigonal R-3m space group. There are two inequivalent Ba sites. In the first Ba site, Ba(1) is bonded to three equivalent O(2) and nine equivalent O(1) atoms to form BaO12 cuboctahedra that share corners with three equivalent Ba(2)O12 cuboctahedra, corners with six equivalent Ba(1)O12 cuboctahedra, faces with three equivalent Ba(1)O12 cuboctahedra, faces with four equivalent Ba(2)O12 cuboctahedra, faces with three equivalent Co(1)O6 octahedra, and faces with four equivalent Re(1)O6 octahedra. All Ba(1)-O(2) bond lengths are 2.82 Å. There are three shorter (2.84 Å) and six longer (2.87 Å) Ba(1)-O(1) bond lengths. In the second Ba site, Ba(2) is bonded to three equivalent O(1) and nine equivalent O(2) atoms to form distorted BaO12 cuboctahedra that share corners with three equivalent Ba(1)O12 cuboctahedra, corners with six equivalent Ba(2)O12 cuboctahedra, corners with three equivalent Re(1)O6 octahedra, faces with three equivalent Ba(2)O12 cuboctahedra, faces with four equivalent Ba(1)O12 cuboctahedra,  a faceface with one Co(1)O6 octahedra, and faces with three equivalent Re(1)O6 octahedra. The corner-sharing octahedral tilt angles are 20°. All Ba(2)-O(1) bond lengths are 3.00 Å. All Ba(2)-O(2) bond lengths are 2.88 Å. Re(1) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form ReO6 octahedra that share corners with three equivalent Ba(2)O12 cuboctahedra, corners with three equivalent Co(1)O6 octahedra, faces with three equivalent Ba(2)O12 cuboctahedra, and faces with four equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 2°. All Re(1)-O(1) bond lengths are 1.96 Å. All Re(1)-O(2) bond lengths are 1.84 Å. Co(1) is bonded to six equivalent O(1) atoms to form CoO6 octahedra that share corners with six equivalent Re(1)O6 octahedra, faces with two equivalent Ba(2)O12 cuboctahedra, and faces with six equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 2°. All Co(1)-O(1) bond lengths are 2.12 Å. There are two inequivalent O sites. In the first O site, O(1) is bonded in a distorted linear geometry to one Ba(2), three equivalent Ba(1), one Re(1), and one Co(1) atom. In the second O site, O(2) is bonded in a distorted single-bond geometry to one Ba(1), three equivalent Ba(2), and one Re(1) atom.