Ba10Re3O22 crystallizes in the monoclinic C2/m space group. There are five inequivalent Ba sites. In the first Ba site, Ba(1) is bonded in a 10-coordinate geometry to one O(7), two equivalent O(4), three equivalent O(3), and four equivalent O(1) atoms. In the second Ba site, Ba(2) is bonded in a 10-coordinate geometry to one O(2), one O(7), two equivalent O(4), two equivalent O(5), and four equivalent O(6) atoms. In the third Ba site, Ba(3) is bonded in a 11-coordinate geometry to one O(5), two equivalent O(1), two equivalent O(2), two equivalent O(6), and four equivalent O(4) atoms. In the fourth Ba site, Ba(4) is bonded in a 8-coordinate geometry to one O(3), one O(5), two equivalent O(6), two equivalent O(7), and two equivalent O(8) atoms. In the fifth Ba site, Ba(5) is bonded in a 9-coordinate geometry to one O(2), two equivalent O(1), two equivalent O(6), two equivalent O(7), and two equivalent O(8) atoms. There are two inequivalent Re sites. In the first Re site, Re(1) is bonded in an octahedral geometry to two equivalent O(5) and four equivalent O(6) atoms. In the second Re site, Re(2) is bonded in an octahedral geometry to one O(2), one O(3), two equivalent O(1), and two equivalent O(4) atoms. There are eight inequivalent O sites. In the first O site, O(3) is bonded in a 5-coordinate geometry to one Ba(4), three equivalent Ba(1), and one Re(2) atom. In the second O site, O(4) is bonded in a distorted single-bond geometry to one Ba(1), one Ba(2), two equivalent Ba(3), and one Re(2) atom. In the third O site, O(5) is bonded to one Ba(3), one Ba(4), two equivalent Ba(2), and one Re(1) atom to form distorted OBa4Re trigonal bipyramids that share corners with two equivalent O(1)Ba4Re square pyramids, corners with two equivalent O(8)Ba4 tetrahedra, corners with three equivalent O(5)Ba4Re trigonal bipyramids, and edges with two equivalent O(7)Ba6 octahedra. In the fourth O site, O(6) is bonded in a distorted single-bond geometry to one Ba(3), one Ba(4), one Ba(5), two equivalent Ba(2), and one Re(1) atom. In the fifth O site, O(7) is bonded to one Ba(1), one Ba(2), two equivalent Ba(4), and two equivalent Ba(5) atoms to form OBa6 octahedra that share corners with two equivalent O(7)Ba6 octahedra, corners with four equivalent O(1)Ba4Re square pyramids,  an edgeedge with one O(7)Ba6 octahedra, edges with two equivalent O(1)Ba4Re square pyramids, edges with four equivalent O(8)Ba4 tetrahedra, and edges with two equivalent O(5)Ba4Re trigonal bipyramids. The corner-sharing octahedral tilt angles are 9°. In the sixth O site, O(8) is bonded to two equivalent Ba(4) and two equivalent Ba(5) atoms to form distorted OBa4 tetrahedra that share corners with four equivalent O(1)Ba4Re square pyramids, corners with two equivalent O(8)Ba4 tetrahedra, corners with two equivalent O(5)Ba4Re trigonal bipyramids, edges with four equivalent O(7)Ba6 octahedra, and  an edgeedge with one O(8)Ba4 tetrahedra. In the seventh O site, O(1) is bonded to one Ba(3), one Ba(5), two equivalent Ba(1), and one Re(2) atom to form distorted OBa4Re square pyramids that share corners with two equivalent O(7)Ba6 octahedra, corners with two equivalent O(1)Ba4Re square pyramids, corners with two equivalent O(8)Ba4 tetrahedra,  a cornercorner with one O(5)Ba4Re trigonal bipyramid,  an edgeedge with one O(7)Ba6 octahedra, edges with two equivalent O(1)Ba4Re square pyramids, and  a faceface with one O(1)Ba4Re square pyramid. The corner-sharing octahedral tilt angles range from 29-47°. In the eighth O site, O(2) is bonded in a 5-coordinate geometry to one Ba(2), one Ba(5), two equivalent Ba(3), and one Re(2) atom.
Ba10Re3O22 crystallizes in the monoclinic C2/m space group. There are five inequivalent Ba sites. In the first Ba site, Ba(1) is bonded in a 10-coordinate geometry to one O(7), two equivalent O(4), three equivalent O(3), and four equivalent O(1) atoms. The Ba(1)-O(7) bond length is 2.76 Å. Both Ba(1)-O(4) bond lengths are 3.10 Å. There is one shorter (2.81 Å) and two longer (2.95 Å) Ba(1)-O(3) bond lengths. There are two shorter (2.74 Å) and two longer (2.87 Å) Ba(1)-O(1) bond lengths. In the second Ba site, Ba(2) is bonded in a 10-coordinate geometry to one O(2), one O(7), two equivalent O(4), two equivalent O(5), and four equivalent O(6) atoms. The Ba(2)-O(2) bond length is 2.74 Å. The Ba(2)-O(7) bond length is 2.84 Å. Both Ba(2)-O(4) bond lengths are 2.90 Å. Both Ba(2)-O(5) bond lengths are 2.93 Å. There are two shorter (2.88 Å) and two longer (2.92 Å) Ba(2)-O(6) bond lengths. In the third Ba site, Ba(3) is bonded in a 11-coordinate geometry to one O(5), two equivalent O(1), two equivalent O(2), two equivalent O(6), and four equivalent O(4) atoms. The Ba(3)-O(5) bond length is 2.74 Å. Both Ba(3)-O(1) bond lengths are 2.93 Å. Both Ba(3)-O(2) bond lengths are 2.93 Å. Both Ba(3)-O(6) bond lengths are 3.38 Å. There are two shorter (2.78 Å) and two longer (3.00 Å) Ba(3)-O(4) bond lengths. In the fourth Ba site, Ba(4) is bonded in a 8-coordinate geometry to one O(3), one O(5), two equivalent O(6), two equivalent O(7), and two equivalent O(8) atoms. The Ba(4)-O(3) bond length is 2.65 Å. The Ba(4)-O(5) bond length is 2.70 Å. Both Ba(4)-O(6) bond lengths are 3.17 Å. Both Ba(4)-O(7) bond lengths are 2.93 Å. There is one shorter (2.52 Å) and one longer (2.58 Å) Ba(4)-O(8) bond length. In the fifth Ba site, Ba(5) is bonded in a 9-coordinate geometry to one O(2), two equivalent O(1), two equivalent O(6), two equivalent O(7), and two equivalent O(8) atoms. The Ba(5)-O(2) bond length is 2.95 Å. Both Ba(5)-O(1) bond lengths are 2.84 Å. Both Ba(5)-O(6) bond lengths are 2.83 Å. There is one shorter (2.89 Å) and one longer (3.22 Å) Ba(5)-O(7) bond length. Both Ba(5)-O(8) bond lengths are 3.06 Å. There are two inequivalent Re sites. In the first Re site, Re(1) is bonded in an octahedral geometry to two equivalent O(5) and four equivalent O(6) atoms. Both Re(1)-O(5) bond lengths are 1.90 Å. All Re(1)-O(6) bond lengths are 1.91 Å. In the second Re site, Re(2) is bonded in an octahedral geometry to one O(2), one O(3), two equivalent O(1), and two equivalent O(4) atoms. The Re(2)-O(2) bond length is 1.91 Å. The Re(2)-O(3) bond length is 1.92 Å. Both Re(2)-O(1) bond lengths are 1.94 Å. Both Re(2)-O(4) bond lengths are 1.87 Å. There are eight inequivalent O sites. In the first O site, O(3) is bonded in a 5-coordinate geometry to one Ba(4), three equivalent Ba(1), and one Re(2) atom. In the second O site, O(4) is bonded in a distorted single-bond geometry to one Ba(1), one Ba(2), two equivalent Ba(3), and one Re(2) atom. In the third O site, O(5) is bonded to one Ba(3), one Ba(4), two equivalent Ba(2), and one Re(1) atom to form distorted OBa4Re trigonal bipyramids that share corners with two equivalent O(1)Ba4Re square pyramids, corners with two equivalent O(8)Ba4 tetrahedra, corners with three equivalent O(5)Ba4Re trigonal bipyramids, and edges with two equivalent O(7)Ba6 octahedra. In the fourth O site, O(6) is bonded in a distorted single-bond geometry to one Ba(3), one Ba(4), one Ba(5), two equivalent Ba(2), and one Re(1) atom. In the fifth O site, O(7) is bonded to one Ba(1), one Ba(2), two equivalent Ba(4), and two equivalent Ba(5) atoms to form OBa6 octahedra that share corners with two equivalent O(7)Ba6 octahedra, corners with four equivalent O(1)Ba4Re square pyramids,  an edgeedge with one O(7)Ba6 octahedra, edges with two equivalent O(1)Ba4Re square pyramids, edges with four equivalent O(8)Ba4 tetrahedra, and edges with two equivalent O(5)Ba4Re trigonal bipyramids. The corner-sharing octahedral tilt angles are 9°. In the sixth O site, O(8) is bonded to two equivalent Ba(4) and two equivalent Ba(5) atoms to form distorted OBa4 tetrahedra that share corners with four equivalent O(1)Ba4Re square pyramids, corners with two equivalent O(8)Ba4 tetrahedra, corners with two equivalent O(5)Ba4Re trigonal bipyramids, edges with four equivalent O(7)Ba6 octahedra, and  an edgeedge with one O(8)Ba4 tetrahedra. In the seventh O site, O(1) is bonded to one Ba(3), one Ba(5), two equivalent Ba(1), and one Re(2) atom to form distorted OBa4Re square pyramids that share corners with two equivalent O(7)Ba6 octahedra, corners with two equivalent O(1)Ba4Re square pyramids, corners with two equivalent O(8)Ba4 tetrahedra,  a cornercorner with one O(5)Ba4Re trigonal bipyramid,  an edgeedge with one O(7)Ba6 octahedra, edges with two equivalent O(1)Ba4Re square pyramids, and  a faceface with one O(1)Ba4Re square pyramid. The corner-sharing octahedral tilt angles range from 29-47°. In the eighth O site, O(2) is bonded in a 5-coordinate geometry to one Ba(2), one Ba(5), two equivalent Ba(3), and one Re(2) atom.