Ba4Cr13O28 crystallizes in the monoclinic Pm space group. There are four inequivalent Ba sites. In the first Ba site, Ba(1) is bonded to one O(16), one O(8), two equivalent O(1), two equivalent O(13), two equivalent O(2), two equivalent O(3), and two equivalent O(6) atoms to form BaO12 cuboctahedra that share corners with two equivalent Ba(1)O12 cuboctahedra, corners with four equivalent Ba(2)O12 cuboctahedra, corners with two equivalent Cr(9)O4 tetrahedra,  an edgeedge with one Cr(7)O6 octahedra, edges with two equivalent Cr(5)O6 octahedra,  an edgeedge with one Cr(10)O4 tetrahedra, edges with two equivalent Cr(11)O4 tetrahedra,  a faceface with one Ba(3)O12 cuboctahedra, faces with two equivalent Ba(4)O12 cuboctahedra,  a faceface with one Cr(2)O6 octahedra,  a faceface with one Cr(4)O6 octahedra, and faces with two equivalent Cr(3)O6 octahedra. In the second Ba site, Ba(2) is bonded to one O(15), one O(7), two equivalent O(1), two equivalent O(14), two equivalent O(2), two equivalent O(4), and two equivalent O(5) atoms to form BaO12 cuboctahedra that share corners with two equivalent Ba(2)O12 cuboctahedra, corners with four equivalent Ba(1)O12 cuboctahedra,  a cornercorner with one Cr(9)O4 tetrahedra,  an edgeedge with one Cr(8)O6 octahedra, edges with two equivalent Cr(6)O6 octahedra,  an edgeedge with one Cr(11)O4 tetrahedra, edges with two equivalent Cr(10)O4 tetrahedra,  a faceface with one Ba(4)O12 cuboctahedra, faces with two equivalent Ba(3)O12 cuboctahedra,  a faceface with one Cr(1)O6 octahedra,  a faceface with one Cr(3)O6 octahedra, and faces with two equivalent Cr(4)O6 octahedra. In the third Ba site, Ba(3) is bonded to one O(12), one O(4), two equivalent O(2), two equivalent O(5), two equivalent O(6), two equivalent O(7), and two equivalent O(9) atoms to form distorted BaO12 cuboctahedra that share corners with two equivalent Ba(3)O12 cuboctahedra, corners with four equivalent Ba(4)O12 cuboctahedra,  a cornercorner with one Cr(10)O4 tetrahedra, corners with two equivalent Cr(11)O4 tetrahedra,  an edgeedge with one Cr(7)O6 octahedra, edges with two equivalent Cr(6)O6 octahedra, edges with two equivalent Cr(9)O4 tetrahedra,  a faceface with one Ba(1)O12 cuboctahedra, faces with two equivalent Ba(2)O12 cuboctahedra,  a faceface with one Cr(2)O6 octahedra,  a faceface with one Cr(4)O6 octahedra, and faces with two equivalent Cr(1)O6 octahedra. In the fourth Ba site, Ba(4) is bonded to one O(11), one O(3), two equivalent O(1), two equivalent O(10), two equivalent O(5), two equivalent O(6), and two equivalent O(8) atoms to form BaO12 cuboctahedra that share corners with two equivalent Ba(4)O12 cuboctahedra, corners with four equivalent Ba(3)O12 cuboctahedra,  a cornercorner with one Cr(11)O4 tetrahedra, corners with two equivalent Cr(10)O4 tetrahedra,  an edgeedge with one Cr(8)O6 octahedra, edges with two equivalent Cr(5)O6 octahedra,  an edgeedge with one Cr(9)O4 tetrahedra,  a faceface with one Ba(2)O12 cuboctahedra, faces with two equivalent Ba(1)O12 cuboctahedra,  a faceface with one Cr(1)O6 octahedra,  a faceface with one Cr(3)O6 octahedra, and faces with two equivalent Cr(2)O6 octahedra. There are eleven inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(11), one O(7), two equivalent O(5), and two equivalent O(9) atoms to form CrO6 octahedra that share corners with two equivalent Cr(5)O6 octahedra, corners with two equivalent Cr(6)O6 octahedra, corners with two equivalent Cr(7)O6 octahedra,  a cornercorner with one Cr(9)O4 tetrahedra,  a faceface with one Ba(2)O12 cuboctahedra,  a faceface with one Ba(4)O12 cuboctahedra, and faces with two equivalent Ba(3)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 49-54°. In the second Cr site, Cr(2) is bonded to one O(12), one O(8), two equivalent O(10), and two equivalent O(6) atoms to form CrO6 octahedra that share corners with two equivalent Cr(5)O6 octahedra, corners with two equivalent Cr(6)O6 octahedra, corners with two equivalent Cr(8)O6 octahedra, corners with two equivalent Cr(9)O4 tetrahedra,  a faceface with one Ba(1)O12 cuboctahedra,  a faceface with one Ba(3)O12 cuboctahedra, and faces with two equivalent Ba(4)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 50-53°. In the third Cr site, Cr(3) is bonded to one O(15), one O(3), two equivalent O(1), and two equivalent O(13) atoms to form CrO6 octahedra that share corners with two equivalent Cr(5)O6 octahedra, corners with two equivalent Cr(6)O6 octahedra, corners with two equivalent Cr(7)O6 octahedra,  a cornercorner with one Cr(11)O4 tetrahedra, corners with two equivalent Cr(10)O4 tetrahedra,  a faceface with one Ba(2)O12 cuboctahedra,  a faceface with one Ba(4)O12 cuboctahedra, and faces with two equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 51-53°. In the fourth Cr site, Cr(4) is bonded to one O(16), one O(4), two equivalent O(14), and two equivalent O(2) atoms to form CrO6 octahedra that share corners with two equivalent Cr(5)O6 octahedra, corners with two equivalent Cr(6)O6 octahedra, corners with two equivalent Cr(8)O6 octahedra,  a cornercorner with one Cr(10)O4 tetrahedra, corners with two equivalent Cr(11)O4 tetrahedra,  a faceface with one Ba(1)O12 cuboctahedra,  a faceface with one Ba(3)O12 cuboctahedra, and faces with two equivalent Ba(2)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 52-53°. In the fifth Cr site, Cr(5) is bonded to one O(10), one O(11), one O(13), one O(16), one O(17), and one O(20) atom to form CrO6 octahedra that share  a cornercorner with one Cr(1)O6 octahedra,  a cornercorner with one Cr(2)O6 octahedra,  a cornercorner with one Cr(3)O6 octahedra,  a cornercorner with one Cr(4)O6 octahedra,  a cornercorner with one Cr(11)O4 tetrahedra,  an edgeedge with one Ba(1)O12 cuboctahedra,  an edgeedge with one Ba(4)O12 cuboctahedra,  an edgeedge with one Cr(7)O6 octahedra,  an edgeedge with one Cr(8)O6 octahedra, and edges with two equivalent Cr(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-53°. In the sixth Cr site, Cr(6) is bonded to one O(12), one O(14), one O(15), one O(18), one O(19), and one O(9) atom to form CrO6 octahedra that share  a cornercorner with one Cr(1)O6 octahedra,  a cornercorner with one Cr(2)O6 octahedra,  a cornercorner with one Cr(3)O6 octahedra,  a cornercorner with one Cr(4)O6 octahedra,  a cornercorner with one Cr(10)O4 tetrahedra,  a cornercorner with one Cr(9)O4 tetrahedra,  an edgeedge with one Ba(2)O12 cuboctahedra,  an edgeedge with one Ba(3)O12 cuboctahedra,  an edgeedge with one Cr(7)O6 octahedra,  an edgeedge with one Cr(8)O6 octahedra, and edges with two equivalent Cr(6)O6 octahedra. The corner-sharing octahedral tilt angles range from 49-53°. In the seventh Cr site, Cr(7) is bonded to one O(17), one O(19), two equivalent O(13), and two equivalent O(9) atoms to form CrO6 octahedra that share corners with two equivalent Cr(1)O6 octahedra, corners with two equivalent Cr(3)O6 octahedra,  a cornercorner with one Cr(10)O4 tetrahedra,  an edgeedge with one Ba(1)O12 cuboctahedra,  an edgeedge with one Ba(3)O12 cuboctahedra, edges with two equivalent Cr(5)O6 octahedra, and edges with two equivalent Cr(6)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-54°. In the eighth Cr site, Cr(8) is bonded to one O(18), one O(20), two equivalent O(10), and two equivalent O(14) atoms to form CrO6 octahedra that share corners with two equivalent Cr(2)O6 octahedra, corners with two equivalent Cr(4)O6 octahedra,  a cornercorner with one Cr(11)O4 tetrahedra,  a cornercorner with one Cr(9)O4 tetrahedra,  an edgeedge with one Ba(2)O12 cuboctahedra,  an edgeedge with one Ba(4)O12 cuboctahedra, edges with two equivalent Cr(5)O6 octahedra, and edges with two equivalent Cr(6)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-53°. In the ninth Cr site, Cr(9) is bonded to one O(18), one O(7), and two equivalent O(6) atoms to form CrO4 tetrahedra that share  a cornercorner with one Ba(2)O12 cuboctahedra, corners with two equivalent Ba(1)O12 cuboctahedra,  a cornercorner with one Cr(1)O6 octahedra,  a cornercorner with one Cr(8)O6 octahedra, corners with two equivalent Cr(2)O6 octahedra, corners with two equivalent Cr(6)O6 octahedra,  an edgeedge with one Ba(4)O12 cuboctahedra, and edges with two equivalent Ba(3)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 41-59°. In the tenth Cr site, Cr(10) is bonded to one O(19), one O(4), and two equivalent O(1) atoms to form CrO4 tetrahedra that share  a cornercorner with one Ba(3)O12 cuboctahedra, corners with two equivalent Ba(4)O12 cuboctahedra,  a cornercorner with one Cr(4)O6 octahedra,  a cornercorner with one Cr(7)O6 octahedra, corners with two equivalent Cr(3)O6 octahedra, corners with two equivalent Cr(6)O6 octahedra,  an edgeedge with one Ba(1)O12 cuboctahedra, and edges with two equivalent Ba(2)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 49-58°. In the eleventh Cr site, Cr(11) is bonded to one O(20), one O(3), and two equivalent O(2) atoms to form CrO4 tetrahedra that share  a cornercorner with one Ba(4)O12 cuboctahedra, corners with two equivalent Ba(3)O12 cuboctahedra,  a cornercorner with one Cr(3)O6 octahedra,  a cornercorner with one Cr(8)O6 octahedra, corners with two equivalent Cr(4)O6 octahedra, corners with two equivalent Cr(5)O6 octahedra,  an edgeedge with one Ba(2)O12 cuboctahedra, and edges with two equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 50-59°. There are twenty inequivalent O sites. In the first O site, O(1) is bonded in a 2-coordinate geometry to one Ba(1), one Ba(2), one Ba(4), one Cr(10), and one Cr(3) atom. In the second O site, O(2) is bonded in a 2-coordinate geometry to one Ba(1), one Ba(2), one Ba(3), one Cr(11), and one Cr(4) atom. In the third O site, O(3) is bonded in a 2-coordinate geometry to one Ba(4), two equivalent Ba(1), one Cr(11), and one Cr(3) atom. In the fourth O site, O(4) is bonded in a 2-coordinate geometry to one Ba(3), two equivalent Ba(2), one Cr(10), and one Cr(4) atom. In the fifth O site, O(5) is bonded in a distorted single-bond geometry to one Ba(2), one Ba(3), one Ba(4), and one Cr(1) atom. In the sixth O site, O(6) is bonded in a 2-coordinate geometry to one Ba(1), one Ba(3), one Ba(4), one Cr(2), and one Cr(9) atom. In the seventh O site, O(7) is bonded in a 2-coordinate geometry to one Ba(2), two equivalent Ba(3), one Cr(1), and one Cr(9) atom. In the eighth O site, O(8) is bonded in a distorted single-bond geometry to one Ba(1), two equivalent Ba(4), and one Cr(2) atom. In the ninth O site, O(9) is bonded in a 4-coordinate geometry to one Ba(3), one Cr(1), one Cr(6), and one Cr(7) atom. In the tenth O site, O(10) is bonded in a 3-coordinate geometry to one Ba(4), one Cr(2), one Cr(5), and one Cr(8) atom. In the eleventh O site, O(11) is bonded in a 3-coordinate geometry to one Ba(4), one Cr(1), and two equivalent Cr(5) atoms. In the twelfth O site, O(12) is bonded in a 3-coordinate geometry to one Ba(3), one Cr(2), and two equivalent Cr(6) atoms. In the thirteenth O site, O(13) is bonded in a 3-coordinate geometry to one Ba(1), one Cr(3), one Cr(5), and one Cr(7) atom. In the fourteenth O site, O(14) is bonded in a 3-coordinate geometry to one Ba(2), one Cr(4), one Cr(6), and one Cr(8) atom. In the fifteenth O site, O(15) is bonded in a 3-coordinate geometry to one Ba(2), one Cr(3), and two equivalent Cr(6) atoms. In the sixteenth O site, O(16) is bonded in a 3-coordinate geometry to one Ba(1), one Cr(4), and two equivalent Cr(5) atoms. In the seventeenth O site, O(17) is bonded in a distorted T-shaped geometry to one Cr(7) and two equivalent Cr(5) atoms. In the eighteenth O site, O(18) is bonded to one Cr(8), one Cr(9), and two equivalent Cr(6) atoms to form distorted corner-sharing OCr4 trigonal pyramids. In the nineteenth O site, O(19) is bonded to one Cr(10), one Cr(7), and two equivalent Cr(6) atoms to form distorted corner-sharing OCr4 trigonal pyramids. In the twentieth O site, O(20) is bonded to one Cr(11), one Cr(8), and two equivalent Cr(5) atoms to form distorted corner-sharing OCr4 trigonal pyramids.
Ba4Cr13O28 crystallizes in the monoclinic Pm space group. There are four inequivalent Ba sites. In the first Ba site, Ba(1) is bonded to one O(16), one O(8), two equivalent O(1), two equivalent O(13), two equivalent O(2), two equivalent O(3), and two equivalent O(6) atoms to form BaO12 cuboctahedra that share corners with two equivalent Ba(1)O12 cuboctahedra, corners with four equivalent Ba(2)O12 cuboctahedra, corners with two equivalent Cr(9)O4 tetrahedra,  an edgeedge with one Cr(7)O6 octahedra, edges with two equivalent Cr(5)O6 octahedra,  an edgeedge with one Cr(10)O4 tetrahedra, edges with two equivalent Cr(11)O4 tetrahedra,  a faceface with one Ba(3)O12 cuboctahedra, faces with two equivalent Ba(4)O12 cuboctahedra,  a faceface with one Cr(2)O6 octahedra,  a faceface with one Cr(4)O6 octahedra, and faces with two equivalent Cr(3)O6 octahedra. The Ba(1)-O(16) bond length is 2.94 Å. The Ba(1)-O(8) bond length is 2.78 Å. Both Ba(1)-O(1) bond lengths are 2.96 Å. Both Ba(1)-O(13) bond lengths are 2.96 Å. Both Ba(1)-O(2) bond lengths are 2.93 Å. Both Ba(1)-O(3) bond lengths are 2.94 Å. Both Ba(1)-O(6) bond lengths are 2.99 Å. In the second Ba site, Ba(2) is bonded to one O(15), one O(7), two equivalent O(1), two equivalent O(14), two equivalent O(2), two equivalent O(4), and two equivalent O(5) atoms to form BaO12 cuboctahedra that share corners with two equivalent Ba(2)O12 cuboctahedra, corners with four equivalent Ba(1)O12 cuboctahedra,  a cornercorner with one Cr(9)O4 tetrahedra,  an edgeedge with one Cr(8)O6 octahedra, edges with two equivalent Cr(6)O6 octahedra,  an edgeedge with one Cr(11)O4 tetrahedra, edges with two equivalent Cr(10)O4 tetrahedra,  a faceface with one Ba(4)O12 cuboctahedra, faces with two equivalent Ba(3)O12 cuboctahedra,  a faceface with one Cr(1)O6 octahedra,  a faceface with one Cr(3)O6 octahedra, and faces with two equivalent Cr(4)O6 octahedra. The Ba(2)-O(15) bond length is 2.94 Å. The Ba(2)-O(7) bond length is 3.08 Å. Both Ba(2)-O(1) bond lengths are 2.95 Å. Both Ba(2)-O(14) bond lengths are 2.87 Å. Both Ba(2)-O(2) bond lengths are 2.93 Å. Both Ba(2)-O(4) bond lengths are 2.94 Å. Both Ba(2)-O(5) bond lengths are 2.93 Å. In the third Ba site, Ba(3) is bonded to one O(12), one O(4), two equivalent O(2), two equivalent O(5), two equivalent O(6), two equivalent O(7), and two equivalent O(9) atoms to form distorted BaO12 cuboctahedra that share corners with two equivalent Ba(3)O12 cuboctahedra, corners with four equivalent Ba(4)O12 cuboctahedra,  a cornercorner with one Cr(10)O4 tetrahedra, corners with two equivalent Cr(11)O4 tetrahedra,  an edgeedge with one Cr(7)O6 octahedra, edges with two equivalent Cr(6)O6 octahedra, edges with two equivalent Cr(9)O4 tetrahedra,  a faceface with one Ba(1)O12 cuboctahedra, faces with two equivalent Ba(2)O12 cuboctahedra,  a faceface with one Cr(2)O6 octahedra,  a faceface with one Cr(4)O6 octahedra, and faces with two equivalent Cr(1)O6 octahedra. The Ba(3)-O(12) bond length is 3.01 Å. The Ba(3)-O(4) bond length is 2.98 Å. Both Ba(3)-O(2) bond lengths are 3.16 Å. Both Ba(3)-O(5) bond lengths are 2.72 Å. Both Ba(3)-O(6) bond lengths are 3.12 Å. Both Ba(3)-O(7) bond lengths are 2.94 Å. Both Ba(3)-O(9) bond lengths are 2.82 Å. In the fourth Ba site, Ba(4) is bonded to one O(11), one O(3), two equivalent O(1), two equivalent O(10), two equivalent O(5), two equivalent O(6), and two equivalent O(8) atoms to form BaO12 cuboctahedra that share corners with two equivalent Ba(4)O12 cuboctahedra, corners with four equivalent Ba(3)O12 cuboctahedra,  a cornercorner with one Cr(11)O4 tetrahedra, corners with two equivalent Cr(10)O4 tetrahedra,  an edgeedge with one Cr(8)O6 octahedra, edges with two equivalent Cr(5)O6 octahedra,  an edgeedge with one Cr(9)O4 tetrahedra,  a faceface with one Ba(2)O12 cuboctahedra, faces with two equivalent Ba(1)O12 cuboctahedra,  a faceface with one Cr(1)O6 octahedra,  a faceface with one Cr(3)O6 octahedra, and faces with two equivalent Cr(2)O6 octahedra. The Ba(4)-O(11) bond length is 2.81 Å. The Ba(4)-O(3) bond length is 3.19 Å. Both Ba(4)-O(1) bond lengths are 3.03 Å. Both Ba(4)-O(10) bond lengths are 2.92 Å. Both Ba(4)-O(5) bond lengths are 2.86 Å. Both Ba(4)-O(6) bond lengths are 3.08 Å. Both Ba(4)-O(8) bond lengths are 2.98 Å. There are eleven inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(11), one O(7), two equivalent O(5), and two equivalent O(9) atoms to form CrO6 octahedra that share corners with two equivalent Cr(5)O6 octahedra, corners with two equivalent Cr(6)O6 octahedra, corners with two equivalent Cr(7)O6 octahedra,  a cornercorner with one Cr(9)O4 tetrahedra,  a faceface with one Ba(2)O12 cuboctahedra,  a faceface with one Ba(4)O12 cuboctahedra, and faces with two equivalent Ba(3)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 49-54°. The Cr(1)-O(11) bond length is 1.92 Å. The Cr(1)-O(7) bond length is 2.07 Å. Both Cr(1)-O(5) bond lengths are 1.73 Å. Both Cr(1)-O(9) bond lengths are 2.18 Å. In the second Cr site, Cr(2) is bonded to one O(12), one O(8), two equivalent O(10), and two equivalent O(6) atoms to form CrO6 octahedra that share corners with two equivalent Cr(5)O6 octahedra, corners with two equivalent Cr(6)O6 octahedra, corners with two equivalent Cr(8)O6 octahedra, corners with two equivalent Cr(9)O4 tetrahedra,  a faceface with one Ba(1)O12 cuboctahedra,  a faceface with one Ba(3)O12 cuboctahedra, and faces with two equivalent Ba(4)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 50-53°. The Cr(2)-O(12) bond length is 2.10 Å. The Cr(2)-O(8) bond length is 1.75 Å. Both Cr(2)-O(10) bond lengths are 1.98 Å. Both Cr(2)-O(6) bond lengths are 2.09 Å. In the third Cr site, Cr(3) is bonded to one O(15), one O(3), two equivalent O(1), and two equivalent O(13) atoms to form CrO6 octahedra that share corners with two equivalent Cr(5)O6 octahedra, corners with two equivalent Cr(6)O6 octahedra, corners with two equivalent Cr(7)O6 octahedra,  a cornercorner with one Cr(11)O4 tetrahedra, corners with two equivalent Cr(10)O4 tetrahedra,  a faceface with one Ba(2)O12 cuboctahedra,  a faceface with one Ba(4)O12 cuboctahedra, and faces with two equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 51-53°. The Cr(3)-O(15) bond length is 2.00 Å. The Cr(3)-O(3) bond length is 2.07 Å. Both Cr(3)-O(1) bond lengths are 2.08 Å. Both Cr(3)-O(13) bond lengths are 2.03 Å. In the fourth Cr site, Cr(4) is bonded to one O(16), one O(4), two equivalent O(14), and two equivalent O(2) atoms to form CrO6 octahedra that share corners with two equivalent Cr(5)O6 octahedra, corners with two equivalent Cr(6)O6 octahedra, corners with two equivalent Cr(8)O6 octahedra,  a cornercorner with one Cr(10)O4 tetrahedra, corners with two equivalent Cr(11)O4 tetrahedra,  a faceface with one Ba(1)O12 cuboctahedra,  a faceface with one Ba(3)O12 cuboctahedra, and faces with two equivalent Ba(2)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 52-53°. The Cr(4)-O(16) bond length is 2.02 Å. The Cr(4)-O(4) bond length is 2.08 Å. Both Cr(4)-O(14) bond lengths are 2.01 Å. Both Cr(4)-O(2) bond lengths are 2.09 Å. In the fifth Cr site, Cr(5) is bonded to one O(10), one O(11), one O(13), one O(16), one O(17), and one O(20) atom to form CrO6 octahedra that share  a cornercorner with one Cr(1)O6 octahedra,  a cornercorner with one Cr(2)O6 octahedra,  a cornercorner with one Cr(3)O6 octahedra,  a cornercorner with one Cr(4)O6 octahedra,  a cornercorner with one Cr(11)O4 tetrahedra,  an edgeedge with one Ba(1)O12 cuboctahedra,  an edgeedge with one Ba(4)O12 cuboctahedra,  an edgeedge with one Cr(7)O6 octahedra,  an edgeedge with one Cr(8)O6 octahedra, and edges with two equivalent Cr(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-53°. The Cr(5)-O(10) bond length is 1.98 Å. The Cr(5)-O(11) bond length is 2.02 Å. The Cr(5)-O(13) bond length is 1.98 Å. The Cr(5)-O(16) bond length is 1.97 Å. The Cr(5)-O(17) bond length is 1.93 Å. The Cr(5)-O(20) bond length is 2.02 Å. In the sixth Cr site, Cr(6) is bonded to one O(12), one O(14), one O(15), one O(18), one O(19), and one O(9) atom to form CrO6 octahedra that share  a cornercorner with one Cr(1)O6 octahedra,  a cornercorner with one Cr(2)O6 octahedra,  a cornercorner with one Cr(3)O6 octahedra,  a cornercorner with one Cr(4)O6 octahedra,  a cornercorner with one Cr(10)O4 tetrahedra,  a cornercorner with one Cr(9)O4 tetrahedra,  an edgeedge with one Ba(2)O12 cuboctahedra,  an edgeedge with one Ba(3)O12 cuboctahedra,  an edgeedge with one Cr(7)O6 octahedra,  an edgeedge with one Cr(8)O6 octahedra, and edges with two equivalent Cr(6)O6 octahedra. The corner-sharing octahedral tilt angles range from 49-53°. The Cr(6)-O(12) bond length is 1.97 Å. The Cr(6)-O(14) bond length is 1.98 Å. The Cr(6)-O(15) bond length is 1.97 Å. The Cr(6)-O(18) bond length is 1.99 Å. The Cr(6)-O(19) bond length is 1.99 Å. The Cr(6)-O(9) bond length is 2.00 Å. In the seventh Cr site, Cr(7) is bonded to one O(17), one O(19), two equivalent O(13), and two equivalent O(9) atoms to form CrO6 octahedra that share corners with two equivalent Cr(1)O6 octahedra, corners with two equivalent Cr(3)O6 octahedra,  a cornercorner with one Cr(10)O4 tetrahedra,  an edgeedge with one Ba(1)O12 cuboctahedra,  an edgeedge with one Ba(3)O12 cuboctahedra, edges with two equivalent Cr(5)O6 octahedra, and edges with two equivalent Cr(6)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-54°. The Cr(7)-O(17) bond length is 1.92 Å. The Cr(7)-O(19) bond length is 2.04 Å. Both Cr(7)-O(13) bond lengths are 1.97 Å. Both Cr(7)-O(9) bond lengths are 1.93 Å. In the eighth Cr site, Cr(8) is bonded to one O(18), one O(20), two equivalent O(10), and two equivalent O(14) atoms to form CrO6 octahedra that share corners with two equivalent Cr(2)O6 octahedra, corners with two equivalent Cr(4)O6 octahedra,  a cornercorner with one Cr(11)O4 tetrahedra,  a cornercorner with one Cr(9)O4 tetrahedra,  an edgeedge with one Ba(2)O12 cuboctahedra,  an edgeedge with one Ba(4)O12 cuboctahedra, edges with two equivalent Cr(5)O6 octahedra, and edges with two equivalent Cr(6)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-53°. The Cr(8)-O(18) bond length is 1.99 Å. The Cr(8)-O(20) bond length is 1.99 Å. Both Cr(8)-O(10) bond lengths are 2.00 Å. Both Cr(8)-O(14) bond lengths are 1.98 Å. In the ninth Cr site, Cr(9) is bonded to one O(18), one O(7), and two equivalent O(6) atoms to form CrO4 tetrahedra that share  a cornercorner with one Ba(2)O12 cuboctahedra, corners with two equivalent Ba(1)O12 cuboctahedra,  a cornercorner with one Cr(1)O6 octahedra,  a cornercorner with one Cr(8)O6 octahedra, corners with two equivalent Cr(2)O6 octahedra, corners with two equivalent Cr(6)O6 octahedra,  an edgeedge with one Ba(4)O12 cuboctahedra, and edges with two equivalent Ba(3)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 41-59°. The Cr(9)-O(18) bond length is 1.88 Å. The Cr(9)-O(7) bond length is 1.77 Å. Both Cr(9)-O(6) bond lengths are 1.76 Å. In the tenth Cr site, Cr(10) is bonded to one O(19), one O(4), and two equivalent O(1) atoms to form CrO4 tetrahedra that share  a cornercorner with one Ba(3)O12 cuboctahedra, corners with two equivalent Ba(4)O12 cuboctahedra,  a cornercorner with one Cr(4)O6 octahedra,  a cornercorner with one Cr(7)O6 octahedra, corners with two equivalent Cr(3)O6 octahedra, corners with two equivalent Cr(6)O6 octahedra,  an edgeedge with one Ba(1)O12 cuboctahedra, and edges with two equivalent Ba(2)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 49-58°. The Cr(10)-O(19) bond length is 1.90 Å. The Cr(10)-O(4) bond length is 1.78 Å. Both Cr(10)-O(1) bond lengths are 1.78 Å. In the eleventh Cr site, Cr(11) is bonded to one O(20), one O(3), and two equivalent O(2) atoms to form CrO4 tetrahedra that share  a cornercorner with one Ba(4)O12 cuboctahedra, corners with two equivalent Ba(3)O12 cuboctahedra,  a cornercorner with one Cr(3)O6 octahedra,  a cornercorner with one Cr(8)O6 octahedra, corners with two equivalent Cr(4)O6 octahedra, corners with two equivalent Cr(5)O6 octahedra,  an edgeedge with one Ba(2)O12 cuboctahedra, and edges with two equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 50-59°. The Cr(11)-O(20) bond length is 1.88 Å. The Cr(11)-O(3) bond length is 1.78 Å. Both Cr(11)-O(2) bond lengths are 1.78 Å. There are twenty inequivalent O sites. In the first O site, O(1) is bonded in a 2-coordinate geometry to one Ba(1), one Ba(2), one Ba(4), one Cr(10), and one Cr(3) atom. In the second O site, O(2) is bonded in a 2-coordinate geometry to one Ba(1), one Ba(2), one Ba(3), one Cr(11), and one Cr(4) atom. In the third O site, O(3) is bonded in a 2-coordinate geometry to one Ba(4), two equivalent Ba(1), one Cr(11), and one Cr(3) atom. In the fourth O site, O(4) is bonded in a 2-coordinate geometry to one Ba(3), two equivalent Ba(2), one Cr(10), and one Cr(4) atom. In the fifth O site, O(5) is bonded in a distorted single-bond geometry to one Ba(2), one Ba(3), one Ba(4), and one Cr(1) atom. In the sixth O site, O(6) is bonded in a 2-coordinate geometry to one Ba(1), one Ba(3), one Ba(4), one Cr(2), and one Cr(9) atom. In the seventh O site, O(7) is bonded in a 2-coordinate geometry to one Ba(2), two equivalent Ba(3), one Cr(1), and one Cr(9) atom. In the eighth O site, O(8) is bonded in a distorted single-bond geometry to one Ba(1), two equivalent Ba(4), and one Cr(2) atom. In the ninth O site, O(9) is bonded in a 4-coordinate geometry to one Ba(3), one Cr(1), one Cr(6), and one Cr(7) atom. In the tenth O site, O(10) is bonded in a 3-coordinate geometry to one Ba(4), one Cr(2), one Cr(5), and one Cr(8) atom. In the eleventh O site, O(11) is bonded in a 3-coordinate geometry to one Ba(4), one Cr(1), and two equivalent Cr(5) atoms. In the twelfth O site, O(12) is bonded in a 3-coordinate geometry to one Ba(3), one Cr(2), and two equivalent Cr(6) atoms. In the thirteenth O site, O(13) is bonded in a 3-coordinate geometry to one Ba(1), one Cr(3), one Cr(5), and one Cr(7) atom. In the fourteenth O site, O(14) is bonded in a 3-coordinate geometry to one Ba(2), one Cr(4), one Cr(6), and one Cr(8) atom. In the fifteenth O site, O(15) is bonded in a 3-coordinate geometry to one Ba(2), one Cr(3), and two equivalent Cr(6) atoms. In the sixteenth O site, O(16) is bonded in a 3-coordinate geometry to one Ba(1), one Cr(4), and two equivalent Cr(5) atoms. In the seventeenth O site, O(17) is bonded in a distorted T-shaped geometry to one Cr(7) and two equivalent Cr(5) atoms. In the eighteenth O site, O(18) is bonded to one Cr(8), one Cr(9), and two equivalent Cr(6) atoms to form distorted corner-sharing OCr4 trigonal pyramids. In the nineteenth O site, O(19) is bonded to one Cr(10), one Cr(7), and two equivalent Cr(6) atoms to form distorted corner-sharing OCr4 trigonal pyramids. In the twentieth O site, O(20) is bonded to one Cr(11), one Cr(8), and two equivalent Cr(5) atoms to form distorted corner-sharing OCr4 trigonal pyramids.