Ba4Ca(RhO3)4 crystallizes in the trigonal P3m1 space group. There are four inequivalent Ba sites. In the first Ba site, Ba(1) is bonded to three equivalent O(3), three equivalent O(4), and six equivalent O(1) atoms to form BaO12 cuboctahedra that share corners with six equivalent Ba(1)O12 cuboctahedra, faces with three equivalent Ba(3)O12 cuboctahedra,  a faceface with one Rh(2)O6 octahedra,  a faceface with one Rh(3)O6 octahedra, faces with three equivalent Rh(1)O6 octahedra, and faces with three equivalent Rh(4)O6 octahedra. In the second Ba site, Ba(2) is bonded in a distorted q6 geometry to three equivalent O(3) and six equivalent O(2) atoms. In the third Ba site, Ba(3) is bonded to three equivalent O(1), three equivalent O(2), and six equivalent O(3) atoms to form BaO12 cuboctahedra that share corners with six equivalent Ba(3)O12 cuboctahedra, corners with three equivalent Rh(1)O6 octahedra, corners with three equivalent Rh(3)O6 octahedra, faces with three equivalent Ba(1)O12 cuboctahedra, faces with three equivalent Rh(2)O6 octahedra, and faces with three equivalent Rh(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 7-8°. In the fourth Ba site, Ba(4) is bonded in a 3-coordinate geometry to three equivalent O(2) atoms. Ca(1) is bonded in a 3-coordinate geometry to three equivalent O(1) atoms. There are four inequivalent Rh sites. In the first Rh site, Rh(1) is bonded to three equivalent O(1) and three equivalent O(4) atoms to form distorted RhO6 octahedra that share corners with three equivalent Ba(3)O12 cuboctahedra, corners with three equivalent Rh(3)O6 octahedra, faces with three equivalent Ba(1)O12 cuboctahedra, and  a faceface with one Rh(4)O6 octahedra. The corner-sharing octahedral tilt angles are 17°. In the second Rh site, Rh(2) is bonded to three equivalent O(2) and three equivalent O(3) atoms to form RhO6 octahedra that share corners with three equivalent Rh(4)O6 octahedra,  a faceface with one Ba(1)O12 cuboctahedra, faces with three equivalent Ba(3)O12 cuboctahedra, and  a faceface with one Rh(3)O6 octahedra. The corner-sharing octahedral tilt angles are 3°. In the third Rh site, Rh(3) is bonded to three equivalent O(2) and three equivalent O(4) atoms to form distorted RhO6 octahedra that share corners with three equivalent Ba(3)O12 cuboctahedra, corners with three equivalent Rh(1)O6 octahedra,  a faceface with one Ba(1)O12 cuboctahedra, and  a faceface with one Rh(2)O6 octahedra. The corner-sharing octahedral tilt angles are 17°. In the fourth Rh site, Rh(4) is bonded to three equivalent O(1) and three equivalent O(3) atoms to form RhO6 octahedra that share corners with three equivalent Rh(2)O6 octahedra, faces with three equivalent Ba(1)O12 cuboctahedra, faces with three equivalent Ba(3)O12 cuboctahedra, and  a faceface with one Rh(1)O6 octahedra. The corner-sharing octahedral tilt angles are 3°. There are four inequivalent O sites. In the first O site, O(1) is bonded in a 6-coordinate geometry to one Ba(3), two equivalent Ba(1), one Ca(1), one Rh(1), and one Rh(4) atom. In the second O site, O(2) is bonded to one Ba(3), one Ba(4), two equivalent Ba(2), one Rh(2), and one Rh(3) atom to form a mixture of distorted corner, face, and edge-sharing OBa4Rh2 octahedra. The corner-sharing octahedral tilt angles range from 9-61°. In the third O site, O(3) is bonded to one Ba(1), one Ba(2), two equivalent Ba(3), one Rh(2), and one Rh(4) atom to form a mixture of distorted corner, face, and edge-sharing OBa4Rh2 octahedra. The corner-sharing octahedral tilt angles range from 2-60°. In the fourth O site, O(4) is bonded in a 2-coordinate geometry to one Ba(1), one Rh(1), and one Rh(3) atom.
Ba4Ca(RhO3)4 crystallizes in the trigonal P3m1 space group. There are four inequivalent Ba sites. In the first Ba site, Ba(1) is bonded to three equivalent O(3), three equivalent O(4), and six equivalent O(1) atoms to form BaO12 cuboctahedra that share corners with six equivalent Ba(1)O12 cuboctahedra, faces with three equivalent Ba(3)O12 cuboctahedra,  a faceface with one Rh(2)O6 octahedra,  a faceface with one Rh(3)O6 octahedra, faces with three equivalent Rh(1)O6 octahedra, and faces with three equivalent Rh(4)O6 octahedra. All Ba(1)-O(3) bond lengths are 3.05 Å. All Ba(1)-O(4) bond lengths are 2.95 Å. All Ba(1)-O(1) bond lengths are 2.92 Å. In the second Ba site, Ba(2) is bonded in a distorted q6 geometry to three equivalent O(3) and six equivalent O(2) atoms. All Ba(2)-O(3) bond lengths are 2.75 Å. All Ba(2)-O(2) bond lengths are 2.93 Å. In the third Ba site, Ba(3) is bonded to three equivalent O(1), three equivalent O(2), and six equivalent O(3) atoms to form BaO12 cuboctahedra that share corners with six equivalent Ba(3)O12 cuboctahedra, corners with three equivalent Rh(1)O6 octahedra, corners with three equivalent Rh(3)O6 octahedra, faces with three equivalent Ba(1)O12 cuboctahedra, faces with three equivalent Rh(2)O6 octahedra, and faces with three equivalent Rh(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 7-8°. All Ba(3)-O(1) bond lengths are 3.18 Å. All Ba(3)-O(2) bond lengths are 3.07 Å. All Ba(3)-O(3) bond lengths are 2.91 Å. In the fourth Ba site, Ba(4) is bonded in a 3-coordinate geometry to three equivalent O(2) atoms. All Ba(4)-O(2) bond lengths are 2.47 Å. Ca(1) is bonded in a 3-coordinate geometry to three equivalent O(1) atoms. All Ca(1)-O(1) bond lengths are 2.12 Å. There are four inequivalent Rh sites. In the first Rh site, Rh(1) is bonded to three equivalent O(1) and three equivalent O(4) atoms to form distorted RhO6 octahedra that share corners with three equivalent Ba(3)O12 cuboctahedra, corners with three equivalent Rh(3)O6 octahedra, faces with three equivalent Ba(1)O12 cuboctahedra, and  a faceface with one Rh(4)O6 octahedra. The corner-sharing octahedral tilt angles are 17°. All Rh(1)-O(1) bond lengths are 2.19 Å. All Rh(1)-O(4) bond lengths are 2.02 Å. In the second Rh site, Rh(2) is bonded to three equivalent O(2) and three equivalent O(3) atoms to form RhO6 octahedra that share corners with three equivalent Rh(4)O6 octahedra,  a faceface with one Ba(1)O12 cuboctahedra, faces with three equivalent Ba(3)O12 cuboctahedra, and  a faceface with one Rh(3)O6 octahedra. The corner-sharing octahedral tilt angles are 3°. All Rh(2)-O(2) bond lengths are 2.02 Å. All Rh(2)-O(3) bond lengths are 2.04 Å. In the third Rh site, Rh(3) is bonded to three equivalent O(2) and three equivalent O(4) atoms to form distorted RhO6 octahedra that share corners with three equivalent Ba(3)O12 cuboctahedra, corners with three equivalent Rh(1)O6 octahedra,  a faceface with one Ba(1)O12 cuboctahedra, and  a faceface with one Rh(2)O6 octahedra. The corner-sharing octahedral tilt angles are 17°. All Rh(3)-O(2) bond lengths are 2.12 Å. All Rh(3)-O(4) bond lengths are 2.16 Å. In the fourth Rh site, Rh(4) is bonded to three equivalent O(1) and three equivalent O(3) atoms to form RhO6 octahedra that share corners with three equivalent Rh(2)O6 octahedra, faces with three equivalent Ba(1)O12 cuboctahedra, faces with three equivalent Ba(3)O12 cuboctahedra, and  a faceface with one Rh(1)O6 octahedra. The corner-sharing octahedral tilt angles are 3°. All Rh(4)-O(1) bond lengths are 2.00 Å. All Rh(4)-O(3) bond lengths are 2.05 Å. There are four inequivalent O sites. In the first O site, O(1) is bonded in a 6-coordinate geometry to one Ba(3), two equivalent Ba(1), one Ca(1), one Rh(1), and one Rh(4) atom. In the second O site, O(2) is bonded to one Ba(3), one Ba(4), two equivalent Ba(2), one Rh(2), and one Rh(3) atom to form a mixture of distorted corner, face, and edge-sharing OBa4Rh2 octahedra. The corner-sharing octahedral tilt angles range from 9-61°. In the third O site, O(3) is bonded to one Ba(1), one Ba(2), two equivalent Ba(3), one Rh(2), and one Rh(4) atom to form a mixture of distorted corner, face, and edge-sharing OBa4Rh2 octahedra. The corner-sharing octahedral tilt angles range from 2-60°. In the fourth O site, O(4) is bonded in a 2-coordinate geometry to one Ba(1), one Rh(1), and one Rh(3) atom.