LiBa4(RhO3)4 crystallizes in the trigonal P3m1 space group. Li(1) is bonded in a 3-coordinate geometry to one Ba(2), one Rh(1), and three equivalent O(4) atoms. 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 distorted BaO12 cuboctahedra that share corners with six equivalent Ba(1)O12 cuboctahedra,  a faceface with one Rh(2)O6 octahedra,  a faceface with one Rh(3)O6 octahedra, and faces with three equivalent Rh(4)O6 octahedra. In the second Ba site, Ba(2) is bonded in a 10-coordinate geometry to one Li(1), three equivalent O(3), and six equivalent O(2) atoms. In the third Ba site, Ba(3) is bonded in a 9-coordinate geometry to three equivalent O(1) and six equivalent O(3) atoms. In the fourth Ba site, Ba(4) is bonded in a 9-coordinate geometry to three equivalent O(2) and six equivalent O(4) atoms. There are four inequivalent Rh sites. In the first Rh site, Rh(1) is bonded in a 7-coordinate geometry to one Li(1), three equivalent O(1), and three equivalent O(4) atoms. 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, 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 RhO6 octahedra that share  a faceface with one Ba(1)O12 cuboctahedra and  a faceface with one Rh(2)O6 octahedra. 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 and faces with three equivalent Ba(1)O12 cuboctahedra. 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 5-coordinate geometry to one Ba(3), two equivalent Ba(1), one Rh(1), and one Rh(4) atom. In the second O site, O(2) is bonded in a distorted L-shaped geometry to one Ba(4), two equivalent Ba(2), one Rh(2), and one Rh(3) atom. In the third O site, O(3) is bonded in a 6-coordinate geometry to one Ba(1), one Ba(2), two equivalent Ba(3), one Rh(2), and one Rh(4) atom. In the fourth O site, O(4) is bonded in a 6-coordinate geometry to one Li(1), one Ba(1), two equivalent Ba(4), one Rh(1), and one Rh(3) atom.
LiBa4(RhO3)4 crystallizes in the trigonal P3m1 space group. Li(1) is bonded in a 3-coordinate geometry to one Ba(2), one Rh(1), and three equivalent O(4) atoms. The Li(1)-Ba(2) bond length is 2.45 Å. The Li(1)-Rh(1) bond length is 2.19 Å. All Li(1)-O(4) bond lengths are 1.82 Å. 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 distorted BaO12 cuboctahedra that share corners with six equivalent Ba(1)O12 cuboctahedra,  a faceface with one Rh(2)O6 octahedra,  a faceface with one Rh(3)O6 octahedra, and faces with three equivalent Rh(4)O6 octahedra. All Ba(1)-O(3) bond lengths are 3.17 Å. All Ba(1)-O(4) bond lengths are 3.01 Å. All Ba(1)-O(1) bond lengths are 2.90 Å. In the second Ba site, Ba(2) is bonded in a 10-coordinate geometry to one Li(1), three equivalent O(3), and six equivalent O(2) atoms. All Ba(2)-O(3) bond lengths are 2.62 Å. All Ba(2)-O(2) bond lengths are 2.97 Å. In the third Ba site, Ba(3) is bonded in a 9-coordinate geometry to three equivalent O(1) and six equivalent O(3) atoms. All Ba(3)-O(1) bond lengths are 2.81 Å. All Ba(3)-O(3) bond lengths are 2.91 Å. In the fourth Ba site, Ba(4) is bonded in a 9-coordinate geometry to three equivalent O(2) and six equivalent O(4) atoms. All Ba(4)-O(2) bond lengths are 2.99 Å. All Ba(4)-O(4) bond lengths are 2.90 Å. There are four inequivalent Rh sites. In the first Rh site, Rh(1) is bonded in a 7-coordinate geometry to one Li(1), three equivalent O(1), and three equivalent O(4) atoms. All Rh(1)-O(1) bond lengths are 2.01 Å. All Rh(1)-O(4) bond lengths are 2.13 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, 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 2.03 Å. All Rh(2)-O(3) bond lengths are 2.07 Å. In the third Rh site, Rh(3) is bonded to three equivalent O(2) and three equivalent O(4) atoms to form RhO6 octahedra that share  a faceface with one Ba(1)O12 cuboctahedra and  a faceface with one Rh(2)O6 octahedra. All Rh(3)-O(2) bond lengths are 2.04 Å. All Rh(3)-O(4) bond lengths are 2.09 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 and faces with three equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 3°. All Rh(4)-O(1) bond lengths are 2.02 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 5-coordinate geometry to one Ba(3), two equivalent Ba(1), one Rh(1), and one Rh(4) atom. In the second O site, O(2) is bonded in a distorted L-shaped geometry to one Ba(4), two equivalent Ba(2), one Rh(2), and one Rh(3) atom. In the third O site, O(3) is bonded in a 6-coordinate geometry to one Ba(1), one Ba(2), two equivalent Ba(3), one Rh(2), and one Rh(4) atom. In the fourth O site, O(4) is bonded in a 6-coordinate geometry to one Li(1), one Ba(1), two equivalent Ba(4), one Rh(1), and one Rh(3) atom.