Li4Cr5BiO12 crystallizes in the monoclinic C2/m space group. Li(1) is bonded to one O(3), one O(4), two equivalent O(1), and two equivalent O(2) atoms to form distorted LiO6 octahedra that share  a cornercorner with one Cr(3)O6 octahedra, corners with two equivalent Cr(1)O6 octahedra, corners with three equivalent Cr(2)O6 octahedra, corners with three equivalent Bi(1)O6 octahedra,  an edgeedge with one Cr(3)O6 octahedra, edges with two equivalent Cr(1)O6 octahedra, edges with three equivalent Li(1)O6 octahedra, and  a faceface with one Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 6-57°. There are three inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to two equivalent O(3) and four equivalent O(2) atoms to form CrO6 octahedra that share corners with four equivalent Li(1)O6 octahedra, edges with three equivalent Cr(1)O6 octahedra, edges with three equivalent Cr(3)O6 octahedra, and edges with four equivalent Li(1)O6 octahedra. The corner-sharing octahedral tilt angles are 6°. In the second Cr site, Cr(2) is bonded to two equivalent O(4) and four equivalent O(1) atoms to form CrO6 octahedra that share corners with six equivalent Li(1)O6 octahedra, edges with three equivalent Cr(2)O6 octahedra, edges with three equivalent Bi(1)O6 octahedra, and faces with two equivalent Li(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 35-45°. In the third Cr site, Cr(3) is bonded to two equivalent O(3) and four equivalent O(2) atoms to form CrO6 octahedra that share corners with four equivalent Li(1)O6 octahedra, edges with four equivalent Li(1)O6 octahedra, and edges with six equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles are 6°. Bi(1) is bonded to two equivalent O(4) and four equivalent O(1) atoms to form BiO6 octahedra that share corners with twelve equivalent Li(1)O6 octahedra and edges with six equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 48-57°. There are four inequivalent O sites. In the first O site, O(1) is bonded to two equivalent Li(1), two equivalent Cr(2), and one Bi(1) atom to form distorted OLi2Cr2Bi trigonal bipyramids that share corners with two equivalent O(2)Li2Cr3 square pyramids, corners with two equivalent O(3)Li2Cr3 square pyramids, corners with three equivalent O(1)Li2Cr2Bi trigonal bipyramids,  an edgeedge with one O(2)Li2Cr3 square pyramid, and edges with four equivalent O(1)Li2Cr2Bi trigonal bipyramids. In the second O site, O(2) is bonded to two equivalent Li(1), one Cr(3), and two equivalent Cr(1) atoms to form OLi2Cr3 square pyramids that share corners with two equivalent O(3)Li2Cr3 square pyramids, corners with three equivalent O(2)Li2Cr3 square pyramids, corners with two equivalent O(1)Li2Cr2Bi trigonal bipyramids, edges with three equivalent O(3)Li2Cr3 square pyramids, edges with four equivalent O(2)Li2Cr3 square pyramids, and  an edgeedge with one O(1)Li2Cr2Bi trigonal bipyramid. In the third O site, O(3) is bonded to two equivalent Li(1), one Cr(3), and two equivalent Cr(1) atoms to form OLi2Cr3 square pyramids that share  a cornercorner with one O(3)Li2Cr3 square pyramid, corners with four equivalent O(2)Li2Cr3 square pyramids, corners with four equivalent O(1)Li2Cr2Bi trigonal bipyramids,  an edgeedge with one O(3)Li2Cr3 square pyramid, and edges with six equivalent O(2)Li2Cr3 square pyramids. In the fourth O site, O(4) is bonded in a 5-coordinate geometry to two equivalent Li(1), two equivalent Cr(2), and one Bi(1) atom.
Li4Cr5BiO12 crystallizes in the monoclinic C2/m space group. Li(1) is bonded to one O(3), one O(4), two equivalent O(1), and two equivalent O(2) atoms to form distorted LiO6 octahedra that share  a cornercorner with one Cr(3)O6 octahedra, corners with two equivalent Cr(1)O6 octahedra, corners with three equivalent Cr(2)O6 octahedra, corners with three equivalent Bi(1)O6 octahedra,  an edgeedge with one Cr(3)O6 octahedra, edges with two equivalent Cr(1)O6 octahedra, edges with three equivalent Li(1)O6 octahedra, and  a faceface with one Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 6-57°. The Li(1)-O(3) bond length is 2.13 Å. The Li(1)-O(4) bond length is 2.46 Å. There is one shorter (2.19 Å) and one longer (2.46 Å) Li(1)-O(1) bond length. There is one shorter (2.11 Å) and one longer (2.13 Å) Li(1)-O(2) bond length. There are three inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to two equivalent O(3) and four equivalent O(2) atoms to form CrO6 octahedra that share corners with four equivalent Li(1)O6 octahedra, edges with three equivalent Cr(1)O6 octahedra, edges with three equivalent Cr(3)O6 octahedra, and edges with four equivalent Li(1)O6 octahedra. The corner-sharing octahedral tilt angles are 6°. Both Cr(1)-O(3) bond lengths are 2.05 Å. There are two shorter (2.01 Å) and two longer (2.06 Å) Cr(1)-O(2) bond lengths. In the second Cr site, Cr(2) is bonded to two equivalent O(4) and four equivalent O(1) atoms to form CrO6 octahedra that share corners with six equivalent Li(1)O6 octahedra, edges with three equivalent Cr(2)O6 octahedra, edges with three equivalent Bi(1)O6 octahedra, and faces with two equivalent Li(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 35-45°. Both Cr(2)-O(4) bond lengths are 2.01 Å. There are two shorter (2.01 Å) and two longer (2.02 Å) Cr(2)-O(1) bond lengths. In the third Cr site, Cr(3) is bonded to two equivalent O(3) and four equivalent O(2) atoms to form CrO6 octahedra that share corners with four equivalent Li(1)O6 octahedra, edges with four equivalent Li(1)O6 octahedra, and edges with six equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles are 6°. Both Cr(3)-O(3) bond lengths are 1.99 Å. All Cr(3)-O(2) bond lengths are 2.07 Å. Bi(1) is bonded to two equivalent O(4) and four equivalent O(1) atoms to form BiO6 octahedra that share corners with twelve equivalent Li(1)O6 octahedra and edges with six equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 48-57°. Both Bi(1)-O(4) bond lengths are 2.22 Å. All Bi(1)-O(1) bond lengths are 2.22 Å. There are four inequivalent O sites. In the first O site, O(1) is bonded to two equivalent Li(1), two equivalent Cr(2), and one Bi(1) atom to form distorted OLi2Cr2Bi trigonal bipyramids that share corners with two equivalent O(2)Li2Cr3 square pyramids, corners with two equivalent O(3)Li2Cr3 square pyramids, corners with three equivalent O(1)Li2Cr2Bi trigonal bipyramids,  an edgeedge with one O(2)Li2Cr3 square pyramid, and edges with four equivalent O(1)Li2Cr2Bi trigonal bipyramids. In the second O site, O(2) is bonded to two equivalent Li(1), one Cr(3), and two equivalent Cr(1) atoms to form OLi2Cr3 square pyramids that share corners with two equivalent O(3)Li2Cr3 square pyramids, corners with three equivalent O(2)Li2Cr3 square pyramids, corners with two equivalent O(1)Li2Cr2Bi trigonal bipyramids, edges with three equivalent O(3)Li2Cr3 square pyramids, edges with four equivalent O(2)Li2Cr3 square pyramids, and  an edgeedge with one O(1)Li2Cr2Bi trigonal bipyramid. In the third O site, O(3) is bonded to two equivalent Li(1), one Cr(3), and two equivalent Cr(1) atoms to form OLi2Cr3 square pyramids that share  a cornercorner with one O(3)Li2Cr3 square pyramid, corners with four equivalent O(2)Li2Cr3 square pyramids, corners with four equivalent O(1)Li2Cr2Bi trigonal bipyramids,  an edgeedge with one O(3)Li2Cr3 square pyramid, and edges with six equivalent O(2)Li2Cr3 square pyramids. In the fourth O site, O(4) is bonded in a 5-coordinate geometry to two equivalent Li(1), two equivalent Cr(2), and one Bi(1) atom.