Li4Cr3O8 crystallizes in the trigonal R32 space group. There are three inequivalent Li sites. In the first Li site, Li(1) is bonded to six equivalent O(2) atoms to form distorted LiO6 octahedra that share corners with six equivalent Li(3)O6 octahedra and edges with six equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles are 13°. In the second Li site, Li(2) is bonded in a 4-coordinate geometry to one O(1) and three equivalent O(2) atoms. In the third Li site, Li(3) is bonded to six equivalent O(2) atoms to form LiO6 octahedra that share corners with six equivalent Li(1)O6 octahedra and edges with six equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles are 13°. Cr(1) is bonded to two equivalent O(1) and four equivalent O(2) atoms to form CrO6 octahedra that share edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(3)O6 octahedra, and edges with four equivalent Cr(1)O6 octahedra. There are two inequivalent O sites. In the first O site, O(1) is bonded to one Li(2) and three equivalent Cr(1) atoms to form distorted OLiCr3 trigonal pyramids that share corners with nine equivalent O(2)Li3Cr2 trigonal bipyramids, corners with three equivalent O(1)LiCr3 trigonal pyramids, and edges with three equivalent O(2)Li3Cr2 trigonal bipyramids. In the second O site, O(2) is bonded to one Li(1), one Li(2), one Li(3), and two equivalent Cr(1) atoms to form OLi3Cr2 trigonal bipyramids that share corners with six equivalent O(2)Li3Cr2 trigonal bipyramids, corners with three equivalent O(1)LiCr3 trigonal pyramids, edges with six equivalent O(2)Li3Cr2 trigonal bipyramids, and  an edgeedge with one O(1)LiCr3 trigonal pyramid.
Li4Cr3O8 crystallizes in the trigonal R32 space group. There are three inequivalent Li sites. In the first Li site, Li(1) is bonded to six equivalent O(2) atoms to form distorted LiO6 octahedra that share corners with six equivalent Li(3)O6 octahedra and edges with six equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles are 13°. All Li(1)-O(2) bond lengths are 2.19 Å. In the second Li site, Li(2) is bonded in a 4-coordinate geometry to one O(1) and three equivalent O(2) atoms. The Li(2)-O(1) bond length is 1.87 Å. All Li(2)-O(2) bond lengths are 2.11 Å. In the third Li site, Li(3) is bonded to six equivalent O(2) atoms to form LiO6 octahedra that share corners with six equivalent Li(1)O6 octahedra and edges with six equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles are 13°. All Li(3)-O(2) bond lengths are 2.05 Å. Cr(1) is bonded to two equivalent O(1) and four equivalent O(2) atoms to form CrO6 octahedra that share edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(3)O6 octahedra, and edges with four equivalent Cr(1)O6 octahedra. Both Cr(1)-O(1) bond lengths are 1.98 Å. There are two shorter (1.93 Å) and two longer (1.94 Å) Cr(1)-O(2) bond lengths. There are two inequivalent O sites. In the first O site, O(1) is bonded to one Li(2) and three equivalent Cr(1) atoms to form distorted OLiCr3 trigonal pyramids that share corners with nine equivalent O(2)Li3Cr2 trigonal bipyramids, corners with three equivalent O(1)LiCr3 trigonal pyramids, and edges with three equivalent O(2)Li3Cr2 trigonal bipyramids. In the second O site, O(2) is bonded to one Li(1), one Li(2), one Li(3), and two equivalent Cr(1) atoms to form OLi3Cr2 trigonal bipyramids that share corners with six equivalent O(2)Li3Cr2 trigonal bipyramids, corners with three equivalent O(1)LiCr3 trigonal pyramids, edges with six equivalent O(2)Li3Cr2 trigonal bipyramids, and  an edgeedge with one O(1)LiCr3 trigonal pyramid.