LuFeO3 crystallizes in the hexagonal P6_3cm space group. There are two inequivalent Lu sites. In the first Lu site, Lu(1) is bonded to one O(3), three equivalent O(1), and three equivalent O(2) atoms to form distorted LuO7 pentagonal bipyramids that share corners with three equivalent Fe(1)O5 trigonal bipyramids and edges with three equivalent Fe(1)O5 trigonal bipyramids. In the second Lu site, Lu(2) is bonded in a 7-coordinate geometry to one O(4), three equivalent O(1), and three equivalent O(2) atoms. Fe(1) is bonded to one O(1), one O(2), one O(3), and two equivalent O(4) atoms to form FeO5 trigonal bipyramids that share  a cornercorner with one Lu(1)O7 pentagonal bipyramid, corners with six equivalent Fe(1)O5 trigonal bipyramids, and  an edgeedge with one Lu(1)O7 pentagonal bipyramid. There are four inequivalent O sites. In the first O site, O(1) is bonded to one Lu(1), two equivalent Lu(2), and one Fe(1) atom to form OLu3Fe tetrahedra that share corners with four equivalent O(2)Lu3Fe tetrahedra, corners with six equivalent O(1)Lu3Fe tetrahedra, corners with two equivalent O(3)LuFe3 trigonal pyramids, edges with three equivalent O(2)Lu3Fe tetrahedra, and edges with two equivalent O(4)LuFe3 trigonal pyramids. In the second O site, O(2) is bonded to one Lu(1), two equivalent Lu(2), and one Fe(1) atom to form distorted OLu3Fe tetrahedra that share corners with four equivalent O(1)Lu3Fe tetrahedra, corners with six equivalent O(2)Lu3Fe tetrahedra, corners with four equivalent O(4)LuFe3 trigonal pyramids, edges with three equivalent O(1)Lu3Fe tetrahedra, and  an edgeedge with one O(3)LuFe3 trigonal pyramid. In the third O site, O(3) is bonded to one Lu(1) and three equivalent Fe(1) atoms to form OLuFe3 trigonal pyramids that share corners with six equivalent O(1)Lu3Fe tetrahedra, corners with six equivalent O(4)LuFe3 trigonal pyramids, and edges with three equivalent O(2)Lu3Fe tetrahedra. In the fourth O site, O(4) is bonded to one Lu(2) and three equivalent Fe(1) atoms to form OLuFe3 trigonal pyramids that share corners with six equivalent O(2)Lu3Fe tetrahedra, corners with three equivalent O(3)LuFe3 trigonal pyramids, corners with three equivalent O(4)LuFe3 trigonal pyramids, and edges with three equivalent O(1)Lu3Fe tetrahedra.
LuFeO3 crystallizes in the hexagonal P6_3cm space group. There are two inequivalent Lu sites. In the first Lu site, Lu(1) is bonded to one O(3), three equivalent O(1), and three equivalent O(2) atoms to form distorted LuO7 pentagonal bipyramids that share corners with three equivalent Fe(1)O5 trigonal bipyramids and edges with three equivalent Fe(1)O5 trigonal bipyramids. The Lu(1)-O(3) bond length is 2.29 Å. All Lu(1)-O(1) bond lengths are 2.20 Å. All Lu(1)-O(2) bond lengths are 2.28 Å. In the second Lu site, Lu(2) is bonded in a 7-coordinate geometry to one O(4), three equivalent O(1), and three equivalent O(2) atoms. The Lu(2)-O(4) bond length is 2.41 Å. All Lu(2)-O(1) bond lengths are 2.21 Å. All Lu(2)-O(2) bond lengths are 2.25 Å. Fe(1) is bonded to one O(1), one O(2), one O(3), and two equivalent O(4) atoms to form FeO5 trigonal bipyramids that share  a cornercorner with one Lu(1)O7 pentagonal bipyramid, corners with six equivalent Fe(1)O5 trigonal bipyramids, and  an edgeedge with one Lu(1)O7 pentagonal bipyramid. The Fe(1)-O(1) bond length is 1.95 Å. The Fe(1)-O(2) bond length is 1.91 Å. The Fe(1)-O(3) bond length is 2.01 Å. Both Fe(1)-O(4) bond lengths are 2.01 Å. There are four inequivalent O sites. In the first O site, O(1) is bonded to one Lu(1), two equivalent Lu(2), and one Fe(1) atom to form OLu3Fe tetrahedra that share corners with four equivalent O(2)Lu3Fe tetrahedra, corners with six equivalent O(1)Lu3Fe tetrahedra, corners with two equivalent O(3)LuFe3 trigonal pyramids, edges with three equivalent O(2)Lu3Fe tetrahedra, and edges with two equivalent O(4)LuFe3 trigonal pyramids. In the second O site, O(2) is bonded to one Lu(1), two equivalent Lu(2), and one Fe(1) atom to form distorted OLu3Fe tetrahedra that share corners with four equivalent O(1)Lu3Fe tetrahedra, corners with six equivalent O(2)Lu3Fe tetrahedra, corners with four equivalent O(4)LuFe3 trigonal pyramids, edges with three equivalent O(1)Lu3Fe tetrahedra, and  an edgeedge with one O(3)LuFe3 trigonal pyramid. In the third O site, O(3) is bonded to one Lu(1) and three equivalent Fe(1) atoms to form OLuFe3 trigonal pyramids that share corners with six equivalent O(1)Lu3Fe tetrahedra, corners with six equivalent O(4)LuFe3 trigonal pyramids, and edges with three equivalent O(2)Lu3Fe tetrahedra. In the fourth O site, O(4) is bonded to one Lu(2) and three equivalent Fe(1) atoms to form OLuFe3 trigonal pyramids that share corners with six equivalent O(2)Lu3Fe tetrahedra, corners with three equivalent O(3)LuFe3 trigonal pyramids, corners with three equivalent O(4)LuFe3 trigonal pyramids, and edges with three equivalent O(1)Lu3Fe tetrahedra.