Lu3MnFe3O10 crystallizes in the trigonal R3m space group. There are three inequivalent Lu sites. In the first Lu site, Lu(1) is bonded in a 6-coordinate geometry to three equivalent O(5) and three equivalent O(6) atoms. In the second Lu site, Lu(2) is bonded to three equivalent O(2) and three equivalent O(7) atoms to form distorted LuO6 octahedra that share corners with three equivalent Fe(1)O5 trigonal bipyramids, corners with three equivalent Fe(2)O5 trigonal bipyramids, and edges with six equivalent Lu(2)O6 octahedra. In the third Lu site, Lu(3) is bonded in a 6-coordinate geometry to three equivalent O(1) and three equivalent O(8) atoms. Mn(1) is bonded in a 5-coordinate geometry to one O(1), one O(9), and three equivalent O(10) atoms. There are three inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to one O(10), one O(2), and three equivalent O(9) atoms to form FeO5 trigonal bipyramids that share corners with three equivalent Lu(2)O6 octahedra and corners with six equivalent Fe(1)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 63°. In the second Fe site, Fe(2) is bonded to one O(5), one O(7), and three equivalent O(3) atoms to form FeO5 trigonal bipyramids that share corners with three equivalent Lu(2)O6 octahedra and corners with six equivalent Fe(2)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 64°. In the third Fe site, Fe(3) is bonded to one O(6), one O(8), and three equivalent O(4) atoms to form corner-sharing FeO5 trigonal bipyramids. There are ten inequivalent O sites. In the first O site, O(1) is bonded to three equivalent Lu(3) and one Mn(1) atom to form OLu3Mn tetrahedra that share corners with three equivalent O(8)Lu3Fe tetrahedra, corners with three equivalent O(10)Mn3Fe tetrahedra, corners with six equivalent O(1)Lu3Mn tetrahedra,  a cornercorner with one O(9)MnFe3 trigonal pyramid, and edges with three equivalent O(8)Lu3Fe tetrahedra. In the second O site, O(2) is bonded to three equivalent Lu(2) and one Fe(1) atom to form OLu3Fe tetrahedra that share  a cornercorner with one O(10)Mn3Fe tetrahedra, corners with three equivalent O(7)Lu3Fe tetrahedra, corners with six equivalent O(2)Lu3Fe tetrahedra, corners with three equivalent O(9)MnFe3 trigonal pyramids, and edges with three equivalent O(7)Lu3Fe tetrahedra. In the third O site, O(3) is bonded in a trigonal planar geometry to three equivalent Fe(2) atoms. In the fourth O site, O(4) is bonded in a trigonal planar geometry to three equivalent Fe(3) atoms. In the fifth O site, O(5) is bonded to three equivalent Lu(1) and one Fe(2) atom to form a mixture of edge and corner-sharing OLu3Fe tetrahedra. In the sixth O site, O(6) is bonded to three equivalent Lu(1) and one Fe(3) atom to form a mixture of edge and corner-sharing OLu3Fe tetrahedra. In the seventh O site, O(7) is bonded to three equivalent Lu(2) and one Fe(2) atom to form a mixture of edge and corner-sharing OLu3Fe tetrahedra. In the eighth O site, O(8) is bonded to three equivalent Lu(3) and one Fe(3) atom to form OLu3Fe tetrahedra that share  a cornercorner with one O(6)Lu3Fe tetrahedra, corners with three equivalent O(1)Lu3Mn tetrahedra, corners with six equivalent O(8)Lu3Fe tetrahedra, and edges with three equivalent O(1)Lu3Mn tetrahedra. In the ninth O site, O(9) is bonded to one Mn(1) and three equivalent Fe(1) atoms to form distorted OMnFe3 trigonal pyramids that share  a cornercorner with one O(1)Lu3Mn tetrahedra, corners with three equivalent O(2)Lu3Fe tetrahedra, corners with six equivalent O(9)MnFe3 trigonal pyramids, and edges with three equivalent O(10)Mn3Fe tetrahedra. In the tenth O site, O(10) is bonded to three equivalent Mn(1) and one Fe(1) atom to form OMn3Fe tetrahedra that share  a cornercorner with one O(2)Lu3Fe tetrahedra, corners with three equivalent O(1)Lu3Mn tetrahedra, corners with six equivalent O(10)Mn3Fe tetrahedra, and edges with three equivalent O(9)MnFe3 trigonal pyramids.
Lu3MnFe3O10 crystallizes in the trigonal R3m space group. There are three inequivalent Lu sites. In the first Lu site, Lu(1) is bonded in a 6-coordinate geometry to three equivalent O(5) and three equivalent O(6) atoms. All Lu(1)-O(5) bond lengths are 2.25 Å. All Lu(1)-O(6) bond lengths are 2.23 Å. In the second Lu site, Lu(2) is bonded to three equivalent O(2) and three equivalent O(7) atoms to form distorted LuO6 octahedra that share corners with three equivalent Fe(1)O5 trigonal bipyramids, corners with three equivalent Fe(2)O5 trigonal bipyramids, and edges with six equivalent Lu(2)O6 octahedra. All Lu(2)-O(2) bond lengths are 2.26 Å. All Lu(2)-O(7) bond lengths are 2.24 Å. In the third Lu site, Lu(3) is bonded in a 6-coordinate geometry to three equivalent O(1) and three equivalent O(8) atoms. All Lu(3)-O(1) bond lengths are 2.25 Å. All Lu(3)-O(8) bond lengths are 2.24 Å. Mn(1) is bonded in a 5-coordinate geometry to one O(1), one O(9), and three equivalent O(10) atoms. The Mn(1)-O(1) bond length is 2.07 Å. The Mn(1)-O(9) bond length is 2.54 Å. All Mn(1)-O(10) bond lengths are 2.09 Å. There are three inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to one O(10), one O(2), and three equivalent O(9) atoms to form FeO5 trigonal bipyramids that share corners with three equivalent Lu(2)O6 octahedra and corners with six equivalent Fe(1)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 63°. The Fe(1)-O(10) bond length is 2.01 Å. The Fe(1)-O(2) bond length is 1.99 Å. All Fe(1)-O(9) bond lengths are 2.01 Å. In the second Fe site, Fe(2) is bonded to one O(5), one O(7), and three equivalent O(3) atoms to form FeO5 trigonal bipyramids that share corners with three equivalent Lu(2)O6 octahedra and corners with six equivalent Fe(2)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 64°. The Fe(2)-O(5) bond length is 1.97 Å. The Fe(2)-O(7) bond length is 2.00 Å. All Fe(2)-O(3) bond lengths are 2.01 Å. In the third Fe site, Fe(3) is bonded to one O(6), one O(8), and three equivalent O(4) atoms to form corner-sharing FeO5 trigonal bipyramids. The Fe(3)-O(6) bond length is 1.97 Å. The Fe(3)-O(8) bond length is 1.96 Å. All Fe(3)-O(4) bond lengths are 2.01 Å. There are ten inequivalent O sites. In the first O site, O(1) is bonded to three equivalent Lu(3) and one Mn(1) atom to form OLu3Mn tetrahedra that share corners with three equivalent O(8)Lu3Fe tetrahedra, corners with three equivalent O(10)Mn3Fe tetrahedra, corners with six equivalent O(1)Lu3Mn tetrahedra,  a cornercorner with one O(9)MnFe3 trigonal pyramid, and edges with three equivalent O(8)Lu3Fe tetrahedra. In the second O site, O(2) is bonded to three equivalent Lu(2) and one Fe(1) atom to form OLu3Fe tetrahedra that share  a cornercorner with one O(10)Mn3Fe tetrahedra, corners with three equivalent O(7)Lu3Fe tetrahedra, corners with six equivalent O(2)Lu3Fe tetrahedra, corners with three equivalent O(9)MnFe3 trigonal pyramids, and edges with three equivalent O(7)Lu3Fe tetrahedra. In the third O site, O(3) is bonded in a trigonal planar geometry to three equivalent Fe(2) atoms. In the fourth O site, O(4) is bonded in a trigonal planar geometry to three equivalent Fe(3) atoms. In the fifth O site, O(5) is bonded to three equivalent Lu(1) and one Fe(2) atom to form a mixture of edge and corner-sharing OLu3Fe tetrahedra. In the sixth O site, O(6) is bonded to three equivalent Lu(1) and one Fe(3) atom to form a mixture of edge and corner-sharing OLu3Fe tetrahedra. In the seventh O site, O(7) is bonded to three equivalent Lu(2) and one Fe(2) atom to form a mixture of edge and corner-sharing OLu3Fe tetrahedra. In the eighth O site, O(8) is bonded to three equivalent Lu(3) and one Fe(3) atom to form OLu3Fe tetrahedra that share  a cornercorner with one O(6)Lu3Fe tetrahedra, corners with three equivalent O(1)Lu3Mn tetrahedra, corners with six equivalent O(8)Lu3Fe tetrahedra, and edges with three equivalent O(1)Lu3Mn tetrahedra. In the ninth O site, O(9) is bonded to one Mn(1) and three equivalent Fe(1) atoms to form distorted OMnFe3 trigonal pyramids that share  a cornercorner with one O(1)Lu3Mn tetrahedra, corners with three equivalent O(2)Lu3Fe tetrahedra, corners with six equivalent O(9)MnFe3 trigonal pyramids, and edges with three equivalent O(10)Mn3Fe tetrahedra. In the tenth O site, O(10) is bonded to three equivalent Mn(1) and one Fe(1) atom to form OMn3Fe tetrahedra that share  a cornercorner with one O(2)Lu3Fe tetrahedra, corners with three equivalent O(1)Lu3Mn tetrahedra, corners with six equivalent O(10)Mn3Fe tetrahedra, and edges with three equivalent O(9)MnFe3 trigonal pyramids.