The compound described by 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. is represented by the CIF file [CIF]
data_Lu3MnFe3O10
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   3.479
_cell_length_b   3.479
_cell_length_c   20.652
_cell_angle_alpha   90.000
_cell_angle_beta   94.832
_cell_angle_gamma   60.000
_symmetry_Int_Tables_number   1
_cell_volume   215.467
_cell_formula_units_Z   1
loop_
 _symmetry_equiv_pos_site_id
 _symmetry_equiv_pos_as_xyz
  1  'x, y, z'
loop_
 _atom_site_type_symbol
 _atom_site_label
 _atom_site_symmetry_multiplicity
 _atom_site_fract_x
 _atom_site_fract_y
 _atom_site_fract_z
 _atom_site_occupancy
  Lu  Lu0  1  1.000  0.000  1.000  1.0
  Lu  Lu1  1  0.806  0.097  0.709  1.0
  Lu  Lu2  1  0.191  0.905  0.286  1.0
  Mn  Mn3  1  0.624  0.188  0.437  1.0
  Fe  Fe4  1  0.375  0.813  0.562  1.0
  Fe  Fe5  1  0.237  0.382  0.855  1.0
  Fe  Fe6  1  0.762  0.619  0.143  1.0
  O  O7  1  0.557  0.221  0.336  1.0
  O  O8  1  0.439  0.780  0.659  1.0
  O  O9  1  0.903  0.048  0.855  1.0
  O  O10  1  0.094  0.953  0.141  1.0
  O  O11  1  0.301  0.350  0.951  1.0
  O  O12  1  0.698  0.651  0.047  1.0
  O  O13  1  0.172  0.414  0.758  1.0
  O  O14  1  0.825  0.587  0.238  1.0
  O  O15  1  0.707  0.147  0.560  1.0
  O  O16  1  0.309  0.845  0.464  1.0
[/CIF]
.
The compound described by 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. is represented by the CIF file [CIF]
data_Lu3MnFe3O10
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   3.479
_cell_length_b   3.479
_cell_length_c   20.652
_cell_angle_alpha   90.000
_cell_angle_beta   94.832
_cell_angle_gamma   60.000
_symmetry_Int_Tables_number   1
_cell_volume   215.467
_cell_formula_units_Z   1
loop_
 _symmetry_equiv_pos_site_id
 _symmetry_equiv_pos_as_xyz
  1  'x, y, z'
loop_
 _atom_site_type_symbol
 _atom_site_label
 _atom_site_symmetry_multiplicity
 _atom_site_fract_x
 _atom_site_fract_y
 _atom_site_fract_z
 _atom_site_occupancy
  Lu  Lu0  1  1.000  0.000  1.000  1.0
  Lu  Lu1  1  0.806  0.097  0.709  1.0
  Lu  Lu2  1  0.191  0.905  0.286  1.0
  Mn  Mn3  1  0.624  0.188  0.437  1.0
  Fe  Fe4  1  0.375  0.813  0.562  1.0
  Fe  Fe5  1  0.237  0.382  0.855  1.0
  Fe  Fe6  1  0.762  0.619  0.143  1.0
  O  O7  1  0.557  0.221  0.336  1.0
  O  O8  1  0.439  0.780  0.659  1.0
  O  O9  1  0.903  0.048  0.855  1.0
  O  O10  1  0.094  0.953  0.141  1.0
  O  O11  1  0.301  0.350  0.951  1.0
  O  O12  1  0.698  0.651  0.047  1.0
  O  O13  1  0.172  0.414  0.758  1.0
  O  O14  1  0.825  0.587  0.238  1.0
  O  O15  1  0.707  0.147  0.560  1.0
  O  O16  1  0.309  0.845  0.464  1.0
[/CIF]
.