The structure described by LuMnO3 crystallizes in the hexagonal P6_3cm space group. There are two inequivalent Lu sites. In the first Lu site, Lu(1) is bonded in a 7-coordinate geometry to one O(1), three equivalent O(3), and three equivalent O(4) atoms. In the second Lu site, Lu(2) is bonded to one O(2), three equivalent O(3), and three equivalent O(4) atoms to form distorted LuO7 pentagonal bipyramids that share corners with three equivalent Mn(1)O5 trigonal bipyramids and edges with three equivalent Mn(1)O5 trigonal bipyramids. Mn(1) is bonded to one O(2), one O(3), one O(4), and two equivalent O(1) atoms to form MnO5 trigonal bipyramids that share  a cornercorner with one Lu(2)O7 pentagonal bipyramid, corners with six equivalent Mn(1)O5 trigonal bipyramids, and  an edgeedge with one Lu(2)O7 pentagonal bipyramid. There are four inequivalent O sites. In the first O site, O(1) is bonded to one Lu(1) and three equivalent Mn(1) atoms to form OLuMn3 trigonal pyramids that share corners with six equivalent O(3)Lu3Mn tetrahedra, corners with three equivalent O(1)LuMn3 trigonal pyramids, corners with three equivalent O(2)LuMn3 trigonal pyramids, and edges with three equivalent O(4)Lu3Mn tetrahedra. In the second O site, O(2) is bonded to one Lu(2) and three equivalent Mn(1) atoms to form OLuMn3 trigonal pyramids that share corners with six equivalent O(4)Lu3Mn tetrahedra, corners with six equivalent O(1)LuMn3 trigonal pyramids, and edges with three equivalent O(3)Lu3Mn tetrahedra. In the third O site, O(3) is bonded to one Lu(2), two equivalent Lu(1), and one Mn(1) atom to form distorted OLu3Mn tetrahedra that share corners with four equivalent O(4)Lu3Mn tetrahedra, corners with six equivalent O(3)Lu3Mn tetrahedra, corners with four equivalent O(1)LuMn3 trigonal pyramids, edges with three equivalent O(4)Lu3Mn tetrahedra, and  an edgeedge with one O(2)LuMn3 trigonal pyramid. In the fourth O site, O(4) is bonded to one Lu(2), two equivalent Lu(1), and one Mn(1) atom to form OLu3Mn tetrahedra that share corners with four equivalent O(3)Lu3Mn tetrahedra, corners with six equivalent O(4)Lu3Mn tetrahedra, corners with two equivalent O(2)LuMn3 trigonal pyramids, edges with three equivalent O(3)Lu3Mn tetrahedra, and edges with two equivalent O(1)LuMn3 trigonal pyramids. is represented by the Crystallographic Information File (CIF) [CIF]
data_LuMnO3
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.006
_cell_length_b   6.006
_cell_length_c   11.312
_cell_angle_alpha   89.999
_cell_angle_beta   90.000
_cell_angle_gamma   120.001
_symmetry_Int_Tables_number   1
_cell_volume   353.343
_cell_formula_units_Z   6
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  0.667  0.333  0.231  1.0
  Lu  Lu1  1  0.333  0.667  0.731  1.0
  Lu  Lu2  1  0.667  0.333  0.731  1.0
  Lu  Lu3  1  0.333  0.667  0.231  1.0
  Lu  Lu4  1  0.000  0.000  0.776  1.0
  Lu  Lu5  1  0.000  0.000  0.276  1.0
  Mn  Mn6  1  0.667  1.000  0.501  1.0
  Mn  Mn7  1  0.667  0.667  0.001  1.0
  Mn  Mn8  1  1.000  0.333  0.001  1.0
  Mn  Mn9  1  0.000  0.667  0.501  1.0
  Mn  Mn10  1  0.333  0.333  0.501  1.0
  Mn  Mn11  1  0.333  1.000  0.001  1.0
  O  O12  1  0.667  0.333  0.022  1.0
  O  O13  1  0.333  0.667  0.522  1.0
  O  O14  1  0.667  0.333  0.522  1.0
  O  O15  1  0.333  0.667  0.022  1.0
  O  O16  1  0.000  0.000  0.975  1.0
  O  O17  1  0.000  0.000  0.475  1.0
  O  O18  1  0.362  0.000  0.836  1.0
  O  O19  1  0.362  0.362  0.336  1.0
  O  O20  1  0.000  0.638  0.335  1.0
  O  O21  1  1.000  0.362  0.836  1.0
  O  O22  1  0.638  0.638  0.836  1.0
  O  O23  1  0.638  0.000  0.336  1.0
  O  O24  1  0.305  0.000  0.166  1.0
  O  O25  1  0.305  0.305  0.666  1.0
  O  O26  1  0.000  0.695  0.666  1.0
  O  O27  1  1.000  0.305  0.166  1.0
  O  O28  1  0.695  0.695  0.166  1.0
  O  O29  1  0.695  0.000  0.666  1.0
[/CIF]
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The structure described by LuMnO3 crystallizes in the hexagonal P6_3cm space group. There are two inequivalent Lu sites. In the first Lu site, Lu(1) is bonded in a 7-coordinate geometry to one O(1), three equivalent O(3), and three equivalent O(4) atoms. In the second Lu site, Lu(2) is bonded to one O(2), three equivalent O(3), and three equivalent O(4) atoms to form distorted LuO7 pentagonal bipyramids that share corners with three equivalent Mn(1)O5 trigonal bipyramids and edges with three equivalent Mn(1)O5 trigonal bipyramids. Mn(1) is bonded to one O(2), one O(3), one O(4), and two equivalent O(1) atoms to form MnO5 trigonal bipyramids that share  a cornercorner with one Lu(2)O7 pentagonal bipyramid, corners with six equivalent Mn(1)O5 trigonal bipyramids, and  an edgeedge with one Lu(2)O7 pentagonal bipyramid. There are four inequivalent O sites. In the first O site, O(1) is bonded to one Lu(1) and three equivalent Mn(1) atoms to form OLuMn3 trigonal pyramids that share corners with six equivalent O(3)Lu3Mn tetrahedra, corners with three equivalent O(1)LuMn3 trigonal pyramids, corners with three equivalent O(2)LuMn3 trigonal pyramids, and edges with three equivalent O(4)Lu3Mn tetrahedra. In the second O site, O(2) is bonded to one Lu(2) and three equivalent Mn(1) atoms to form OLuMn3 trigonal pyramids that share corners with six equivalent O(4)Lu3Mn tetrahedra, corners with six equivalent O(1)LuMn3 trigonal pyramids, and edges with three equivalent O(3)Lu3Mn tetrahedra. In the third O site, O(3) is bonded to one Lu(2), two equivalent Lu(1), and one Mn(1) atom to form distorted OLu3Mn tetrahedra that share corners with four equivalent O(4)Lu3Mn tetrahedra, corners with six equivalent O(3)Lu3Mn tetrahedra, corners with four equivalent O(1)LuMn3 trigonal pyramids, edges with three equivalent O(4)Lu3Mn tetrahedra, and  an edgeedge with one O(2)LuMn3 trigonal pyramid. In the fourth O site, O(4) is bonded to one Lu(2), two equivalent Lu(1), and one Mn(1) atom to form OLu3Mn tetrahedra that share corners with four equivalent O(3)Lu3Mn tetrahedra, corners with six equivalent O(4)Lu3Mn tetrahedra, corners with two equivalent O(2)LuMn3 trigonal pyramids, edges with three equivalent O(3)Lu3Mn tetrahedra, and edges with two equivalent O(1)LuMn3 trigonal pyramids. is represented by the Crystallographic Information File (CIF) [CIF]
data_LuMnO3
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.006
_cell_length_b   6.006
_cell_length_c   11.312
_cell_angle_alpha   89.999
_cell_angle_beta   90.000
_cell_angle_gamma   120.001
_symmetry_Int_Tables_number   1
_cell_volume   353.343
_cell_formula_units_Z   6
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  0.667  0.333  0.231  1.0
  Lu  Lu1  1  0.333  0.667  0.731  1.0
  Lu  Lu2  1  0.667  0.333  0.731  1.0
  Lu  Lu3  1  0.333  0.667  0.231  1.0
  Lu  Lu4  1  0.000  0.000  0.776  1.0
  Lu  Lu5  1  0.000  0.000  0.276  1.0
  Mn  Mn6  1  0.667  1.000  0.501  1.0
  Mn  Mn7  1  0.667  0.667  0.001  1.0
  Mn  Mn8  1  1.000  0.333  0.001  1.0
  Mn  Mn9  1  0.000  0.667  0.501  1.0
  Mn  Mn10  1  0.333  0.333  0.501  1.0
  Mn  Mn11  1  0.333  1.000  0.001  1.0
  O  O12  1  0.667  0.333  0.022  1.0
  O  O13  1  0.333  0.667  0.522  1.0
  O  O14  1  0.667  0.333  0.522  1.0
  O  O15  1  0.333  0.667  0.022  1.0
  O  O16  1  0.000  0.000  0.975  1.0
  O  O17  1  0.000  0.000  0.475  1.0
  O  O18  1  0.362  0.000  0.836  1.0
  O  O19  1  0.362  0.362  0.336  1.0
  O  O20  1  0.000  0.638  0.335  1.0
  O  O21  1  1.000  0.362  0.836  1.0
  O  O22  1  0.638  0.638  0.836  1.0
  O  O23  1  0.638  0.000  0.336  1.0
  O  O24  1  0.305  0.000  0.166  1.0
  O  O25  1  0.305  0.305  0.666  1.0
  O  O26  1  0.000  0.695  0.666  1.0
  O  O27  1  1.000  0.305  0.166  1.0
  O  O28  1  0.695  0.695  0.166  1.0
  O  O29  1  0.695  0.000  0.666  1.0
[/CIF]
.