The crystal structure described by Na3Mn8O16 is beta indium sulfide-derived structured and crystallizes in the orthorhombic Pmmn space group. There are two inequivalent Na sites. In the first Na site, Na(1) is bonded to two equivalent O(2) and two equivalent O(5) atoms to form NaO4 tetrahedra that share corners with two equivalent Mn(2)O6 octahedra, corners with two equivalent Mn(4)O6 octahedra, corners with four equivalent Mn(1)O6 octahedra, and corners with four equivalent Mn(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 60-67°. In the second Na site, Na(2) is bonded to one O(6), one O(7), and two equivalent O(3) atoms to form NaO4 tetrahedra that share corners with two equivalent Mn(1)O6 octahedra, corners with three equivalent Mn(2)O6 octahedra, corners with three equivalent Mn(3)O6 octahedra, and corners with four equivalent Mn(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 60-63°. There are four inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(3) atoms to form MnO6 octahedra that share corners with two equivalent Na(1)O4 tetrahedra, corners with two equivalent Na(2)O4 tetrahedra, edges with two equivalent Mn(1)O6 octahedra, edges with two equivalent Mn(2)O6 octahedra, and edges with two equivalent Mn(3)O6 octahedra. In the second Mn site, Mn(2) is bonded to one O(2), one O(6), two equivalent O(3), and two equivalent O(4) atoms to form MnO6 octahedra that share  a cornercorner with one Na(1)O4 tetrahedra, corners with three equivalent Na(2)O4 tetrahedra,  an edgeedge with one Mn(2)O6 octahedra,  an edgeedge with one Mn(3)O6 octahedra, edges with two equivalent Mn(1)O6 octahedra, and edges with two equivalent Mn(4)O6 octahedra. In the third Mn site, Mn(3) is bonded to one O(1), one O(7), two equivalent O(3), and two equivalent O(5) atoms to form MnO6 octahedra that share corners with two equivalent Na(1)O4 tetrahedra, corners with three equivalent Na(2)O4 tetrahedra,  an edgeedge with one Mn(2)O6 octahedra,  an edgeedge with one Mn(3)O6 octahedra, edges with two equivalent Mn(1)O6 octahedra, and edges with two equivalent Mn(4)O6 octahedra. In the fourth Mn site, Mn(4) is bonded to one O(4), one O(5), two equivalent O(6), and two equivalent O(7) atoms to form MnO6 octahedra that share  a cornercorner with one Na(1)O4 tetrahedra, corners with four equivalent Na(2)O4 tetrahedra, edges with two equivalent Mn(2)O6 octahedra, edges with two equivalent Mn(3)O6 octahedra, and edges with two equivalent Mn(4)O6 octahedra. There are seven inequivalent O sites. In the first O site, O(5) is bonded to one Na(1), one Mn(4), and two equivalent Mn(3) atoms to form a mixture of edge and corner-sharing ONaMn3 tetrahedra. In the second O site, O(6) is bonded to one Na(2), one Mn(2), and two equivalent Mn(4) atoms to form a mixture of edge and corner-sharing ONaMn3 tetrahedra. In the third O site, O(7) is bonded to one Na(2), one Mn(3), and two equivalent Mn(4) atoms to form a mixture of edge and corner-sharing ONaMn3 tetrahedra. In the fourth O site, O(1) is bonded in a distorted trigonal non-coplanar geometry to one Mn(3) and two equivalent Mn(1) atoms. In the fifth O site, O(2) is bonded to one Na(1), one Mn(2), and two equivalent Mn(1) atoms to form a mixture of edge and corner-sharing ONaMn3 tetrahedra. In the sixth O site, O(3) is bonded to one Na(2), one Mn(1), one Mn(2), and one Mn(3) atom to form a mixture of edge and corner-sharing ONaMn3 tetrahedra. In the seventh O site, O(4) is bonded in a distorted trigonal non-coplanar geometry to one Mn(4) and two equivalent Mn(2) atoms. is represented by the Crystallographic Information File (CIF) [CIF]
data_Na3Mn8O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.168
_cell_length_b   12.374
_cell_length_c   8.432
_cell_angle_alpha   89.998
_cell_angle_beta   89.962
_cell_angle_gamma   90.002
_symmetry_Int_Tables_number   1
_cell_volume   643.513
_cell_formula_units_Z   2
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
  Na  Na0  1  0.750  0.000  0.121  1.0
  Na  Na1  1  0.750  0.749  0.373  1.0
  Na  Na2  1  0.750  0.251  0.373  1.0
  Na  Na3  1  0.250  0.751  0.627  1.0
  Na  Na4  1  0.250  0.249  0.627  1.0
  Na  Na5  1  0.250  0.500  0.879  1.0
  Mn  Mn6  1  0.500  0.250  0.000  1.0
  Mn  Mn7  1  0.500  0.750  1.000  1.0
  Mn  Mn8  1  0.000  0.750  0.000  1.0
  Mn  Mn9  1  0.000  0.250  0.000  1.0
  Mn  Mn10  1  0.250  0.623  0.248  1.0
  Mn  Mn11  1  0.250  0.377  0.248  1.0
  Mn  Mn12  1  0.250  0.876  0.248  1.0
  Mn  Mn13  1  0.250  0.124  0.248  1.0
  Mn  Mn14  1  0.002  1.000  0.503  1.0
  Mn  Mn15  1  0.498  0.000  0.503  1.0
  Mn  Mn16  1  0.502  0.500  0.497  1.0
  Mn  Mn17  1  0.998  0.500  0.497  1.0
  Mn  Mn18  1  0.750  0.624  0.753  1.0
  Mn  Mn19  1  0.750  0.878  0.752  1.0
  Mn  Mn20  1  0.750  0.376  0.753  1.0
  Mn  Mn21  1  0.750  0.123  0.752  1.0
  O  O22  1  0.250  0.856  0.017  1.0
  O  O23  1  0.250  0.647  0.014  1.0
  O  O24  1  0.250  0.144  0.017  1.0
  O  O25  1  0.250  0.353  0.014  1.0
  O  O26  1  0.460  0.747  0.229  1.0
  O  O27  1  0.040  0.747  0.229  1.0
  O  O28  1  0.460  0.253  0.229  1.0
  O  O29  1  0.040  0.253  0.229  1.0
  O  O30  1  0.039  0.500  0.263  1.0
  O  O31  1  0.461  0.500  0.263  1.0
  O  O32  1  0.034  1.000  0.273  1.0
  O  O33  1  0.466  1.000  0.273  1.0
  O  O34  1  0.249  0.394  0.476  1.0
  O  O35  1  0.250  0.893  0.479  1.0
  O  O36  1  0.249  0.606  0.476  1.0
  O  O37  1  0.250  0.107  0.479  1.0
  O  O38  1  0.751  0.607  0.521  1.0
  O  O39  1  0.750  0.894  0.524  1.0
  O  O40  1  0.751  0.393  0.521  1.0
  O  O41  1  0.750  0.106  0.524  1.0
  O  O42  1  0.539  1.000  0.737  1.0
  O  O43  1  0.961  1.000  0.737  1.0
  O  O44  1  0.534  0.500  0.727  1.0
  O  O45  1  0.966  0.500  0.727  1.0
  O  O46  1  0.540  0.753  0.771  1.0
  O  O47  1  0.960  0.753  0.771  1.0
  O  O48  1  0.540  0.247  0.771  1.0
  O  O49  1  0.960  0.247  0.771  1.0
  O  O50  1  0.750  0.356  0.983  1.0
  O  O51  1  0.750  0.644  0.983  1.0
  O  O52  1  0.750  0.853  0.986  1.0
  O  O53  1  0.750  0.147  0.986  1.0
[/CIF]
.
The crystal structure described by Na3Mn8O16 is beta indium sulfide-derived structured and crystallizes in the orthorhombic Pmmn space group. There are two inequivalent Na sites. In the first Na site, Na(1) is bonded to two equivalent O(2) and two equivalent O(5) atoms to form NaO4 tetrahedra that share corners with two equivalent Mn(2)O6 octahedra, corners with two equivalent Mn(4)O6 octahedra, corners with four equivalent Mn(1)O6 octahedra, and corners with four equivalent Mn(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 60-67°. In the second Na site, Na(2) is bonded to one O(6), one O(7), and two equivalent O(3) atoms to form NaO4 tetrahedra that share corners with two equivalent Mn(1)O6 octahedra, corners with three equivalent Mn(2)O6 octahedra, corners with three equivalent Mn(3)O6 octahedra, and corners with four equivalent Mn(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 60-63°. There are four inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(3) atoms to form MnO6 octahedra that share corners with two equivalent Na(1)O4 tetrahedra, corners with two equivalent Na(2)O4 tetrahedra, edges with two equivalent Mn(1)O6 octahedra, edges with two equivalent Mn(2)O6 octahedra, and edges with two equivalent Mn(3)O6 octahedra. In the second Mn site, Mn(2) is bonded to one O(2), one O(6), two equivalent O(3), and two equivalent O(4) atoms to form MnO6 octahedra that share  a cornercorner with one Na(1)O4 tetrahedra, corners with three equivalent Na(2)O4 tetrahedra,  an edgeedge with one Mn(2)O6 octahedra,  an edgeedge with one Mn(3)O6 octahedra, edges with two equivalent Mn(1)O6 octahedra, and edges with two equivalent Mn(4)O6 octahedra. In the third Mn site, Mn(3) is bonded to one O(1), one O(7), two equivalent O(3), and two equivalent O(5) atoms to form MnO6 octahedra that share corners with two equivalent Na(1)O4 tetrahedra, corners with three equivalent Na(2)O4 tetrahedra,  an edgeedge with one Mn(2)O6 octahedra,  an edgeedge with one Mn(3)O6 octahedra, edges with two equivalent Mn(1)O6 octahedra, and edges with two equivalent Mn(4)O6 octahedra. In the fourth Mn site, Mn(4) is bonded to one O(4), one O(5), two equivalent O(6), and two equivalent O(7) atoms to form MnO6 octahedra that share  a cornercorner with one Na(1)O4 tetrahedra, corners with four equivalent Na(2)O4 tetrahedra, edges with two equivalent Mn(2)O6 octahedra, edges with two equivalent Mn(3)O6 octahedra, and edges with two equivalent Mn(4)O6 octahedra. There are seven inequivalent O sites. In the first O site, O(5) is bonded to one Na(1), one Mn(4), and two equivalent Mn(3) atoms to form a mixture of edge and corner-sharing ONaMn3 tetrahedra. In the second O site, O(6) is bonded to one Na(2), one Mn(2), and two equivalent Mn(4) atoms to form a mixture of edge and corner-sharing ONaMn3 tetrahedra. In the third O site, O(7) is bonded to one Na(2), one Mn(3), and two equivalent Mn(4) atoms to form a mixture of edge and corner-sharing ONaMn3 tetrahedra. In the fourth O site, O(1) is bonded in a distorted trigonal non-coplanar geometry to one Mn(3) and two equivalent Mn(1) atoms. In the fifth O site, O(2) is bonded to one Na(1), one Mn(2), and two equivalent Mn(1) atoms to form a mixture of edge and corner-sharing ONaMn3 tetrahedra. In the sixth O site, O(3) is bonded to one Na(2), one Mn(1), one Mn(2), and one Mn(3) atom to form a mixture of edge and corner-sharing ONaMn3 tetrahedra. In the seventh O site, O(4) is bonded in a distorted trigonal non-coplanar geometry to one Mn(4) and two equivalent Mn(2) atoms. is represented by the Crystallographic Information File (CIF) [CIF]
data_Na3Mn8O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.168
_cell_length_b   12.374
_cell_length_c   8.432
_cell_angle_alpha   89.998
_cell_angle_beta   89.962
_cell_angle_gamma   90.002
_symmetry_Int_Tables_number   1
_cell_volume   643.513
_cell_formula_units_Z   2
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
  Na  Na0  1  0.750  0.000  0.121  1.0
  Na  Na1  1  0.750  0.749  0.373  1.0
  Na  Na2  1  0.750  0.251  0.373  1.0
  Na  Na3  1  0.250  0.751  0.627  1.0
  Na  Na4  1  0.250  0.249  0.627  1.0
  Na  Na5  1  0.250  0.500  0.879  1.0
  Mn  Mn6  1  0.500  0.250  0.000  1.0
  Mn  Mn7  1  0.500  0.750  1.000  1.0
  Mn  Mn8  1  0.000  0.750  0.000  1.0
  Mn  Mn9  1  0.000  0.250  0.000  1.0
  Mn  Mn10  1  0.250  0.623  0.248  1.0
  Mn  Mn11  1  0.250  0.377  0.248  1.0
  Mn  Mn12  1  0.250  0.876  0.248  1.0
  Mn  Mn13  1  0.250  0.124  0.248  1.0
  Mn  Mn14  1  0.002  1.000  0.503  1.0
  Mn  Mn15  1  0.498  0.000  0.503  1.0
  Mn  Mn16  1  0.502  0.500  0.497  1.0
  Mn  Mn17  1  0.998  0.500  0.497  1.0
  Mn  Mn18  1  0.750  0.624  0.753  1.0
  Mn  Mn19  1  0.750  0.878  0.752  1.0
  Mn  Mn20  1  0.750  0.376  0.753  1.0
  Mn  Mn21  1  0.750  0.123  0.752  1.0
  O  O22  1  0.250  0.856  0.017  1.0
  O  O23  1  0.250  0.647  0.014  1.0
  O  O24  1  0.250  0.144  0.017  1.0
  O  O25  1  0.250  0.353  0.014  1.0
  O  O26  1  0.460  0.747  0.229  1.0
  O  O27  1  0.040  0.747  0.229  1.0
  O  O28  1  0.460  0.253  0.229  1.0
  O  O29  1  0.040  0.253  0.229  1.0
  O  O30  1  0.039  0.500  0.263  1.0
  O  O31  1  0.461  0.500  0.263  1.0
  O  O32  1  0.034  1.000  0.273  1.0
  O  O33  1  0.466  1.000  0.273  1.0
  O  O34  1  0.249  0.394  0.476  1.0
  O  O35  1  0.250  0.893  0.479  1.0
  O  O36  1  0.249  0.606  0.476  1.0
  O  O37  1  0.250  0.107  0.479  1.0
  O  O38  1  0.751  0.607  0.521  1.0
  O  O39  1  0.750  0.894  0.524  1.0
  O  O40  1  0.751  0.393  0.521  1.0
  O  O41  1  0.750  0.106  0.524  1.0
  O  O42  1  0.539  1.000  0.737  1.0
  O  O43  1  0.961  1.000  0.737  1.0
  O  O44  1  0.534  0.500  0.727  1.0
  O  O45  1  0.966  0.500  0.727  1.0
  O  O46  1  0.540  0.753  0.771  1.0
  O  O47  1  0.960  0.753  0.771  1.0
  O  O48  1  0.540  0.247  0.771  1.0
  O  O49  1  0.960  0.247  0.771  1.0
  O  O50  1  0.750  0.356  0.983  1.0
  O  O51  1  0.750  0.644  0.983  1.0
  O  O52  1  0.750  0.853  0.986  1.0
  O  O53  1  0.750  0.147  0.986  1.0
[/CIF]
.