The structure described by Mn3Ti2V is Frank-Kasper $\mu$ Phase-derived structured and crystallizes in the orthorhombic Amm2 space group. There are five inequivalent Ti sites. In the first Ti site, Ti(1) is bonded in a 16-coordinate geometry to one Ti(1), three equivalent Ti(2), four equivalent V(1), one Mn(3), two equivalent Mn(1), two equivalent Mn(2), and three equivalent Mn(4) atoms. In the second Ti site, Ti(2) is bonded in a 16-coordinate geometry to one Ti(2), three equivalent Ti(1), two equivalent V(1), one Mn(1), two equivalent Mn(3), three equivalent Mn(4), and four equivalent Mn(2) atoms. In the third Ti site, Ti(2) is bonded in a 16-coordinate geometry to one Ti(2); three Ti(1,1); two equivalent V(1); one Mn(1); two equivalent Mn(3); three equivalent Mn(4); and four equivalent Mn(2) atoms. In the fourth Ti site, Ti(1) is bonded in a 16-coordinate geometry to one Ti(1), three equivalent Ti(2), four equivalent V(1), one Mn(3), two equivalent Mn(1), two equivalent Mn(2), and three equivalent Mn(4) atoms. In the fifth Ti site, Ti(1) is bonded in a 16-coordinate geometry to one Ti(1), three equivalent Ti(2), four equivalent V(1), one Mn(3), two equivalent Mn(1), two equivalent Mn(2), and three equivalent Mn(4) atoms. V(1) is bonded to two Ti(2,2); four Ti(1,1,1); two equivalent V(1); two equivalent Mn(1); and two equivalent Mn(4) atoms to form distorted VTi6Mn4V2 cuboctahedra that share corners with four equivalent V(1)Ti6Mn4V2 cuboctahedra, corners with four equivalent Mn(4)Ti6Mn4V2 cuboctahedra, corners with four equivalent Mn(3)Ti6Mn6 cuboctahedra, corners with six equivalent Mn(2)Ti6Mn6 cuboctahedra, edges with two equivalent V(1)Ti6Mn4V2 cuboctahedra, edges with four equivalent Mn(2)Ti6Mn6 cuboctahedra, faces with two equivalent Mn(2)Ti6Mn6 cuboctahedra, faces with two equivalent Mn(3)Ti6Mn6 cuboctahedra, faces with four equivalent V(1)Ti6Mn4V2 cuboctahedra, faces with four equivalent Mn(1)Ti6Mn2V4 cuboctahedra, and faces with six equivalent Mn(4)Ti6Mn4V2 cuboctahedra. There are four inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to two Ti(2,2); four Ti(1,1); four equivalent V(1); and two equivalent Mn(4) atoms to form distorted MnTi6Mn2V4 cuboctahedra that share corners with two equivalent Mn(3)Ti6Mn6 cuboctahedra, corners with four equivalent Mn(1)Ti6Mn2V4 cuboctahedra, corners with four equivalent Mn(4)Ti6Mn4V2 cuboctahedra, corners with eight equivalent Mn(2)Ti6Mn6 cuboctahedra, edges with two equivalent Mn(1)Ti6Mn2V4 cuboctahedra, edges with four equivalent Mn(3)Ti6Mn6 cuboctahedra, faces with four equivalent Mn(2)Ti6Mn6 cuboctahedra, faces with six equivalent Mn(4)Ti6Mn4V2 cuboctahedra, and faces with eight equivalent V(1)Ti6Mn4V2 cuboctahedra. In the second Mn site, Mn(2) is bonded to two Ti(1,1); four Ti(2,2); two equivalent Mn(2); two equivalent Mn(3); and two equivalent Mn(4) atoms to form MnTi6Mn6 cuboctahedra that share corners with four equivalent Mn(1)Ti6Mn2V4 cuboctahedra, corners with four equivalent Mn(4)Ti6Mn4V2 cuboctahedra, corners with four equivalent Mn(2)Ti6Mn6 cuboctahedra, corners with six equivalent V(1)Ti6Mn4V2 cuboctahedra, edges with two equivalent Mn(2)Ti6Mn6 cuboctahedra, edges with four equivalent V(1)Ti6Mn4V2 cuboctahedra, faces with two equivalent V(1)Ti6Mn4V2 cuboctahedra, faces with two equivalent Mn(1)Ti6Mn2V4 cuboctahedra, faces with four equivalent Mn(2)Ti6Mn6 cuboctahedra, faces with four equivalent Mn(3)Ti6Mn6 cuboctahedra, and faces with six equivalent Mn(4)Ti6Mn4V2 cuboctahedra. In the third Mn site, Mn(3) is bonded to two Ti(1,1); four Ti(2,2); two equivalent Mn(4); and four equivalent Mn(2) atoms to form MnTi6Mn6 cuboctahedra that share corners with two equivalent Mn(1)Ti6Mn2V4 cuboctahedra, corners with four equivalent Mn(4)Ti6Mn4V2 cuboctahedra, corners with four equivalent Mn(3)Ti6Mn6 cuboctahedra, corners with eight equivalent V(1)Ti6Mn4V2 cuboctahedra, edges with two equivalent Mn(3)Ti6Mn6 cuboctahedra, edges with four equivalent Mn(1)Ti6Mn2V4 cuboctahedra, faces with four equivalent V(1)Ti6Mn4V2 cuboctahedra, faces with six equivalent Mn(4)Ti6Mn4V2 cuboctahedra, and faces with eight equivalent Mn(2)Ti6Mn6 cuboctahedra. In the fourth Mn site, Mn(4) is bonded to three equivalent Ti(1), three equivalent Ti(2), two equivalent V(1), one Mn(1), one Mn(3), and two equivalent Mn(2) atoms to form distorted MnTi6Mn4V2 cuboctahedra that share corners with two equivalent Mn(1)Ti6Mn2V4 cuboctahedra, corners with two equivalent Mn(3)Ti6Mn6 cuboctahedra, corners with four equivalent V(1)Ti6Mn4V2 cuboctahedra, corners with four equivalent Mn(2)Ti6Mn6 cuboctahedra, edges with six equivalent Mn(4)Ti6Mn4V2 cuboctahedra, faces with two equivalent Mn(4)Ti6Mn4V2 cuboctahedra, faces with three equivalent Mn(1)Ti6Mn2V4 cuboctahedra, faces with three equivalent Mn(3)Ti6Mn6 cuboctahedra, faces with six equivalent V(1)Ti6Mn4V2 cuboctahedra, and faces with six equivalent Mn(2)Ti6Mn6 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_Ti2Mn3V
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   4.786
_cell_length_b   4.786
_cell_length_c   7.898
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   119.236
_symmetry_Int_Tables_number   1
_cell_volume   157.891
_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
  Ti  Ti0  1  0.667  0.333  0.303  1.0
  Ti  Ti1  1  0.333  0.667  0.183  1.0
  Ti  Ti2  1  0.333  0.667  0.817  1.0
  Ti  Ti3  1  0.667  0.333  0.697  1.0
  Mn  Mn4  1  0.170  0.830  0.500  1.0
  Mn  Mn5  1  0.343  0.171  0.000  1.0
  Mn  Mn6  1  0.829  0.657  0.000  1.0
  Mn  Mn7  1  0.828  0.172  0.000  1.0
  Mn  Mn8  1  0.002  0.998  0.241  1.0
  Mn  Mn9  1  0.002  0.998  0.759  1.0
  V  V10  1  0.662  0.834  0.500  1.0
  V  V11  1  0.166  0.338  0.500  1.0
[/CIF]
.
The structure described by Mn3Ti2V is Frank-Kasper $\mu$ Phase-derived structured and crystallizes in the orthorhombic Amm2 space group. There are five inequivalent Ti sites. In the first Ti site, Ti(1) is bonded in a 16-coordinate geometry to one Ti(1), three equivalent Ti(2), four equivalent V(1), one Mn(3), two equivalent Mn(1), two equivalent Mn(2), and three equivalent Mn(4) atoms. In the second Ti site, Ti(2) is bonded in a 16-coordinate geometry to one Ti(2), three equivalent Ti(1), two equivalent V(1), one Mn(1), two equivalent Mn(3), three equivalent Mn(4), and four equivalent Mn(2) atoms. In the third Ti site, Ti(2) is bonded in a 16-coordinate geometry to one Ti(2); three Ti(1,1); two equivalent V(1); one Mn(1); two equivalent Mn(3); three equivalent Mn(4); and four equivalent Mn(2) atoms. In the fourth Ti site, Ti(1) is bonded in a 16-coordinate geometry to one Ti(1), three equivalent Ti(2), four equivalent V(1), one Mn(3), two equivalent Mn(1), two equivalent Mn(2), and three equivalent Mn(4) atoms. In the fifth Ti site, Ti(1) is bonded in a 16-coordinate geometry to one Ti(1), three equivalent Ti(2), four equivalent V(1), one Mn(3), two equivalent Mn(1), two equivalent Mn(2), and three equivalent Mn(4) atoms. V(1) is bonded to two Ti(2,2); four Ti(1,1,1); two equivalent V(1); two equivalent Mn(1); and two equivalent Mn(4) atoms to form distorted VTi6Mn4V2 cuboctahedra that share corners with four equivalent V(1)Ti6Mn4V2 cuboctahedra, corners with four equivalent Mn(4)Ti6Mn4V2 cuboctahedra, corners with four equivalent Mn(3)Ti6Mn6 cuboctahedra, corners with six equivalent Mn(2)Ti6Mn6 cuboctahedra, edges with two equivalent V(1)Ti6Mn4V2 cuboctahedra, edges with four equivalent Mn(2)Ti6Mn6 cuboctahedra, faces with two equivalent Mn(2)Ti6Mn6 cuboctahedra, faces with two equivalent Mn(3)Ti6Mn6 cuboctahedra, faces with four equivalent V(1)Ti6Mn4V2 cuboctahedra, faces with four equivalent Mn(1)Ti6Mn2V4 cuboctahedra, and faces with six equivalent Mn(4)Ti6Mn4V2 cuboctahedra. There are four inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to two Ti(2,2); four Ti(1,1); four equivalent V(1); and two equivalent Mn(4) atoms to form distorted MnTi6Mn2V4 cuboctahedra that share corners with two equivalent Mn(3)Ti6Mn6 cuboctahedra, corners with four equivalent Mn(1)Ti6Mn2V4 cuboctahedra, corners with four equivalent Mn(4)Ti6Mn4V2 cuboctahedra, corners with eight equivalent Mn(2)Ti6Mn6 cuboctahedra, edges with two equivalent Mn(1)Ti6Mn2V4 cuboctahedra, edges with four equivalent Mn(3)Ti6Mn6 cuboctahedra, faces with four equivalent Mn(2)Ti6Mn6 cuboctahedra, faces with six equivalent Mn(4)Ti6Mn4V2 cuboctahedra, and faces with eight equivalent V(1)Ti6Mn4V2 cuboctahedra. In the second Mn site, Mn(2) is bonded to two Ti(1,1); four Ti(2,2); two equivalent Mn(2); two equivalent Mn(3); and two equivalent Mn(4) atoms to form MnTi6Mn6 cuboctahedra that share corners with four equivalent Mn(1)Ti6Mn2V4 cuboctahedra, corners with four equivalent Mn(4)Ti6Mn4V2 cuboctahedra, corners with four equivalent Mn(2)Ti6Mn6 cuboctahedra, corners with six equivalent V(1)Ti6Mn4V2 cuboctahedra, edges with two equivalent Mn(2)Ti6Mn6 cuboctahedra, edges with four equivalent V(1)Ti6Mn4V2 cuboctahedra, faces with two equivalent V(1)Ti6Mn4V2 cuboctahedra, faces with two equivalent Mn(1)Ti6Mn2V4 cuboctahedra, faces with four equivalent Mn(2)Ti6Mn6 cuboctahedra, faces with four equivalent Mn(3)Ti6Mn6 cuboctahedra, and faces with six equivalent Mn(4)Ti6Mn4V2 cuboctahedra. In the third Mn site, Mn(3) is bonded to two Ti(1,1); four Ti(2,2); two equivalent Mn(4); and four equivalent Mn(2) atoms to form MnTi6Mn6 cuboctahedra that share corners with two equivalent Mn(1)Ti6Mn2V4 cuboctahedra, corners with four equivalent Mn(4)Ti6Mn4V2 cuboctahedra, corners with four equivalent Mn(3)Ti6Mn6 cuboctahedra, corners with eight equivalent V(1)Ti6Mn4V2 cuboctahedra, edges with two equivalent Mn(3)Ti6Mn6 cuboctahedra, edges with four equivalent Mn(1)Ti6Mn2V4 cuboctahedra, faces with four equivalent V(1)Ti6Mn4V2 cuboctahedra, faces with six equivalent Mn(4)Ti6Mn4V2 cuboctahedra, and faces with eight equivalent Mn(2)Ti6Mn6 cuboctahedra. In the fourth Mn site, Mn(4) is bonded to three equivalent Ti(1), three equivalent Ti(2), two equivalent V(1), one Mn(1), one Mn(3), and two equivalent Mn(2) atoms to form distorted MnTi6Mn4V2 cuboctahedra that share corners with two equivalent Mn(1)Ti6Mn2V4 cuboctahedra, corners with two equivalent Mn(3)Ti6Mn6 cuboctahedra, corners with four equivalent V(1)Ti6Mn4V2 cuboctahedra, corners with four equivalent Mn(2)Ti6Mn6 cuboctahedra, edges with six equivalent Mn(4)Ti6Mn4V2 cuboctahedra, faces with two equivalent Mn(4)Ti6Mn4V2 cuboctahedra, faces with three equivalent Mn(1)Ti6Mn2V4 cuboctahedra, faces with three equivalent Mn(3)Ti6Mn6 cuboctahedra, faces with six equivalent V(1)Ti6Mn4V2 cuboctahedra, and faces with six equivalent Mn(2)Ti6Mn6 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_Ti2Mn3V
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   4.786
_cell_length_b   4.786
_cell_length_c   7.898
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   119.236
_symmetry_Int_Tables_number   1
_cell_volume   157.891
_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
  Ti  Ti0  1  0.667  0.333  0.303  1.0
  Ti  Ti1  1  0.333  0.667  0.183  1.0
  Ti  Ti2  1  0.333  0.667  0.817  1.0
  Ti  Ti3  1  0.667  0.333  0.697  1.0
  Mn  Mn4  1  0.170  0.830  0.500  1.0
  Mn  Mn5  1  0.343  0.171  0.000  1.0
  Mn  Mn6  1  0.829  0.657  0.000  1.0
  Mn  Mn7  1  0.828  0.172  0.000  1.0
  Mn  Mn8  1  0.002  0.998  0.241  1.0
  Mn  Mn9  1  0.002  0.998  0.759  1.0
  V  V10  1  0.662  0.834  0.500  1.0
  V  V11  1  0.166  0.338  0.500  1.0
[/CIF]
.