The compound described by Nb19Fe20 is Frank-Kasper $\mu$ Phase-like structured and crystallizes in the trigonal P-3m1 space group. There are ten inequivalent Nb sites. In the first Nb site, Nb(1) is bonded in a 14-coordinate geometry to one Nb(3), one Nb(7), three equivalent Nb(4), three equivalent Nb(6), and six equivalent Fe(3) atoms. In the second Nb site, Nb(2) is bonded in a 14-coordinate geometry to one Nb(2), one Nb(8), six equivalent Nb(5), and six equivalent Fe(2) atoms. In the third Nb site, Nb(3) is bonded in a 14-coordinate geometry to one Nb(1), one Nb(9), three equivalent Nb(4), three equivalent Nb(6), and six equivalent Fe(1) atoms. In the fourth Nb site, Nb(4) is bonded in a 15-coordinate geometry to three equivalent Nb(1), three equivalent Nb(3), three equivalent Nb(6), three equivalent Fe(1), and three equivalent Fe(3) atoms. In the fifth Nb site, Nb(5) is bonded in a 15-coordinate geometry to three equivalent Nb(5), six equivalent Nb(2), and six equivalent Fe(2) atoms. In the sixth Nb site, Nb(6) is bonded in a 15-coordinate geometry to three equivalent Nb(1), three equivalent Nb(3), three equivalent Nb(4), three equivalent Fe(1), and three equivalent Fe(3) atoms. In the seventh Nb site, Nb(7) is bonded in a 16-coordinate geometry to one Nb(1), three equivalent Nb(8), three equivalent Fe(2), three equivalent Fe(4), and six equivalent Fe(3) atoms. In the eighth Nb site, Nb(8) is bonded in a 16-coordinate geometry to one Nb(2), three equivalent Nb(7), three equivalent Fe(3), three equivalent Fe(4), and six equivalent Fe(2) atoms. In the ninth Nb site, Nb(9) is bonded in a 16-coordinate geometry to one Nb(3), three equivalent Nb(10), three equivalent Nb(9), and nine equivalent Fe(1) atoms. In the tenth Nb site, Nb(10) is bonded to six equivalent Nb(9) and six equivalent Fe(1) atoms to form distorted NbNb6Fe6 cuboctahedra that share corners with twelve equivalent Fe(1)Nb8Fe4 cuboctahedra, edges with six equivalent Nb(10)Nb6Fe6 cuboctahedra, and faces with eighteen equivalent Fe(1)Nb8Fe4 cuboctahedra. There are four inequivalent Fe sites. In the first Fe site, Fe(4) is bonded to three equivalent Nb(7), three equivalent Nb(8), three equivalent Fe(2), and three equivalent Fe(3) atoms to form FeNb6Fe6 cuboctahedra that share corners with six equivalent Fe(2)Nb7Fe5 cuboctahedra, corners with six equivalent Fe(3)Nb7Fe5 cuboctahedra, edges with six equivalent Fe(4)Nb6Fe6 cuboctahedra, faces with nine equivalent Fe(2)Nb7Fe5 cuboctahedra, and faces with nine equivalent Fe(3)Nb7Fe5 cuboctahedra. In the second Fe site, Fe(1) is bonded to one Nb(10), one Nb(4), one Nb(6), two equivalent Nb(3), three equivalent Nb(9), and four equivalent Fe(1) atoms to form distorted FeNb8Fe4 cuboctahedra that share corners with two equivalent Nb(10)Nb6Fe6 cuboctahedra, corners with four equivalent Fe(3)Nb7Fe5 cuboctahedra, corners with nine equivalent Fe(1)Nb8Fe4 cuboctahedra,  an edgeedge with one Fe(3)Nb7Fe5 cuboctahedra, edges with four equivalent Fe(1)Nb8Fe4 cuboctahedra, faces with three equivalent Nb(10)Nb6Fe6 cuboctahedra, and faces with ten equivalent Fe(1)Nb8Fe4 cuboctahedra. In the third Fe site, Fe(2) is bonded to one Nb(7), two equivalent Nb(2), two equivalent Nb(5), two equivalent Nb(8), one Fe(4), and four equivalent Fe(2) atoms to form FeNb7Fe5 cuboctahedra that share corners with two equivalent Fe(4)Nb6Fe6 cuboctahedra, corners with five equivalent Fe(3)Nb7Fe5 cuboctahedra, corners with eight equivalent Fe(2)Nb7Fe5 cuboctahedra, edges with two equivalent Fe(3)Nb7Fe5 cuboctahedra, edges with three equivalent Fe(2)Nb7Fe5 cuboctahedra, faces with two equivalent Fe(3)Nb7Fe5 cuboctahedra, faces with three equivalent Fe(4)Nb6Fe6 cuboctahedra, and faces with eight equivalent Fe(2)Nb7Fe5 cuboctahedra. In the fourth Fe site, Fe(3) is bonded to one Nb(4), one Nb(6), one Nb(8), two equivalent Nb(1), two equivalent Nb(7), one Fe(4), and four equivalent Fe(3) atoms to form FeNb7Fe5 cuboctahedra that share corners with two equivalent Fe(4)Nb6Fe6 cuboctahedra, corners with four equivalent Fe(3)Nb7Fe5 cuboctahedra, corners with four equivalent Fe(1)Nb8Fe4 cuboctahedra, corners with five equivalent Fe(2)Nb7Fe5 cuboctahedra,  an edgeedge with one Fe(1)Nb8Fe4 cuboctahedra, edges with two equivalent Fe(2)Nb7Fe5 cuboctahedra, edges with two equivalent Fe(3)Nb7Fe5 cuboctahedra, faces with two equivalent Fe(2)Nb7Fe5 cuboctahedra, faces with three equivalent Fe(4)Nb6Fe6 cuboctahedra, and faces with eight equivalent Fe(3)Nb7Fe5 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_Nb19Fe20
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   4.929
_cell_length_b   4.929
_cell_length_c   26.935
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   566.814
_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
  Nb  Nb0  1  0.333  0.667  0.217  1.0
  Nb  Nb1  1  0.000  0.000  0.549  1.0
  Nb  Nb2  1  0.667  0.333  0.881  1.0
  Nb  Nb3  1  0.333  0.667  0.119  1.0
  Nb  Nb4  1  0.000  0.000  0.451  1.0
  Nb  Nb5  1  0.667  0.333  0.783  1.0
  Nb  Nb6  1  0.667  0.333  0.168  1.0
  Nb  Nb7  1  0.333  0.667  0.500  1.0
  Nb  Nb8  1  0.000  0.000  0.832  1.0
  Nb  Nb9  1  0.000  0.000  0.168  1.0
  Nb  Nb10  1  0.667  0.333  0.500  1.0
  Nb  Nb11  1  0.333  0.667  0.832  1.0
  Nb  Nb12  1  0.333  0.667  0.320  1.0
  Nb  Nb13  1  0.000  0.000  0.653  1.0
  Nb  Nb14  1  0.667  0.333  0.984  1.0
  Nb  Nb15  1  0.333  0.667  0.016  1.0
  Nb  Nb16  1  0.000  0.000  0.347  1.0
  Nb  Nb17  1  0.667  0.333  0.680  1.0
  Nb  Nb18  1  0.000  0.000  0.000  1.0
  Fe  Fe19  1  0.341  0.170  0.079  1.0
  Fe  Fe20  1  1.000  0.500  0.409  1.0
  Fe  Fe21  1  0.666  0.833  0.741  1.0
  Fe  Fe22  1  0.830  0.659  0.079  1.0
  Fe  Fe23  1  0.500  0.000  0.409  1.0
  Fe  Fe24  1  0.167  0.334  0.741  1.0
  Fe  Fe25  1  0.830  0.170  0.079  1.0
  Fe  Fe26  1  0.500  0.500  0.409  1.0
  Fe  Fe27  1  0.167  0.833  0.741  1.0
  Fe  Fe28  1  0.334  0.167  0.259  1.0
  Fe  Fe29  1  0.000  0.500  0.591  1.0
  Fe  Fe30  1  0.659  0.830  0.921  1.0
  Fe  Fe31  1  0.833  0.666  0.259  1.0
  Fe  Fe32  1  0.500  1.000  0.591  1.0
  Fe  Fe33  1  0.170  0.341  0.921  1.0
  Fe  Fe34  1  0.833  0.167  0.259  1.0
  Fe  Fe35  1  0.500  0.500  0.591  1.0
  Fe  Fe36  1  0.170  0.830  0.921  1.0
  Fe  Fe37  1  0.667  0.333  0.334  1.0
  Fe  Fe38  1  0.333  0.667  0.666  1.0
[/CIF]
.
The compound described by Nb19Fe20 is Frank-Kasper $\mu$ Phase-like structured and crystallizes in the trigonal P-3m1 space group. There are ten inequivalent Nb sites. In the first Nb site, Nb(1) is bonded in a 14-coordinate geometry to one Nb(3), one Nb(7), three equivalent Nb(4), three equivalent Nb(6), and six equivalent Fe(3) atoms. In the second Nb site, Nb(2) is bonded in a 14-coordinate geometry to one Nb(2), one Nb(8), six equivalent Nb(5), and six equivalent Fe(2) atoms. In the third Nb site, Nb(3) is bonded in a 14-coordinate geometry to one Nb(1), one Nb(9), three equivalent Nb(4), three equivalent Nb(6), and six equivalent Fe(1) atoms. In the fourth Nb site, Nb(4) is bonded in a 15-coordinate geometry to three equivalent Nb(1), three equivalent Nb(3), three equivalent Nb(6), three equivalent Fe(1), and three equivalent Fe(3) atoms. In the fifth Nb site, Nb(5) is bonded in a 15-coordinate geometry to three equivalent Nb(5), six equivalent Nb(2), and six equivalent Fe(2) atoms. In the sixth Nb site, Nb(6) is bonded in a 15-coordinate geometry to three equivalent Nb(1), three equivalent Nb(3), three equivalent Nb(4), three equivalent Fe(1), and three equivalent Fe(3) atoms. In the seventh Nb site, Nb(7) is bonded in a 16-coordinate geometry to one Nb(1), three equivalent Nb(8), three equivalent Fe(2), three equivalent Fe(4), and six equivalent Fe(3) atoms. In the eighth Nb site, Nb(8) is bonded in a 16-coordinate geometry to one Nb(2), three equivalent Nb(7), three equivalent Fe(3), three equivalent Fe(4), and six equivalent Fe(2) atoms. In the ninth Nb site, Nb(9) is bonded in a 16-coordinate geometry to one Nb(3), three equivalent Nb(10), three equivalent Nb(9), and nine equivalent Fe(1) atoms. In the tenth Nb site, Nb(10) is bonded to six equivalent Nb(9) and six equivalent Fe(1) atoms to form distorted NbNb6Fe6 cuboctahedra that share corners with twelve equivalent Fe(1)Nb8Fe4 cuboctahedra, edges with six equivalent Nb(10)Nb6Fe6 cuboctahedra, and faces with eighteen equivalent Fe(1)Nb8Fe4 cuboctahedra. There are four inequivalent Fe sites. In the first Fe site, Fe(4) is bonded to three equivalent Nb(7), three equivalent Nb(8), three equivalent Fe(2), and three equivalent Fe(3) atoms to form FeNb6Fe6 cuboctahedra that share corners with six equivalent Fe(2)Nb7Fe5 cuboctahedra, corners with six equivalent Fe(3)Nb7Fe5 cuboctahedra, edges with six equivalent Fe(4)Nb6Fe6 cuboctahedra, faces with nine equivalent Fe(2)Nb7Fe5 cuboctahedra, and faces with nine equivalent Fe(3)Nb7Fe5 cuboctahedra. In the second Fe site, Fe(1) is bonded to one Nb(10), one Nb(4), one Nb(6), two equivalent Nb(3), three equivalent Nb(9), and four equivalent Fe(1) atoms to form distorted FeNb8Fe4 cuboctahedra that share corners with two equivalent Nb(10)Nb6Fe6 cuboctahedra, corners with four equivalent Fe(3)Nb7Fe5 cuboctahedra, corners with nine equivalent Fe(1)Nb8Fe4 cuboctahedra,  an edgeedge with one Fe(3)Nb7Fe5 cuboctahedra, edges with four equivalent Fe(1)Nb8Fe4 cuboctahedra, faces with three equivalent Nb(10)Nb6Fe6 cuboctahedra, and faces with ten equivalent Fe(1)Nb8Fe4 cuboctahedra. In the third Fe site, Fe(2) is bonded to one Nb(7), two equivalent Nb(2), two equivalent Nb(5), two equivalent Nb(8), one Fe(4), and four equivalent Fe(2) atoms to form FeNb7Fe5 cuboctahedra that share corners with two equivalent Fe(4)Nb6Fe6 cuboctahedra, corners with five equivalent Fe(3)Nb7Fe5 cuboctahedra, corners with eight equivalent Fe(2)Nb7Fe5 cuboctahedra, edges with two equivalent Fe(3)Nb7Fe5 cuboctahedra, edges with three equivalent Fe(2)Nb7Fe5 cuboctahedra, faces with two equivalent Fe(3)Nb7Fe5 cuboctahedra, faces with three equivalent Fe(4)Nb6Fe6 cuboctahedra, and faces with eight equivalent Fe(2)Nb7Fe5 cuboctahedra. In the fourth Fe site, Fe(3) is bonded to one Nb(4), one Nb(6), one Nb(8), two equivalent Nb(1), two equivalent Nb(7), one Fe(4), and four equivalent Fe(3) atoms to form FeNb7Fe5 cuboctahedra that share corners with two equivalent Fe(4)Nb6Fe6 cuboctahedra, corners with four equivalent Fe(3)Nb7Fe5 cuboctahedra, corners with four equivalent Fe(1)Nb8Fe4 cuboctahedra, corners with five equivalent Fe(2)Nb7Fe5 cuboctahedra,  an edgeedge with one Fe(1)Nb8Fe4 cuboctahedra, edges with two equivalent Fe(2)Nb7Fe5 cuboctahedra, edges with two equivalent Fe(3)Nb7Fe5 cuboctahedra, faces with two equivalent Fe(2)Nb7Fe5 cuboctahedra, faces with three equivalent Fe(4)Nb6Fe6 cuboctahedra, and faces with eight equivalent Fe(3)Nb7Fe5 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_Nb19Fe20
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   4.929
_cell_length_b   4.929
_cell_length_c   26.935
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   566.814
_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
  Nb  Nb0  1  0.333  0.667  0.217  1.0
  Nb  Nb1  1  0.000  0.000  0.549  1.0
  Nb  Nb2  1  0.667  0.333  0.881  1.0
  Nb  Nb3  1  0.333  0.667  0.119  1.0
  Nb  Nb4  1  0.000  0.000  0.451  1.0
  Nb  Nb5  1  0.667  0.333  0.783  1.0
  Nb  Nb6  1  0.667  0.333  0.168  1.0
  Nb  Nb7  1  0.333  0.667  0.500  1.0
  Nb  Nb8  1  0.000  0.000  0.832  1.0
  Nb  Nb9  1  0.000  0.000  0.168  1.0
  Nb  Nb10  1  0.667  0.333  0.500  1.0
  Nb  Nb11  1  0.333  0.667  0.832  1.0
  Nb  Nb12  1  0.333  0.667  0.320  1.0
  Nb  Nb13  1  0.000  0.000  0.653  1.0
  Nb  Nb14  1  0.667  0.333  0.984  1.0
  Nb  Nb15  1  0.333  0.667  0.016  1.0
  Nb  Nb16  1  0.000  0.000  0.347  1.0
  Nb  Nb17  1  0.667  0.333  0.680  1.0
  Nb  Nb18  1  0.000  0.000  0.000  1.0
  Fe  Fe19  1  0.341  0.170  0.079  1.0
  Fe  Fe20  1  1.000  0.500  0.409  1.0
  Fe  Fe21  1  0.666  0.833  0.741  1.0
  Fe  Fe22  1  0.830  0.659  0.079  1.0
  Fe  Fe23  1  0.500  0.000  0.409  1.0
  Fe  Fe24  1  0.167  0.334  0.741  1.0
  Fe  Fe25  1  0.830  0.170  0.079  1.0
  Fe  Fe26  1  0.500  0.500  0.409  1.0
  Fe  Fe27  1  0.167  0.833  0.741  1.0
  Fe  Fe28  1  0.334  0.167  0.259  1.0
  Fe  Fe29  1  0.000  0.500  0.591  1.0
  Fe  Fe30  1  0.659  0.830  0.921  1.0
  Fe  Fe31  1  0.833  0.666  0.259  1.0
  Fe  Fe32  1  0.500  1.000  0.591  1.0
  Fe  Fe33  1  0.170  0.341  0.921  1.0
  Fe  Fe34  1  0.833  0.167  0.259  1.0
  Fe  Fe35  1  0.500  0.500  0.591  1.0
  Fe  Fe36  1  0.170  0.830  0.921  1.0
  Fe  Fe37  1  0.667  0.333  0.334  1.0
  Fe  Fe38  1  0.333  0.667  0.666  1.0
[/CIF]
.