The crystal structure described by CrCoV is Frank-Kasper $\mu$ Phase-derived structured and crystallizes in the orthorhombic Amm2 space group. There are five inequivalent V sites. In the first V site, V(1) is bonded in a 16-coordinate geometry to one V(1), three equivalent V(2), one Cr(3), two equivalent Cr(1), two equivalent Cr(2), three equivalent Co(1), and four equivalent Co(2) atoms. In the second V site, V(2) is bonded in a 16-coordinate geometry to one V(2); three V(1,1); one Cr(1); two equivalent Cr(3); four equivalent Cr(2); two equivalent Co(2); and three equivalent Co(1) atoms. In the third V site, V(2) is bonded in a 16-coordinate geometry to one V(2), three equivalent V(1), one Cr(1), two equivalent Cr(3), four equivalent Cr(2), two equivalent Co(2), and three equivalent Co(1) atoms. In the fourth V site, V(1) is bonded in a 16-coordinate geometry to one V(1), three equivalent V(2), one Cr(3), two equivalent Cr(1), two equivalent Cr(2), three equivalent Co(1), and four equivalent Co(2) atoms. In the fifth V site, V(1) is bonded in a 16-coordinate geometry to one V(1), three equivalent V(2), one Cr(3), two equivalent Cr(1), two equivalent Cr(2), three equivalent Co(1), and four equivalent Co(2) atoms. There are three inequivalent Cr sites. In the first Cr site, Cr(1) is bonded in a 6-coordinate geometry to two V(2,2); four V(1,1); two equivalent Co(1); and four equivalent Co(2) atoms. In the second Cr site, Cr(2) is bonded to two V(1,1); four V(2,2); two equivalent Cr(2); two equivalent Cr(3); and two equivalent Co(1) atoms to form distorted CrV6Cr4Co2 cuboctahedra that share corners with four equivalent Cr(2)V6Cr4Co2 cuboctahedra, corners with four equivalent Co(1)V6Cr4Co2 cuboctahedra, corners with six equivalent Co(2)V6Cr2Co4 cuboctahedra, edges with two equivalent Cr(2)V6Cr4Co2 cuboctahedra, edges with four equivalent Co(2)V6Cr2Co4 cuboctahedra, faces with two equivalent Co(2)V6Cr2Co4 cuboctahedra, faces with four equivalent Cr(2)V6Cr4Co2 cuboctahedra, faces with four equivalent Cr(3)V6Cr4Co2 cuboctahedra, and faces with six equivalent Co(1)V6Cr4Co2 cuboctahedra. In the third Cr site, Cr(3) is bonded to two V(1,1); four V(2,2); four equivalent Cr(2); and two equivalent Co(1) atoms to form distorted CrV6Cr4Co2 cuboctahedra that share corners with four equivalent Cr(3)V6Cr4Co2 cuboctahedra, corners with four equivalent Co(1)V6Cr4Co2 cuboctahedra, corners with eight equivalent Co(2)V6Cr2Co4 cuboctahedra, edges with two equivalent Cr(3)V6Cr4Co2 cuboctahedra, faces with four equivalent Co(2)V6Cr2Co4 cuboctahedra, faces with six equivalent Co(1)V6Cr4Co2 cuboctahedra, and faces with eight equivalent Cr(2)V6Cr4Co2 cuboctahedra. There are two inequivalent Co sites. In the first Co site, Co(1) is bonded to three V(1,1); three equivalent V(2); one Cr(1); one Cr(3); two equivalent Cr(2); and two equivalent Co(2) atoms to form CoV6Cr4Co2 cuboctahedra that share corners with two equivalent Cr(3)V6Cr4Co2 cuboctahedra, corners with four equivalent Cr(2)V6Cr4Co2 cuboctahedra, corners with four equivalent Co(2)V6Cr2Co4 cuboctahedra, edges with six equivalent Co(1)V6Cr4Co2 cuboctahedra, faces with two equivalent Co(1)V6Cr4Co2 cuboctahedra, faces with three equivalent Cr(3)V6Cr4Co2 cuboctahedra, faces with six equivalent Cr(2)V6Cr4Co2 cuboctahedra, and faces with six equivalent Co(2)V6Cr2Co4 cuboctahedra. In the second Co site, Co(2) is bonded to two V(2,2); four V(1,1,1); two equivalent Cr(1); two equivalent Co(1); and two equivalent Co(2) atoms to form distorted CoV6Cr2Co4 cuboctahedra that share corners with four equivalent Cr(3)V6Cr4Co2 cuboctahedra, corners with four equivalent Co(2)V6Cr2Co4 cuboctahedra, corners with four equivalent Co(1)V6Cr4Co2 cuboctahedra, corners with six equivalent Cr(2)V6Cr4Co2 cuboctahedra, edges with two equivalent Co(2)V6Cr2Co4 cuboctahedra, edges with four equivalent Cr(2)V6Cr4Co2 cuboctahedra, faces with two equivalent Cr(2)V6Cr4Co2 cuboctahedra, faces with two equivalent Cr(3)V6Cr4Co2 cuboctahedra, faces with four equivalent Co(2)V6Cr2Co4 cuboctahedra, and faces with six equivalent Co(1)V6Cr4Co2 cuboctahedra. is represented by the CIF file [CIF]
data_VCrCo
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   4.620
_cell_length_b   4.620
_cell_length_c   7.744
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   119.161
_symmetry_Int_Tables_number   1
_cell_volume   144.332
_cell_formula_units_Z   4
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
  V  V0  1  0.669  0.331  0.316  1.0
  V  V1  1  0.338  0.662  0.191  1.0
  V  V2  1  0.338  0.662  0.809  1.0
  V  V3  1  0.669  0.331  0.684  1.0
  Cr  Cr4  1  0.169  0.831  0.500  1.0
  Cr  Cr5  1  0.343  0.170  0.000  1.0
  Cr  Cr6  1  0.830  0.657  0.000  1.0
  Cr  Cr7  1  0.828  0.172  0.000  1.0
  Co  Co8  1  1.000  0.000  0.256  1.0
  Co  Co9  1  1.000  0.000  0.744  1.0
  Co  Co10  1  0.653  0.838  0.500  1.0
  Co  Co11  1  0.162  0.347  0.500  1.0
[/CIF]
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The crystal structure described by CrCoV is Frank-Kasper $\mu$ Phase-derived structured and crystallizes in the orthorhombic Amm2 space group. There are five inequivalent V sites. In the first V site, V(1) is bonded in a 16-coordinate geometry to one V(1), three equivalent V(2), one Cr(3), two equivalent Cr(1), two equivalent Cr(2), three equivalent Co(1), and four equivalent Co(2) atoms. In the second V site, V(2) is bonded in a 16-coordinate geometry to one V(2); three V(1,1); one Cr(1); two equivalent Cr(3); four equivalent Cr(2); two equivalent Co(2); and three equivalent Co(1) atoms. In the third V site, V(2) is bonded in a 16-coordinate geometry to one V(2), three equivalent V(1), one Cr(1), two equivalent Cr(3), four equivalent Cr(2), two equivalent Co(2), and three equivalent Co(1) atoms. In the fourth V site, V(1) is bonded in a 16-coordinate geometry to one V(1), three equivalent V(2), one Cr(3), two equivalent Cr(1), two equivalent Cr(2), three equivalent Co(1), and four equivalent Co(2) atoms. In the fifth V site, V(1) is bonded in a 16-coordinate geometry to one V(1), three equivalent V(2), one Cr(3), two equivalent Cr(1), two equivalent Cr(2), three equivalent Co(1), and four equivalent Co(2) atoms. There are three inequivalent Cr sites. In the first Cr site, Cr(1) is bonded in a 6-coordinate geometry to two V(2,2); four V(1,1); two equivalent Co(1); and four equivalent Co(2) atoms. In the second Cr site, Cr(2) is bonded to two V(1,1); four V(2,2); two equivalent Cr(2); two equivalent Cr(3); and two equivalent Co(1) atoms to form distorted CrV6Cr4Co2 cuboctahedra that share corners with four equivalent Cr(2)V6Cr4Co2 cuboctahedra, corners with four equivalent Co(1)V6Cr4Co2 cuboctahedra, corners with six equivalent Co(2)V6Cr2Co4 cuboctahedra, edges with two equivalent Cr(2)V6Cr4Co2 cuboctahedra, edges with four equivalent Co(2)V6Cr2Co4 cuboctahedra, faces with two equivalent Co(2)V6Cr2Co4 cuboctahedra, faces with four equivalent Cr(2)V6Cr4Co2 cuboctahedra, faces with four equivalent Cr(3)V6Cr4Co2 cuboctahedra, and faces with six equivalent Co(1)V6Cr4Co2 cuboctahedra. In the third Cr site, Cr(3) is bonded to two V(1,1); four V(2,2); four equivalent Cr(2); and two equivalent Co(1) atoms to form distorted CrV6Cr4Co2 cuboctahedra that share corners with four equivalent Cr(3)V6Cr4Co2 cuboctahedra, corners with four equivalent Co(1)V6Cr4Co2 cuboctahedra, corners with eight equivalent Co(2)V6Cr2Co4 cuboctahedra, edges with two equivalent Cr(3)V6Cr4Co2 cuboctahedra, faces with four equivalent Co(2)V6Cr2Co4 cuboctahedra, faces with six equivalent Co(1)V6Cr4Co2 cuboctahedra, and faces with eight equivalent Cr(2)V6Cr4Co2 cuboctahedra. There are two inequivalent Co sites. In the first Co site, Co(1) is bonded to three V(1,1); three equivalent V(2); one Cr(1); one Cr(3); two equivalent Cr(2); and two equivalent Co(2) atoms to form CoV6Cr4Co2 cuboctahedra that share corners with two equivalent Cr(3)V6Cr4Co2 cuboctahedra, corners with four equivalent Cr(2)V6Cr4Co2 cuboctahedra, corners with four equivalent Co(2)V6Cr2Co4 cuboctahedra, edges with six equivalent Co(1)V6Cr4Co2 cuboctahedra, faces with two equivalent Co(1)V6Cr4Co2 cuboctahedra, faces with three equivalent Cr(3)V6Cr4Co2 cuboctahedra, faces with six equivalent Cr(2)V6Cr4Co2 cuboctahedra, and faces with six equivalent Co(2)V6Cr2Co4 cuboctahedra. In the second Co site, Co(2) is bonded to two V(2,2); four V(1,1,1); two equivalent Cr(1); two equivalent Co(1); and two equivalent Co(2) atoms to form distorted CoV6Cr2Co4 cuboctahedra that share corners with four equivalent Cr(3)V6Cr4Co2 cuboctahedra, corners with four equivalent Co(2)V6Cr2Co4 cuboctahedra, corners with four equivalent Co(1)V6Cr4Co2 cuboctahedra, corners with six equivalent Cr(2)V6Cr4Co2 cuboctahedra, edges with two equivalent Co(2)V6Cr2Co4 cuboctahedra, edges with four equivalent Cr(2)V6Cr4Co2 cuboctahedra, faces with two equivalent Cr(2)V6Cr4Co2 cuboctahedra, faces with two equivalent Cr(3)V6Cr4Co2 cuboctahedra, faces with four equivalent Co(2)V6Cr2Co4 cuboctahedra, and faces with six equivalent Co(1)V6Cr4Co2 cuboctahedra. is represented by the CIF file [CIF]
data_VCrCo
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   4.620
_cell_length_b   4.620
_cell_length_c   7.744
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   119.161
_symmetry_Int_Tables_number   1
_cell_volume   144.332
_cell_formula_units_Z   4
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
  V  V0  1  0.669  0.331  0.316  1.0
  V  V1  1  0.338  0.662  0.191  1.0
  V  V2  1  0.338  0.662  0.809  1.0
  V  V3  1  0.669  0.331  0.684  1.0
  Cr  Cr4  1  0.169  0.831  0.500  1.0
  Cr  Cr5  1  0.343  0.170  0.000  1.0
  Cr  Cr6  1  0.830  0.657  0.000  1.0
  Cr  Cr7  1  0.828  0.172  0.000  1.0
  Co  Co8  1  1.000  0.000  0.256  1.0
  Co  Co9  1  1.000  0.000  0.744  1.0
  Co  Co10  1  0.653  0.838  0.500  1.0
  Co  Co11  1  0.162  0.347  0.500  1.0
[/CIF]
.