The structure described by Mg7Dy13Co4 crystallizes in the trigonal R3m space group. There are three inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to three equivalent Mg(2), three equivalent Dy(2), three equivalent Dy(4), and three equivalent Dy(5) atoms to form MgDy9Mg3 cuboctahedra that share corners with three equivalent Mg(2)Dy7Mg5 cuboctahedra, edges with three equivalent Mg(3)Dy8Mg2Co2 cuboctahedra, faces with three equivalent Mg(2)Dy7Mg5 cuboctahedra, and faces with six equivalent Mg(3)Dy8Mg2Co2 cuboctahedra. In the second Mg site, Mg(2) is bonded to one Mg(1), two equivalent Mg(2), two equivalent Mg(3), one Dy(2), one Dy(3), one Dy(5), two equivalent Dy(1), and two equivalent Dy(4) atoms to form MgDy7Mg5 cuboctahedra that share  a cornercorner with one Mg(1)Dy9Mg3 cuboctahedra, corners with two equivalent Mg(2)Dy7Mg5 cuboctahedra, corners with two equivalent Mg(3)Dy8Mg2Co2 cuboctahedra,  a faceface with one Mg(1)Dy9Mg3 cuboctahedra, faces with two equivalent Mg(2)Dy7Mg5 cuboctahedra, and faces with four equivalent Mg(3)Dy8Mg2Co2 cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(2), two equivalent Dy(1), two equivalent Dy(2), two equivalent Dy(4), two equivalent Dy(5), one Co(1), and one Co(2) atom to form distorted MgDy8Mg2Co2 cuboctahedra that share corners with two equivalent Mg(2)Dy7Mg5 cuboctahedra,  an edgeedge with one Mg(1)Dy9Mg3 cuboctahedra, faces with two equivalent Mg(1)Dy9Mg3 cuboctahedra, faces with four equivalent Mg(2)Dy7Mg5 cuboctahedra, and faces with four equivalent Mg(3)Dy8Mg2Co2 cuboctahedra. There are five inequivalent Dy sites. In the first Dy site, Dy(1) is bonded in a bent 150 degrees geometry to two equivalent Mg(2), two equivalent Mg(3), two equivalent Dy(5), one Co(1), and one Co(2) atom. In the second Dy site, Dy(2) is bonded in a bent 150 degrees geometry to one Mg(1), one Mg(2), two equivalent Mg(3), two equivalent Dy(5), and two equivalent Co(2) atoms. In the third Dy site, Dy(3) is bonded in a 3-coordinate geometry to three equivalent Mg(2), three equivalent Dy(5), and three equivalent Co(2) atoms. In the fourth Dy site, Dy(4) is bonded in a 3-coordinate geometry to one Mg(1), two equivalent Mg(2), two equivalent Mg(3), one Dy(5), one Co(1), and two equivalent Co(2) atoms. In the fifth Dy site, Dy(5) is bonded in a 14-coordinate geometry to one Mg(1), one Mg(2), two equivalent Mg(3), one Dy(3), one Dy(4), two equivalent Dy(1), two equivalent Dy(2), two equivalent Dy(5), and two equivalent Co(2) atoms. There are two inequivalent Co sites. In the first Co site, Co(1) is bonded in a 6-coordinate geometry to three equivalent Mg(3), three equivalent Dy(1), and three equivalent Dy(4) atoms. In the second Co site, Co(2) is bonded in a 6-coordinate geometry to one Mg(3), one Dy(1), one Dy(3), two equivalent Dy(2), two equivalent Dy(4), and two equivalent Dy(5) atoms. is represented by the CIF file [CIF]
data_Dy13Mg7Co4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   9.445
_cell_length_b   9.445
_cell_length_c   9.445
_cell_angle_alpha   60.426
_cell_angle_beta   60.426
_cell_angle_gamma   60.426
_symmetry_Int_Tables_number   1
_cell_volume   601.451
_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
  Dy  Dy0  1  0.188  0.188  0.812  1.0
  Dy  Dy1  1  0.812  0.188  0.188  1.0
  Dy  Dy2  1  0.188  0.812  0.188  1.0
  Dy  Dy3  1  0.810  0.810  0.189  1.0
  Dy  Dy4  1  0.189  0.810  0.810  1.0
  Dy  Dy5  1  0.810  0.189  0.810  1.0
  Dy  Dy6  1  0.345  0.345  0.345  1.0
  Dy  Dy7  1  0.342  0.967  0.342  1.0
  Dy  Dy8  1  0.967  0.342  0.342  1.0
  Dy  Dy9  1  0.342  0.342  0.967  1.0
  Dy  Dy10  1  0.562  0.562  0.940  1.0
  Dy  Dy11  1  0.940  0.562  0.562  1.0
  Dy  Dy12  1  0.562  0.940  0.562  1.0
  Mg  Mg13  1  0.580  0.580  0.580  1.0
  Mg  Mg14  1  0.583  0.256  0.583  1.0
  Mg  Mg15  1  0.256  0.583  0.583  1.0
  Mg  Mg16  1  0.583  0.583  0.256  1.0
  Mg  Mg17  1  0.939  0.939  0.559  1.0
  Mg  Mg18  1  0.559  0.939  0.939  1.0
  Mg  Mg19  1  0.939  0.559  0.939  1.0
  Co  Co20  1  0.140  0.140  0.140  1.0
  Co  Co21  1  0.141  0.584  0.141  1.0
  Co  Co22  1  0.584  0.141  0.141  1.0
  Co  Co23  1  0.141  0.141  0.584  1.0
[/CIF]
.
The structure described by Mg7Dy13Co4 crystallizes in the trigonal R3m space group. There are three inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to three equivalent Mg(2), three equivalent Dy(2), three equivalent Dy(4), and three equivalent Dy(5) atoms to form MgDy9Mg3 cuboctahedra that share corners with three equivalent Mg(2)Dy7Mg5 cuboctahedra, edges with three equivalent Mg(3)Dy8Mg2Co2 cuboctahedra, faces with three equivalent Mg(2)Dy7Mg5 cuboctahedra, and faces with six equivalent Mg(3)Dy8Mg2Co2 cuboctahedra. In the second Mg site, Mg(2) is bonded to one Mg(1), two equivalent Mg(2), two equivalent Mg(3), one Dy(2), one Dy(3), one Dy(5), two equivalent Dy(1), and two equivalent Dy(4) atoms to form MgDy7Mg5 cuboctahedra that share  a cornercorner with one Mg(1)Dy9Mg3 cuboctahedra, corners with two equivalent Mg(2)Dy7Mg5 cuboctahedra, corners with two equivalent Mg(3)Dy8Mg2Co2 cuboctahedra,  a faceface with one Mg(1)Dy9Mg3 cuboctahedra, faces with two equivalent Mg(2)Dy7Mg5 cuboctahedra, and faces with four equivalent Mg(3)Dy8Mg2Co2 cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(2), two equivalent Dy(1), two equivalent Dy(2), two equivalent Dy(4), two equivalent Dy(5), one Co(1), and one Co(2) atom to form distorted MgDy8Mg2Co2 cuboctahedra that share corners with two equivalent Mg(2)Dy7Mg5 cuboctahedra,  an edgeedge with one Mg(1)Dy9Mg3 cuboctahedra, faces with two equivalent Mg(1)Dy9Mg3 cuboctahedra, faces with four equivalent Mg(2)Dy7Mg5 cuboctahedra, and faces with four equivalent Mg(3)Dy8Mg2Co2 cuboctahedra. There are five inequivalent Dy sites. In the first Dy site, Dy(1) is bonded in a bent 150 degrees geometry to two equivalent Mg(2), two equivalent Mg(3), two equivalent Dy(5), one Co(1), and one Co(2) atom. In the second Dy site, Dy(2) is bonded in a bent 150 degrees geometry to one Mg(1), one Mg(2), two equivalent Mg(3), two equivalent Dy(5), and two equivalent Co(2) atoms. In the third Dy site, Dy(3) is bonded in a 3-coordinate geometry to three equivalent Mg(2), three equivalent Dy(5), and three equivalent Co(2) atoms. In the fourth Dy site, Dy(4) is bonded in a 3-coordinate geometry to one Mg(1), two equivalent Mg(2), two equivalent Mg(3), one Dy(5), one Co(1), and two equivalent Co(2) atoms. In the fifth Dy site, Dy(5) is bonded in a 14-coordinate geometry to one Mg(1), one Mg(2), two equivalent Mg(3), one Dy(3), one Dy(4), two equivalent Dy(1), two equivalent Dy(2), two equivalent Dy(5), and two equivalent Co(2) atoms. There are two inequivalent Co sites. In the first Co site, Co(1) is bonded in a 6-coordinate geometry to three equivalent Mg(3), three equivalent Dy(1), and three equivalent Dy(4) atoms. In the second Co site, Co(2) is bonded in a 6-coordinate geometry to one Mg(3), one Dy(1), one Dy(3), two equivalent Dy(2), two equivalent Dy(4), and two equivalent Dy(5) atoms. is represented by the CIF file [CIF]
data_Dy13Mg7Co4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   9.445
_cell_length_b   9.445
_cell_length_c   9.445
_cell_angle_alpha   60.426
_cell_angle_beta   60.426
_cell_angle_gamma   60.426
_symmetry_Int_Tables_number   1
_cell_volume   601.451
_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
  Dy  Dy0  1  0.188  0.188  0.812  1.0
  Dy  Dy1  1  0.812  0.188  0.188  1.0
  Dy  Dy2  1  0.188  0.812  0.188  1.0
  Dy  Dy3  1  0.810  0.810  0.189  1.0
  Dy  Dy4  1  0.189  0.810  0.810  1.0
  Dy  Dy5  1  0.810  0.189  0.810  1.0
  Dy  Dy6  1  0.345  0.345  0.345  1.0
  Dy  Dy7  1  0.342  0.967  0.342  1.0
  Dy  Dy8  1  0.967  0.342  0.342  1.0
  Dy  Dy9  1  0.342  0.342  0.967  1.0
  Dy  Dy10  1  0.562  0.562  0.940  1.0
  Dy  Dy11  1  0.940  0.562  0.562  1.0
  Dy  Dy12  1  0.562  0.940  0.562  1.0
  Mg  Mg13  1  0.580  0.580  0.580  1.0
  Mg  Mg14  1  0.583  0.256  0.583  1.0
  Mg  Mg15  1  0.256  0.583  0.583  1.0
  Mg  Mg16  1  0.583  0.583  0.256  1.0
  Mg  Mg17  1  0.939  0.939  0.559  1.0
  Mg  Mg18  1  0.559  0.939  0.939  1.0
  Mg  Mg19  1  0.939  0.559  0.939  1.0
  Co  Co20  1  0.140  0.140  0.140  1.0
  Co  Co21  1  0.141  0.584  0.141  1.0
  Co  Co22  1  0.584  0.141  0.141  1.0
  Co  Co23  1  0.141  0.141  0.584  1.0
[/CIF]
.