The crystal structure described by KMg14Zr crystallizes in the hexagonal P-6m2 space group. K(1) is bonded to six Mg(2,2) and six Mg(3,3) atoms to form KMg12 cuboctahedra that share corners with six equivalent K(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(1)Mg10Zr2 cuboctahedra; edges with six Mg(2,2)K2Mg10 cuboctahedra; edges with twelve Mg(3,3)KMg10Zr cuboctahedra; faces with two equivalent Zr(1)Mg12 cuboctahedra; faces with six Mg(2,2)K2Mg10 cuboctahedra; faces with six Mg(3,3)KMg10Zr cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. There are six inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(4); four equivalent Mg(1); four Mg(3,3); and two equivalent Zr(1) atoms to form MgMg10Zr2 cuboctahedra that share corners with four equivalent K(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Zr2 cuboctahedra; corners with eight Mg(2,2)K2Mg10 cuboctahedra; edges with two equivalent Zr(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Mg10Zr2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)KMg10Zr cuboctahedra; faces with two equivalent Mg(2)K2Mg10 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Zr(1)Mg12 cuboctahedra; faces with four equivalent Mg(1)Mg10Zr2 cuboctahedra; and faces with ten Mg(3,3)KMg10Zr cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent K(1); two equivalent Mg(4); four Mg(2,2); and four Mg(3,3) atoms to form distorted MgK2Mg10 cuboctahedra that share corners with four equivalent Zr(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)K2Mg10 cuboctahedra; corners with eight equivalent Mg(1)Mg10Zr2 cuboctahedra; edges with two equivalent K(1)Mg12 cuboctahedra; edges with four Mg(2,2)K2Mg10 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)KMg10Zr cuboctahedra; faces with two equivalent K(1)Mg12 cuboctahedra; faces with two equivalent Mg(1)Mg10Zr2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with four Mg(2,2)K2Mg10 cuboctahedra; and faces with ten Mg(3,3)KMg10Zr cuboctahedra. In the third Mg site, Mg(2) is bonded to two equivalent K(1); two equivalent Mg(4); four equivalent Mg(2); and four Mg(3,3) atoms to form distorted MgK2Mg10 cuboctahedra that share corners with four equivalent Zr(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)K2Mg10 cuboctahedra; corners with eight equivalent Mg(1)Mg10Zr2 cuboctahedra; edges with two equivalent K(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)K2Mg10 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)KMg10Zr cuboctahedra; faces with two equivalent K(1)Mg12 cuboctahedra; faces with two equivalent Mg(1)Mg10Zr2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with four equivalent Mg(2)K2Mg10 cuboctahedra; and faces with ten Mg(3,3)KMg10Zr cuboctahedra. In the fourth Mg site, Mg(3) is bonded to one K(1); two equivalent Mg(1); two equivalent Mg(2); two equivalent Mg(4); four Mg(3,3); and one Zr(1) atom to form distorted MgKMg10Zr cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)KMg10Zr cuboctahedra; edges with two equivalent K(1)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Zr(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)K2Mg10 cuboctahedra; edges with four Mg(3,3)KMg10Zr cuboctahedra; edges with four equivalent Mg(1)Mg10Zr2 cuboctahedra;  a faceface with one K(1)Mg12 cuboctahedra;  a faceface with one Zr(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(2,2)K2Mg10 cuboctahedra; faces with five equivalent Mg(1)Mg10Zr2 cuboctahedra; and faces with six Mg(3,3)KMg10Zr cuboctahedra. In the fifth Mg site, Mg(3) is bonded to one K(1); two equivalent Mg(1); two Mg(2,2); two equivalent Mg(4); four equivalent Mg(3); and one Zr(1) atom to form distorted MgKMg10Zr cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)KMg10Zr cuboctahedra; edges with two equivalent K(1)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Zr(1)Mg12 cuboctahedra; edges with four Mg(2,2)K2Mg10 cuboctahedra; edges with four equivalent Mg(3)KMg10Zr cuboctahedra; edges with four equivalent Mg(1)Mg10Zr2 cuboctahedra;  a faceface with one K(1)Mg12 cuboctahedra;  a faceface with one Zr(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(2,2)K2Mg10 cuboctahedra; faces with five equivalent Mg(1)Mg10Zr2 cuboctahedra; and faces with six Mg(3,3)KMg10Zr cuboctahedra. In the sixth Mg site, Mg(4) is bonded to three equivalent Mg(1); three Mg(2,2); and six Mg(3,3) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(4)Mg12 cuboctahedra; corners with twelve Mg(3,3)KMg10Zr cuboctahedra; edges with six Mg(2,2)K2Mg10 cuboctahedra; edges with six Mg(3,3)KMg10Zr cuboctahedra; edges with six equivalent Mg(1)Mg10Zr2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent K(1)Mg12 cuboctahedra; faces with three Mg(2,2)K2Mg10 cuboctahedra; faces with three equivalent Mg(1)Mg10Zr2 cuboctahedra; faces with three equivalent Zr(1)Mg12 cuboctahedra; and faces with six Mg(3,3)KMg10Zr cuboctahedra. Zr(1) is bonded to six equivalent Mg(1) and six Mg(3,3) atoms to form ZrMg12 cuboctahedra that share corners with six equivalent Zr(1)Mg12 cuboctahedra; corners with twelve Mg(2,2)K2Mg10 cuboctahedra; edges with six equivalent Mg(1)Mg10Zr2 cuboctahedra; edges with twelve Mg(3,3)KMg10Zr cuboctahedra; faces with two equivalent K(1)Mg12 cuboctahedra; faces with six Mg(3,3)KMg10Zr cuboctahedra; faces with six equivalent Mg(1)Mg10Zr2 cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. is represented by the CIF file [CIF]
data_KMg14Zr
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.618
_cell_length_b   6.618
_cell_length_c   10.276
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   389.769
_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
  K  K0  1  0.167  0.333  0.625  1.0
  Mg  Mg1  1  0.169  0.834  0.125  1.0
  Mg  Mg2  1  0.174  0.837  0.625  1.0
  Mg  Mg3  1  0.666  0.331  0.125  1.0
  Mg  Mg4  1  0.663  0.326  0.625  1.0
  Mg  Mg5  1  0.666  0.834  0.125  1.0
  Mg  Mg6  1  0.663  0.837  0.625  1.0
  Mg  Mg7  1  0.336  0.164  0.364  1.0
  Mg  Mg8  1  0.336  0.164  0.886  1.0
  Mg  Mg9  1  0.336  0.672  0.364  1.0
  Mg  Mg10  1  0.336  0.672  0.886  1.0
  Mg  Mg11  1  0.828  0.164  0.364  1.0
  Mg  Mg12  1  0.828  0.164  0.886  1.0
  Mg  Mg13  1  0.833  0.667  0.376  1.0
  Mg  Mg14  1  0.833  0.667  0.874  1.0
  Zr  Zr15  1  0.167  0.333  0.125  1.0
[/CIF]
.
The crystal structure described by KMg14Zr crystallizes in the hexagonal P-6m2 space group. K(1) is bonded to six Mg(2,2) and six Mg(3,3) atoms to form KMg12 cuboctahedra that share corners with six equivalent K(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(1)Mg10Zr2 cuboctahedra; edges with six Mg(2,2)K2Mg10 cuboctahedra; edges with twelve Mg(3,3)KMg10Zr cuboctahedra; faces with two equivalent Zr(1)Mg12 cuboctahedra; faces with six Mg(2,2)K2Mg10 cuboctahedra; faces with six Mg(3,3)KMg10Zr cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. There are six inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(4); four equivalent Mg(1); four Mg(3,3); and two equivalent Zr(1) atoms to form MgMg10Zr2 cuboctahedra that share corners with four equivalent K(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Zr2 cuboctahedra; corners with eight Mg(2,2)K2Mg10 cuboctahedra; edges with two equivalent Zr(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Mg10Zr2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)KMg10Zr cuboctahedra; faces with two equivalent Mg(2)K2Mg10 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Zr(1)Mg12 cuboctahedra; faces with four equivalent Mg(1)Mg10Zr2 cuboctahedra; and faces with ten Mg(3,3)KMg10Zr cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent K(1); two equivalent Mg(4); four Mg(2,2); and four Mg(3,3) atoms to form distorted MgK2Mg10 cuboctahedra that share corners with four equivalent Zr(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)K2Mg10 cuboctahedra; corners with eight equivalent Mg(1)Mg10Zr2 cuboctahedra; edges with two equivalent K(1)Mg12 cuboctahedra; edges with four Mg(2,2)K2Mg10 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)KMg10Zr cuboctahedra; faces with two equivalent K(1)Mg12 cuboctahedra; faces with two equivalent Mg(1)Mg10Zr2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with four Mg(2,2)K2Mg10 cuboctahedra; and faces with ten Mg(3,3)KMg10Zr cuboctahedra. In the third Mg site, Mg(2) is bonded to two equivalent K(1); two equivalent Mg(4); four equivalent Mg(2); and four Mg(3,3) atoms to form distorted MgK2Mg10 cuboctahedra that share corners with four equivalent Zr(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)K2Mg10 cuboctahedra; corners with eight equivalent Mg(1)Mg10Zr2 cuboctahedra; edges with two equivalent K(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)K2Mg10 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)KMg10Zr cuboctahedra; faces with two equivalent K(1)Mg12 cuboctahedra; faces with two equivalent Mg(1)Mg10Zr2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with four equivalent Mg(2)K2Mg10 cuboctahedra; and faces with ten Mg(3,3)KMg10Zr cuboctahedra. In the fourth Mg site, Mg(3) is bonded to one K(1); two equivalent Mg(1); two equivalent Mg(2); two equivalent Mg(4); four Mg(3,3); and one Zr(1) atom to form distorted MgKMg10Zr cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)KMg10Zr cuboctahedra; edges with two equivalent K(1)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Zr(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)K2Mg10 cuboctahedra; edges with four Mg(3,3)KMg10Zr cuboctahedra; edges with four equivalent Mg(1)Mg10Zr2 cuboctahedra;  a faceface with one K(1)Mg12 cuboctahedra;  a faceface with one Zr(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(2,2)K2Mg10 cuboctahedra; faces with five equivalent Mg(1)Mg10Zr2 cuboctahedra; and faces with six Mg(3,3)KMg10Zr cuboctahedra. In the fifth Mg site, Mg(3) is bonded to one K(1); two equivalent Mg(1); two Mg(2,2); two equivalent Mg(4); four equivalent Mg(3); and one Zr(1) atom to form distorted MgKMg10Zr cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)KMg10Zr cuboctahedra; edges with two equivalent K(1)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Zr(1)Mg12 cuboctahedra; edges with four Mg(2,2)K2Mg10 cuboctahedra; edges with four equivalent Mg(3)KMg10Zr cuboctahedra; edges with four equivalent Mg(1)Mg10Zr2 cuboctahedra;  a faceface with one K(1)Mg12 cuboctahedra;  a faceface with one Zr(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(2,2)K2Mg10 cuboctahedra; faces with five equivalent Mg(1)Mg10Zr2 cuboctahedra; and faces with six Mg(3,3)KMg10Zr cuboctahedra. In the sixth Mg site, Mg(4) is bonded to three equivalent Mg(1); three Mg(2,2); and six Mg(3,3) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(4)Mg12 cuboctahedra; corners with twelve Mg(3,3)KMg10Zr cuboctahedra; edges with six Mg(2,2)K2Mg10 cuboctahedra; edges with six Mg(3,3)KMg10Zr cuboctahedra; edges with six equivalent Mg(1)Mg10Zr2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent K(1)Mg12 cuboctahedra; faces with three Mg(2,2)K2Mg10 cuboctahedra; faces with three equivalent Mg(1)Mg10Zr2 cuboctahedra; faces with three equivalent Zr(1)Mg12 cuboctahedra; and faces with six Mg(3,3)KMg10Zr cuboctahedra. Zr(1) is bonded to six equivalent Mg(1) and six Mg(3,3) atoms to form ZrMg12 cuboctahedra that share corners with six equivalent Zr(1)Mg12 cuboctahedra; corners with twelve Mg(2,2)K2Mg10 cuboctahedra; edges with six equivalent Mg(1)Mg10Zr2 cuboctahedra; edges with twelve Mg(3,3)KMg10Zr cuboctahedra; faces with two equivalent K(1)Mg12 cuboctahedra; faces with six Mg(3,3)KMg10Zr cuboctahedra; faces with six equivalent Mg(1)Mg10Zr2 cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. is represented by the CIF file [CIF]
data_KMg14Zr
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.618
_cell_length_b   6.618
_cell_length_c   10.276
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   389.769
_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
  K  K0  1  0.167  0.333  0.625  1.0
  Mg  Mg1  1  0.169  0.834  0.125  1.0
  Mg  Mg2  1  0.174  0.837  0.625  1.0
  Mg  Mg3  1  0.666  0.331  0.125  1.0
  Mg  Mg4  1  0.663  0.326  0.625  1.0
  Mg  Mg5  1  0.666  0.834  0.125  1.0
  Mg  Mg6  1  0.663  0.837  0.625  1.0
  Mg  Mg7  1  0.336  0.164  0.364  1.0
  Mg  Mg8  1  0.336  0.164  0.886  1.0
  Mg  Mg9  1  0.336  0.672  0.364  1.0
  Mg  Mg10  1  0.336  0.672  0.886  1.0
  Mg  Mg11  1  0.828  0.164  0.364  1.0
  Mg  Mg12  1  0.828  0.164  0.886  1.0
  Mg  Mg13  1  0.833  0.667  0.376  1.0
  Mg  Mg14  1  0.833  0.667  0.874  1.0
  Zr  Zr15  1  0.167  0.333  0.125  1.0
[/CIF]
.