The material described by CaMg14Hf crystallizes in the orthorhombic Amm2 space group. Ca(1) is bonded to two equivalent Mg(6); four Mg(3,3); four Mg(5,5,5); and two equivalent Hf(1) atoms to form CaHf2Mg10 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with six equivalent Ca(1)Hf2Mg10 cuboctahedra; corners with eight Mg(4,4)Mg12 cuboctahedra; edges with two equivalent Hf(1)Ca2Mg10 cuboctahedra; edges with four Mg(3,3)Ca2Hf2Mg8 cuboctahedra; edges with four equivalent Mg(6)CaMg11 cuboctahedra; edges with eight Mg(5,5,5)CaHfMg10 cuboctahedra; faces with two equivalent Mg(6)CaMg11 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Hf(1)Ca2Mg10 cuboctahedra; faces with four Mg(3,3)Ca2Hf2Mg8 cuboctahedra; faces with four Mg(5,5,5)CaHfMg10 cuboctahedra; and faces with six equivalent Mg(7)HfMg11 cuboctahedra. There are eleven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(2); two equivalent Mg(6); four Mg(4,4); and four Mg(5,5,5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Hf(1)Ca2Mg10 cuboctahedra; corners with six equivalent Mg(1)Mg12 cuboctahedra; corners with eight Mg(3,3)Ca2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with four equivalent Mg(6)CaMg11 cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra; edges with eight Mg(5,5,5)CaHfMg10 cuboctahedra; faces with two equivalent Ca(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(6)CaMg11 cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with four Mg(5,5,5)CaHfMg10 cuboctahedra; faces with four Mg(4,4)Mg12 cuboctahedra; and faces with six equivalent Mg(7)HfMg11 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(1); two equivalent Mg(7); four Mg(4,4); and four Mg(5,5,5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Ca(1)Hf2Mg10 cuboctahedra; corners with six equivalent Mg(2)Mg12 cuboctahedra; corners with eight Mg(3,3)Ca2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Mg(7)HfMg11 cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra; edges with eight Mg(5,5,5)CaHfMg10 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Hf(1)Ca2Mg10 cuboctahedra; faces with four Mg(5,5,5)CaHfMg10 cuboctahedra; faces with four Mg(4,4)Mg12 cuboctahedra; and faces with six equivalent Mg(6)CaMg11 cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Ca(1); two equivalent Mg(3); two Mg(5,5); two equivalent Mg(6); two equivalent Mg(7); and two equivalent Hf(1) atoms to form distorted MgCa2Hf2Mg8 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with six equivalent Mg(3)Ca2Hf2Mg8 cuboctahedra; edges with two equivalent Ca(1)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)Ca2Hf2Mg8 cuboctahedra; edges with two equivalent Hf(1)Ca2Mg10 cuboctahedra; edges with four equivalent Mg(5)CaHfMg10 cuboctahedra; edges with four equivalent Mg(6)CaMg11 cuboctahedra; edges with four equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Ca(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(3)Ca2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(6)CaMg11 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Hf(1)Ca2Mg10 cuboctahedra; and faces with eight Mg(5,5,5)CaHfMg10 cuboctahedra. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(1); two equivalent Mg(2); two equivalent Mg(4); two Mg(5,5); two equivalent Mg(6); and two equivalent Mg(7) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Ca(1)Hf2Mg10 cuboctahedra; corners with four equivalent Mg(3)Ca2Hf2Mg8 cuboctahedra; corners with four equivalent Hf(1)Ca2Mg10 cuboctahedra; corners with six Mg(4,4)Mg12 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with four equivalent Mg(5)CaHfMg10 cuboctahedra; edges with four equivalent Mg(6)CaMg11 cuboctahedra; edges with four equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(3)Ca2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(6)CaMg11 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; and faces with eight Mg(5,5,5)CaHfMg10 cuboctahedra. In the fifth Mg site, Mg(3) is bonded to two equivalent Ca(1); two equivalent Mg(3); two Mg(5,5); two equivalent Mg(6); two equivalent Mg(7); and two equivalent Hf(1) atoms to form distorted MgCa2Hf2Mg8 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with six Mg(3,3)Ca2Hf2Mg8 cuboctahedra; edges with two equivalent Ca(1)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)Ca2Hf2Mg8 cuboctahedra; edges with two equivalent Hf(1)Ca2Mg10 cuboctahedra; edges with four equivalent Mg(5)CaHfMg10 cuboctahedra; edges with four equivalent Mg(6)CaMg11 cuboctahedra; edges with four equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Ca(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(3)Ca2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(6)CaMg11 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Hf(1)Ca2Mg10 cuboctahedra; and faces with eight Mg(5,5,5)CaHfMg10 cuboctahedra. In the sixth Mg site, Mg(4) is bonded to two equivalent Mg(1); two equivalent Mg(2); two equivalent Mg(4); two Mg(5,5); two equivalent Mg(6); and two equivalent Mg(7) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Ca(1)Hf2Mg10 cuboctahedra; corners with four equivalent Mg(3)Ca2Hf2Mg8 cuboctahedra; corners with four equivalent Hf(1)Ca2Mg10 cuboctahedra; corners with six Mg(4,4)Mg12 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with four equivalent Mg(5)CaHfMg10 cuboctahedra; edges with four equivalent Mg(6)CaMg11 cuboctahedra; edges with four equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(3)Ca2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(6)CaMg11 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; and faces with eight Mg(5,5,5)CaHfMg10 cuboctahedra. In the seventh Mg site, Mg(5) is bonded to one Ca(1), one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and one Hf(1) atom to form distorted MgCaHfMg10 cuboctahedra that share corners with four equivalent Mg(6)CaMg11 cuboctahedra; corners with four equivalent Mg(7)HfMg11 cuboctahedra; corners with ten Mg(5,5)CaHfMg10 cuboctahedra; edges with two equivalent Ca(1)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)Ca2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(5)CaHfMg10 cuboctahedra; edges with two equivalent Mg(6)CaMg11 cuboctahedra; edges with two equivalent Mg(7)HfMg11 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Hf(1)Ca2Mg10 cuboctahedra;  a faceface with one Ca(1)Hf2Mg10 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Hf(1)Ca2Mg10 cuboctahedra; faces with two equivalent Mg(6)CaMg11 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with four Mg(3,3)Ca2Hf2Mg8 cuboctahedra; faces with four Mg(5,5)CaHfMg10 cuboctahedra; and faces with four Mg(4,4)Mg12 cuboctahedra. In the eighth Mg site, Mg(5) is bonded to one Ca(1), one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and one Hf(1) atom to form distorted MgCaHfMg10 cuboctahedra that share corners with four equivalent Mg(6)CaMg11 cuboctahedra; corners with four equivalent Mg(7)HfMg11 cuboctahedra; corners with ten Mg(5,5,5)CaHfMg10 cuboctahedra; edges with two equivalent Ca(1)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)Ca2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(5)CaHfMg10 cuboctahedra; edges with two equivalent Mg(6)CaMg11 cuboctahedra; edges with two equivalent Mg(7)HfMg11 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Hf(1)Ca2Mg10 cuboctahedra;  a faceface with one Ca(1)Hf2Mg10 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Hf(1)Ca2Mg10 cuboctahedra; faces with two equivalent Mg(6)CaMg11 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with four Mg(3,3)Ca2Hf2Mg8 cuboctahedra; faces with four Mg(5,5)CaHfMg10 cuboctahedra; and faces with four Mg(4,4)Mg12 cuboctahedra. In the ninth Mg site, Mg(5) is bonded to one Ca(1), one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and one Hf(1) atom to form distorted MgCaHfMg10 cuboctahedra that share corners with four equivalent Mg(6)CaMg11 cuboctahedra; corners with four equivalent Mg(7)HfMg11 cuboctahedra; corners with ten Mg(5,5)CaHfMg10 cuboctahedra; edges with two equivalent Ca(1)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)Ca2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(5)CaHfMg10 cuboctahedra; edges with two equivalent Mg(6)CaMg11 cuboctahedra; edges with two equivalent Mg(7)HfMg11 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Hf(1)Ca2Mg10 cuboctahedra;  a faceface with one Ca(1)Hf2Mg10 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Hf(1)Ca2Mg10 cuboctahedra; faces with two equivalent Mg(6)CaMg11 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with four Mg(3,3)Ca2Hf2Mg8 cuboctahedra; faces with four Mg(5,5)CaHfMg10 cuboctahedra; and faces with four Mg(4,4)Mg12 cuboctahedra. In the tenth Mg site, Mg(6) is bonded to one Ca(1); one Mg(1); two equivalent Mg(3); two equivalent Mg(4); two equivalent Mg(7); and four Mg(5,5,5) atoms to form distorted MgCaMg11 cuboctahedra that share corners with four equivalent Mg(7)HfMg11 cuboctahedra; corners with six equivalent Mg(6)CaMg11 cuboctahedra; corners with eight Mg(5,5,5)CaHfMg10 cuboctahedra; edges with two equivalent Ca(1)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(7)HfMg11 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four Mg(3,3)Ca2Hf2Mg8 cuboctahedra; edges with four Mg(5,5,5)CaHfMg10 cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra;  a faceface with one Ca(1)Hf2Mg10 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(3)Ca2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(6)CaMg11 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Mg(2)Mg12 cuboctahedra; faces with three equivalent Hf(1)Ca2Mg10 cuboctahedra; and faces with four Mg(5,5,5)CaHfMg10 cuboctahedra. In the eleventh Mg site, Mg(7) is bonded to one Mg(2); two equivalent Mg(3); two equivalent Mg(4); two equivalent Mg(6); four Mg(5,5,5); and one Hf(1) atom to form MgHfMg11 cuboctahedra that share corners with four equivalent Mg(6)CaMg11 cuboctahedra; corners with six equivalent Mg(7)HfMg11 cuboctahedra; corners with eight Mg(5,5,5)CaHfMg10 cuboctahedra; edges with two equivalent Mg(6)CaMg11 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Hf(1)Ca2Mg10 cuboctahedra; edges with four Mg(3,3)Ca2Hf2Mg8 cuboctahedra; edges with four Mg(5,5,5)CaHfMg10 cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Hf(1)Ca2Mg10 cuboctahedra; faces with two equivalent Mg(3)Ca2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(6)CaMg11 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Ca(1)Hf2Mg10 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; and faces with four Mg(5,5,5)CaHfMg10 cuboctahedra. Hf(1) is bonded to two equivalent Ca(1); two equivalent Mg(7); four Mg(3,3); and four Mg(5,5,5) atoms to form HfCa2Mg10 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Hf(1)Ca2Mg10 cuboctahedra; corners with eight Mg(4,4)Mg12 cuboctahedra; edges with two equivalent Ca(1)Hf2Mg10 cuboctahedra; edges with four Mg(3,3)Ca2Hf2Mg8 cuboctahedra; edges with four equivalent Mg(7)HfMg11 cuboctahedra; edges with eight Mg(5,5,5)CaHfMg10 cuboctahedra; faces with two equivalent Ca(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with four Mg(3,3)Ca2Hf2Mg8 cuboctahedra; faces with four Mg(5,5,5)CaHfMg10 cuboctahedra; and faces with six equivalent Mg(6)CaMg11 cuboctahedra. is represented by the CIF file [CIF]
data_CaHfMg14
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.490
_cell_length_b   6.551
_cell_length_c   10.328
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.315
_symmetry_Int_Tables_number   1
_cell_volume   379.070
_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
  Ca  Ca0  1  0.167  0.334  0.125  1.0
  Hf  Hf1  1  0.182  0.841  0.125  1.0
  Mg  Mg2  1  0.167  0.333  0.625  1.0
  Mg  Mg3  1  0.166  0.833  0.625  1.0
  Mg  Mg4  1  0.664  0.333  0.125  1.0
  Mg  Mg5  1  0.667  0.334  0.625  1.0
  Mg  Mg6  1  0.664  0.830  0.125  1.0
  Mg  Mg7  1  0.667  0.833  0.625  1.0
  Mg  Mg8  1  0.332  0.159  0.379  1.0
  Mg  Mg9  1  0.332  0.159  0.871  1.0
  Mg  Mg10  1  0.332  0.673  0.379  1.0
  Mg  Mg11  1  0.332  0.673  0.871  1.0
  Mg  Mg12  1  0.826  0.163  0.380  1.0
  Mg  Mg13  1  0.826  0.163  0.870  1.0
  Mg  Mg14  1  0.838  0.669  0.371  1.0
  Mg  Mg15  1  0.838  0.669  0.879  1.0
[/CIF]
.
The material described by CaMg14Hf crystallizes in the orthorhombic Amm2 space group. Ca(1) is bonded to two equivalent Mg(6); four Mg(3,3); four Mg(5,5,5); and two equivalent Hf(1) atoms to form CaHf2Mg10 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with six equivalent Ca(1)Hf2Mg10 cuboctahedra; corners with eight Mg(4,4)Mg12 cuboctahedra; edges with two equivalent Hf(1)Ca2Mg10 cuboctahedra; edges with four Mg(3,3)Ca2Hf2Mg8 cuboctahedra; edges with four equivalent Mg(6)CaMg11 cuboctahedra; edges with eight Mg(5,5,5)CaHfMg10 cuboctahedra; faces with two equivalent Mg(6)CaMg11 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Hf(1)Ca2Mg10 cuboctahedra; faces with four Mg(3,3)Ca2Hf2Mg8 cuboctahedra; faces with four Mg(5,5,5)CaHfMg10 cuboctahedra; and faces with six equivalent Mg(7)HfMg11 cuboctahedra. There are eleven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(2); two equivalent Mg(6); four Mg(4,4); and four Mg(5,5,5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Hf(1)Ca2Mg10 cuboctahedra; corners with six equivalent Mg(1)Mg12 cuboctahedra; corners with eight Mg(3,3)Ca2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with four equivalent Mg(6)CaMg11 cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra; edges with eight Mg(5,5,5)CaHfMg10 cuboctahedra; faces with two equivalent Ca(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(6)CaMg11 cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with four Mg(5,5,5)CaHfMg10 cuboctahedra; faces with four Mg(4,4)Mg12 cuboctahedra; and faces with six equivalent Mg(7)HfMg11 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(1); two equivalent Mg(7); four Mg(4,4); and four Mg(5,5,5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Ca(1)Hf2Mg10 cuboctahedra; corners with six equivalent Mg(2)Mg12 cuboctahedra; corners with eight Mg(3,3)Ca2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Mg(7)HfMg11 cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra; edges with eight Mg(5,5,5)CaHfMg10 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Hf(1)Ca2Mg10 cuboctahedra; faces with four Mg(5,5,5)CaHfMg10 cuboctahedra; faces with four Mg(4,4)Mg12 cuboctahedra; and faces with six equivalent Mg(6)CaMg11 cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Ca(1); two equivalent Mg(3); two Mg(5,5); two equivalent Mg(6); two equivalent Mg(7); and two equivalent Hf(1) atoms to form distorted MgCa2Hf2Mg8 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with six equivalent Mg(3)Ca2Hf2Mg8 cuboctahedra; edges with two equivalent Ca(1)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)Ca2Hf2Mg8 cuboctahedra; edges with two equivalent Hf(1)Ca2Mg10 cuboctahedra; edges with four equivalent Mg(5)CaHfMg10 cuboctahedra; edges with four equivalent Mg(6)CaMg11 cuboctahedra; edges with four equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Ca(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(3)Ca2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(6)CaMg11 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Hf(1)Ca2Mg10 cuboctahedra; and faces with eight Mg(5,5,5)CaHfMg10 cuboctahedra. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(1); two equivalent Mg(2); two equivalent Mg(4); two Mg(5,5); two equivalent Mg(6); and two equivalent Mg(7) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Ca(1)Hf2Mg10 cuboctahedra; corners with four equivalent Mg(3)Ca2Hf2Mg8 cuboctahedra; corners with four equivalent Hf(1)Ca2Mg10 cuboctahedra; corners with six Mg(4,4)Mg12 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with four equivalent Mg(5)CaHfMg10 cuboctahedra; edges with four equivalent Mg(6)CaMg11 cuboctahedra; edges with four equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(3)Ca2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(6)CaMg11 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; and faces with eight Mg(5,5,5)CaHfMg10 cuboctahedra. In the fifth Mg site, Mg(3) is bonded to two equivalent Ca(1); two equivalent Mg(3); two Mg(5,5); two equivalent Mg(6); two equivalent Mg(7); and two equivalent Hf(1) atoms to form distorted MgCa2Hf2Mg8 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with six Mg(3,3)Ca2Hf2Mg8 cuboctahedra; edges with two equivalent Ca(1)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)Ca2Hf2Mg8 cuboctahedra; edges with two equivalent Hf(1)Ca2Mg10 cuboctahedra; edges with four equivalent Mg(5)CaHfMg10 cuboctahedra; edges with four equivalent Mg(6)CaMg11 cuboctahedra; edges with four equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Ca(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(3)Ca2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(6)CaMg11 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Hf(1)Ca2Mg10 cuboctahedra; and faces with eight Mg(5,5,5)CaHfMg10 cuboctahedra. In the sixth Mg site, Mg(4) is bonded to two equivalent Mg(1); two equivalent Mg(2); two equivalent Mg(4); two Mg(5,5); two equivalent Mg(6); and two equivalent Mg(7) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Ca(1)Hf2Mg10 cuboctahedra; corners with four equivalent Mg(3)Ca2Hf2Mg8 cuboctahedra; corners with four equivalent Hf(1)Ca2Mg10 cuboctahedra; corners with six Mg(4,4)Mg12 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with four equivalent Mg(5)CaHfMg10 cuboctahedra; edges with four equivalent Mg(6)CaMg11 cuboctahedra; edges with four equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(3)Ca2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(6)CaMg11 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; and faces with eight Mg(5,5,5)CaHfMg10 cuboctahedra. In the seventh Mg site, Mg(5) is bonded to one Ca(1), one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and one Hf(1) atom to form distorted MgCaHfMg10 cuboctahedra that share corners with four equivalent Mg(6)CaMg11 cuboctahedra; corners with four equivalent Mg(7)HfMg11 cuboctahedra; corners with ten Mg(5,5)CaHfMg10 cuboctahedra; edges with two equivalent Ca(1)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)Ca2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(5)CaHfMg10 cuboctahedra; edges with two equivalent Mg(6)CaMg11 cuboctahedra; edges with two equivalent Mg(7)HfMg11 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Hf(1)Ca2Mg10 cuboctahedra;  a faceface with one Ca(1)Hf2Mg10 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Hf(1)Ca2Mg10 cuboctahedra; faces with two equivalent Mg(6)CaMg11 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with four Mg(3,3)Ca2Hf2Mg8 cuboctahedra; faces with four Mg(5,5)CaHfMg10 cuboctahedra; and faces with four Mg(4,4)Mg12 cuboctahedra. In the eighth Mg site, Mg(5) is bonded to one Ca(1), one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and one Hf(1) atom to form distorted MgCaHfMg10 cuboctahedra that share corners with four equivalent Mg(6)CaMg11 cuboctahedra; corners with four equivalent Mg(7)HfMg11 cuboctahedra; corners with ten Mg(5,5,5)CaHfMg10 cuboctahedra; edges with two equivalent Ca(1)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)Ca2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(5)CaHfMg10 cuboctahedra; edges with two equivalent Mg(6)CaMg11 cuboctahedra; edges with two equivalent Mg(7)HfMg11 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Hf(1)Ca2Mg10 cuboctahedra;  a faceface with one Ca(1)Hf2Mg10 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Hf(1)Ca2Mg10 cuboctahedra; faces with two equivalent Mg(6)CaMg11 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with four Mg(3,3)Ca2Hf2Mg8 cuboctahedra; faces with four Mg(5,5)CaHfMg10 cuboctahedra; and faces with four Mg(4,4)Mg12 cuboctahedra. In the ninth Mg site, Mg(5) is bonded to one Ca(1), one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and one Hf(1) atom to form distorted MgCaHfMg10 cuboctahedra that share corners with four equivalent Mg(6)CaMg11 cuboctahedra; corners with four equivalent Mg(7)HfMg11 cuboctahedra; corners with ten Mg(5,5)CaHfMg10 cuboctahedra; edges with two equivalent Ca(1)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)Ca2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(5)CaHfMg10 cuboctahedra; edges with two equivalent Mg(6)CaMg11 cuboctahedra; edges with two equivalent Mg(7)HfMg11 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Hf(1)Ca2Mg10 cuboctahedra;  a faceface with one Ca(1)Hf2Mg10 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Hf(1)Ca2Mg10 cuboctahedra; faces with two equivalent Mg(6)CaMg11 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with four Mg(3,3)Ca2Hf2Mg8 cuboctahedra; faces with four Mg(5,5)CaHfMg10 cuboctahedra; and faces with four Mg(4,4)Mg12 cuboctahedra. In the tenth Mg site, Mg(6) is bonded to one Ca(1); one Mg(1); two equivalent Mg(3); two equivalent Mg(4); two equivalent Mg(7); and four Mg(5,5,5) atoms to form distorted MgCaMg11 cuboctahedra that share corners with four equivalent Mg(7)HfMg11 cuboctahedra; corners with six equivalent Mg(6)CaMg11 cuboctahedra; corners with eight Mg(5,5,5)CaHfMg10 cuboctahedra; edges with two equivalent Ca(1)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(7)HfMg11 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four Mg(3,3)Ca2Hf2Mg8 cuboctahedra; edges with four Mg(5,5,5)CaHfMg10 cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra;  a faceface with one Ca(1)Hf2Mg10 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(3)Ca2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(6)CaMg11 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Mg(2)Mg12 cuboctahedra; faces with three equivalent Hf(1)Ca2Mg10 cuboctahedra; and faces with four Mg(5,5,5)CaHfMg10 cuboctahedra. In the eleventh Mg site, Mg(7) is bonded to one Mg(2); two equivalent Mg(3); two equivalent Mg(4); two equivalent Mg(6); four Mg(5,5,5); and one Hf(1) atom to form MgHfMg11 cuboctahedra that share corners with four equivalent Mg(6)CaMg11 cuboctahedra; corners with six equivalent Mg(7)HfMg11 cuboctahedra; corners with eight Mg(5,5,5)CaHfMg10 cuboctahedra; edges with two equivalent Mg(6)CaMg11 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Hf(1)Ca2Mg10 cuboctahedra; edges with four Mg(3,3)Ca2Hf2Mg8 cuboctahedra; edges with four Mg(5,5,5)CaHfMg10 cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Hf(1)Ca2Mg10 cuboctahedra; faces with two equivalent Mg(3)Ca2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(6)CaMg11 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Ca(1)Hf2Mg10 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; and faces with four Mg(5,5,5)CaHfMg10 cuboctahedra. Hf(1) is bonded to two equivalent Ca(1); two equivalent Mg(7); four Mg(3,3); and four Mg(5,5,5) atoms to form HfCa2Mg10 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Hf(1)Ca2Mg10 cuboctahedra; corners with eight Mg(4,4)Mg12 cuboctahedra; edges with two equivalent Ca(1)Hf2Mg10 cuboctahedra; edges with four Mg(3,3)Ca2Hf2Mg8 cuboctahedra; edges with four equivalent Mg(7)HfMg11 cuboctahedra; edges with eight Mg(5,5,5)CaHfMg10 cuboctahedra; faces with two equivalent Ca(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with four Mg(3,3)Ca2Hf2Mg8 cuboctahedra; faces with four Mg(5,5,5)CaHfMg10 cuboctahedra; and faces with six equivalent Mg(6)CaMg11 cuboctahedra. is represented by the CIF file [CIF]
data_CaHfMg14
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.490
_cell_length_b   6.551
_cell_length_c   10.328
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.315
_symmetry_Int_Tables_number   1
_cell_volume   379.070
_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
  Ca  Ca0  1  0.167  0.334  0.125  1.0
  Hf  Hf1  1  0.182  0.841  0.125  1.0
  Mg  Mg2  1  0.167  0.333  0.625  1.0
  Mg  Mg3  1  0.166  0.833  0.625  1.0
  Mg  Mg4  1  0.664  0.333  0.125  1.0
  Mg  Mg5  1  0.667  0.334  0.625  1.0
  Mg  Mg6  1  0.664  0.830  0.125  1.0
  Mg  Mg7  1  0.667  0.833  0.625  1.0
  Mg  Mg8  1  0.332  0.159  0.379  1.0
  Mg  Mg9  1  0.332  0.159  0.871  1.0
  Mg  Mg10  1  0.332  0.673  0.379  1.0
  Mg  Mg11  1  0.332  0.673  0.871  1.0
  Mg  Mg12  1  0.826  0.163  0.380  1.0
  Mg  Mg13  1  0.826  0.163  0.870  1.0
  Mg  Mg14  1  0.838  0.669  0.371  1.0
  Mg  Mg15  1  0.838  0.669  0.879  1.0
[/CIF]
.