Mg6HfSb crystallizes in the orthorhombic Amm2 space group. There are eight inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Hf(1), and two equivalent Sb(1) atoms to form distorted MgHf2Mg8Sb2 cuboctahedra that share corners with four equivalent Mg(2)Mg10Sb2 cuboctahedra; corners with four equivalent Sb(1)Hf2Mg10 cuboctahedra; corners with ten Mg(1,1)Hf2Mg8Sb2 cuboctahedra; edges with two equivalent Mg(1)Hf2Mg8Sb2 cuboctahedra; edges with two equivalent Mg(2)Mg10Sb2 cuboctahedra; edges with two equivalent Sb(1)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(3)Hf2Mg8Sb2 cuboctahedra; edges with four equivalent Hf(1)Mg10Sb2 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Mg10Sb2 cuboctahedra; faces with two equivalent Hf(1)Mg10Sb2 cuboctahedra; faces with two equivalent Sb(1)Hf2Mg10 cuboctahedra; faces with four equivalent Mg(1)Hf2Mg8Sb2 cuboctahedra; and faces with eight Mg(3,3,3)Hf2Mg8Sb2 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(4); four Mg(1,1,1); four Mg(3,3); and two equivalent Sb(1) atoms to form distorted MgMg10Sb2 cuboctahedra that share corners with four equivalent Sb(1)Hf2Mg10 cuboctahedra; corners with six equivalent Mg(2)Mg10Sb2 cuboctahedra; corners with eight Mg(1,1,1)Hf2Mg8Sb2 cuboctahedra; edges with two equivalent Sb(1)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with four Mg(1,1,1)Hf2Mg8Sb2 cuboctahedra; edges with eight Mg(3,3,3)Hf2Mg8Sb2 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Mg10Sb2 cuboctahedra; faces with two equivalent Sb(1)Hf2Mg10 cuboctahedra; faces with four Mg(1,1,1)Hf2Mg8Sb2 cuboctahedra; faces with four Mg(3,3)Hf2Mg8Sb2 cuboctahedra; and faces with six equivalent Hf(1)Mg10Sb2 cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Hf(1), and two equivalent Sb(1) atoms to form distorted MgHf2Mg8Sb2 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra; corners with four equivalent Hf(1)Mg10Sb2 cuboctahedra; corners with ten Mg(3,3)Hf2Mg8Sb2 cuboctahedra; edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)Hf2Mg8Sb2 cuboctahedra; edges with two equivalent Hf(1)Mg10Sb2 cuboctahedra; edges with four equivalent Mg(1)Hf2Mg8Sb2 cuboctahedra; edges with four equivalent Mg(2)Mg10Sb2 cuboctahedra; edges with four equivalent Sb(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Mg10Sb2 cuboctahedra; faces with two equivalent Hf(1)Mg10Sb2 cuboctahedra; faces with two equivalent Sb(1)Hf2Mg10 cuboctahedra; faces with four Mg(3,3)Hf2Mg8Sb2 cuboctahedra; and faces with eight Mg(1,1)Hf2Mg8Sb2 cuboctahedra. In the fourth Mg site, Mg(3) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Hf(1), and two equivalent Sb(1) atoms to form distorted MgHf2Mg8Sb2 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra; corners with four equivalent Hf(1)Mg10Sb2 cuboctahedra; corners with ten Mg(3,3,3)Hf2Mg8Sb2 cuboctahedra; edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)Hf2Mg8Sb2 cuboctahedra; edges with two equivalent Hf(1)Mg10Sb2 cuboctahedra; edges with four equivalent Mg(1)Hf2Mg8Sb2 cuboctahedra; edges with four equivalent Mg(2)Mg10Sb2 cuboctahedra; edges with four equivalent Sb(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Mg10Sb2 cuboctahedra; faces with two equivalent Hf(1)Mg10Sb2 cuboctahedra; faces with two equivalent Sb(1)Hf2Mg10 cuboctahedra; faces with four Mg(3,3)Hf2Mg8Sb2 cuboctahedra; and faces with eight Mg(1,1)Hf2Mg8Sb2 cuboctahedra. In the fifth Mg site, Mg(4) is bonded to two equivalent Mg(2); four Mg(1,1); four Mg(3,3,3); and two equivalent Hf(1) atoms to form MgHf2Mg10 cuboctahedra that share corners with four equivalent Hf(1)Mg10Sb2 cuboctahedra; corners with six equivalent Mg(4)Hf2Mg10 cuboctahedra; corners with eight Mg(3,3,3)Hf2Mg8Sb2 cuboctahedra; edges with two equivalent Hf(1)Mg10Sb2 cuboctahedra; edges with four Mg(3,3,3)Hf2Mg8Sb2 cuboctahedra; edges with four equivalent Mg(2)Mg10Sb2 cuboctahedra; edges with eight Mg(1,1,1)Hf2Mg8Sb2 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Mg10Sb2 cuboctahedra; faces with two equivalent Hf(1)Mg10Sb2 cuboctahedra; faces with four Mg(1,1)Hf2Mg8Sb2 cuboctahedra; faces with four Mg(3,3,3)Hf2Mg8Sb2 cuboctahedra; and faces with six equivalent Sb(1)Hf2Mg10 cuboctahedra. In the sixth Mg site, Mg(1) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Hf(1), and two equivalent Sb(1) atoms to form distorted MgHf2Mg8Sb2 cuboctahedra that share corners with four equivalent Mg(2)Mg10Sb2 cuboctahedra; corners with four equivalent Sb(1)Hf2Mg10 cuboctahedra; corners with ten Mg(1,1,1)Hf2Mg8Sb2 cuboctahedra; edges with two equivalent Mg(1)Hf2Mg8Sb2 cuboctahedra; edges with two equivalent Mg(2)Mg10Sb2 cuboctahedra; edges with two equivalent Sb(1)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(3)Hf2Mg8Sb2 cuboctahedra; edges with four equivalent Hf(1)Mg10Sb2 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Mg10Sb2 cuboctahedra; faces with two equivalent Hf(1)Mg10Sb2 cuboctahedra; faces with two equivalent Sb(1)Hf2Mg10 cuboctahedra; faces with four Mg(1,1)Hf2Mg8Sb2 cuboctahedra; and faces with eight Mg(3,3)Hf2Mg8Sb2 cuboctahedra. In the seventh Mg site, Mg(1) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Hf(1), and two equivalent Sb(1) atoms to form distorted MgHf2Mg8Sb2 cuboctahedra that share corners with four equivalent Mg(2)Mg10Sb2 cuboctahedra; corners with four equivalent Sb(1)Hf2Mg10 cuboctahedra; corners with ten Mg(1,1,1)Hf2Mg8Sb2 cuboctahedra; edges with two equivalent Mg(1)Hf2Mg8Sb2 cuboctahedra; edges with two equivalent Mg(2)Mg10Sb2 cuboctahedra; edges with two equivalent Sb(1)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(3)Hf2Mg8Sb2 cuboctahedra; edges with four equivalent Hf(1)Mg10Sb2 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Mg10Sb2 cuboctahedra; faces with two equivalent Hf(1)Mg10Sb2 cuboctahedra; faces with two equivalent Sb(1)Hf2Mg10 cuboctahedra; faces with four Mg(1,1)Hf2Mg8Sb2 cuboctahedra; and faces with eight Mg(3,3,3)Hf2Mg8Sb2 cuboctahedra. In the eighth Mg site, Mg(3) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Hf(1), and two equivalent Sb(1) atoms to form distorted MgHf2Mg8Sb2 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra; corners with four equivalent Hf(1)Mg10Sb2 cuboctahedra; corners with ten Mg(3,3)Hf2Mg8Sb2 cuboctahedra; edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)Hf2Mg8Sb2 cuboctahedra; edges with two equivalent Hf(1)Mg10Sb2 cuboctahedra; edges with four equivalent Mg(1)Hf2Mg8Sb2 cuboctahedra; edges with four equivalent Mg(2)Mg10Sb2 cuboctahedra; edges with four equivalent Sb(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Mg10Sb2 cuboctahedra; faces with two equivalent Hf(1)Mg10Sb2 cuboctahedra; faces with two equivalent Sb(1)Hf2Mg10 cuboctahedra; faces with four Mg(3,3)Hf2Mg8Sb2 cuboctahedra; and faces with eight Mg(1,1,1)Hf2Mg8Sb2 cuboctahedra. Hf(1) is bonded to two equivalent Mg(4); four equivalent Mg(1); four Mg(3,3,3); and two equivalent Sb(1) atoms to form distorted HfMg10Sb2 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra; corners with six equivalent Hf(1)Mg10Sb2 cuboctahedra; corners with eight Mg(3,3,3)Hf2Mg8Sb2 cuboctahedra; edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with four Mg(3,3,3)Hf2Mg8Sb2 cuboctahedra; edges with four equivalent Sb(1)Hf2Mg10 cuboctahedra; edges with eight Mg(1,1,1)Hf2Mg8Sb2 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Hf(1)Mg10Sb2 cuboctahedra; faces with two equivalent Sb(1)Hf2Mg10 cuboctahedra; faces with four equivalent Mg(1)Hf2Mg8Sb2 cuboctahedra; faces with four Mg(3,3,3)Hf2Mg8Sb2 cuboctahedra; and faces with six equivalent Mg(2)Mg10Sb2 cuboctahedra. Sb(1) is bonded to two equivalent Mg(2); four Mg(1,1,1); four Mg(3,3); and two equivalent Hf(1) atoms to form SbHf2Mg10 cuboctahedra that share corners with four equivalent Mg(2)Mg10Sb2 cuboctahedra; corners with six equivalent Sb(1)Hf2Mg10 cuboctahedra; corners with eight Mg(1,1,1)Hf2Mg8Sb2 cuboctahedra; edges with two equivalent Mg(2)Mg10Sb2 cuboctahedra; edges with four Mg(1,1,1)Hf2Mg8Sb2 cuboctahedra; edges with four equivalent Hf(1)Mg10Sb2 cuboctahedra; edges with eight Mg(3,3,3)Hf2Mg8Sb2 cuboctahedra; faces with two equivalent Mg(2)Mg10Sb2 cuboctahedra; faces with two equivalent Hf(1)Mg10Sb2 cuboctahedra; faces with two equivalent Sb(1)Hf2Mg10 cuboctahedra; faces with four Mg(1,1,1)Hf2Mg8Sb2 cuboctahedra; faces with four Mg(3,3)Hf2Mg8Sb2 cuboctahedra; and faces with six equivalent Mg(4)Hf2Mg10 cuboctahedra.
Mg6HfSb crystallizes in the orthorhombic Amm2 space group. There are eight inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Hf(1), and two equivalent Sb(1) atoms to form distorted MgHf2Mg8Sb2 cuboctahedra that share corners with four equivalent Mg(2)Mg10Sb2 cuboctahedra; corners with four equivalent Sb(1)Hf2Mg10 cuboctahedra; corners with ten Mg(1,1)Hf2Mg8Sb2 cuboctahedra; edges with two equivalent Mg(1)Hf2Mg8Sb2 cuboctahedra; edges with two equivalent Mg(2)Mg10Sb2 cuboctahedra; edges with two equivalent Sb(1)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(3)Hf2Mg8Sb2 cuboctahedra; edges with four equivalent Hf(1)Mg10Sb2 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Mg10Sb2 cuboctahedra; faces with two equivalent Hf(1)Mg10Sb2 cuboctahedra; faces with two equivalent Sb(1)Hf2Mg10 cuboctahedra; faces with four equivalent Mg(1)Hf2Mg8Sb2 cuboctahedra; and faces with eight Mg(3,3,3)Hf2Mg8Sb2 cuboctahedra. There is one shorter (3.22 Å) and one longer (3.26 Å) Mg(1)-Mg(1) bond length. There is one shorter (3.16 Å) and one longer (3.17 Å) Mg(1)-Mg(2) bond length. Both Mg(1)-Mg(3) bond lengths are 3.11 Å. Both Mg(1)-Mg(4) bond lengths are 3.15 Å. Both Mg(1)-Hf(1) bond lengths are 3.17 Å. There is one shorter (3.13 Å) and one longer (3.20 Å) Mg(1)-Sb(1) bond length. In the second Mg site, Mg(2) is bonded to two equivalent Mg(4); four Mg(1,1,1); four Mg(3,3); and two equivalent Sb(1) atoms to form distorted MgMg10Sb2 cuboctahedra that share corners with four equivalent Sb(1)Hf2Mg10 cuboctahedra; corners with six equivalent Mg(2)Mg10Sb2 cuboctahedra; corners with eight Mg(1,1,1)Hf2Mg8Sb2 cuboctahedra; edges with two equivalent Sb(1)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with four Mg(1,1,1)Hf2Mg8Sb2 cuboctahedra; edges with eight Mg(3,3,3)Hf2Mg8Sb2 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Mg10Sb2 cuboctahedra; faces with two equivalent Sb(1)Hf2Mg10 cuboctahedra; faces with four Mg(1,1,1)Hf2Mg8Sb2 cuboctahedra; faces with four Mg(3,3)Hf2Mg8Sb2 cuboctahedra; and faces with six equivalent Hf(1)Mg10Sb2 cuboctahedra. Both Mg(2)-Mg(4) bond lengths are 3.14 Å. Both Mg(2)-Mg(1,1) bond lengths are 3.17 Å. All Mg(2)-Mg(3,3) bond lengths are 3.14 Å. Both Mg(2)-Sb(1) bond lengths are 3.24 Å. In the third Mg site, Mg(3) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Hf(1), and two equivalent Sb(1) atoms to form distorted MgHf2Mg8Sb2 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra; corners with four equivalent Hf(1)Mg10Sb2 cuboctahedra; corners with ten Mg(3,3)Hf2Mg8Sb2 cuboctahedra; edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)Hf2Mg8Sb2 cuboctahedra; edges with two equivalent Hf(1)Mg10Sb2 cuboctahedra; edges with four equivalent Mg(1)Hf2Mg8Sb2 cuboctahedra; edges with four equivalent Mg(2)Mg10Sb2 cuboctahedra; edges with four equivalent Sb(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Mg10Sb2 cuboctahedra; faces with two equivalent Hf(1)Mg10Sb2 cuboctahedra; faces with two equivalent Sb(1)Hf2Mg10 cuboctahedra; faces with four Mg(3,3)Hf2Mg8Sb2 cuboctahedra; and faces with eight Mg(1,1)Hf2Mg8Sb2 cuboctahedra. There is one shorter (3.16 Å) and one longer (3.31 Å) Mg(3)-Mg(3) bond length. There is one shorter (3.14 Å) and one longer (3.18 Å) Mg(3)-Mg(4) bond length. There is one shorter (3.14 Å) and one longer (3.18 Å) Mg(3)-Hf(1) bond length. Both Mg(3)-Sb(1) bond lengths are 3.20 Å. In the fourth Mg site, Mg(3) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Hf(1), and two equivalent Sb(1) atoms to form distorted MgHf2Mg8Sb2 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra; corners with four equivalent Hf(1)Mg10Sb2 cuboctahedra; corners with ten Mg(3,3,3)Hf2Mg8Sb2 cuboctahedra; edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)Hf2Mg8Sb2 cuboctahedra; edges with two equivalent Hf(1)Mg10Sb2 cuboctahedra; edges with four equivalent Mg(1)Hf2Mg8Sb2 cuboctahedra; edges with four equivalent Mg(2)Mg10Sb2 cuboctahedra; edges with four equivalent Sb(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Mg10Sb2 cuboctahedra; faces with two equivalent Hf(1)Mg10Sb2 cuboctahedra; faces with two equivalent Sb(1)Hf2Mg10 cuboctahedra; faces with four Mg(3,3)Hf2Mg8Sb2 cuboctahedra; and faces with eight Mg(1,1)Hf2Mg8Sb2 cuboctahedra. Both Mg(3)-Mg(1) bond lengths are 3.11 Å. There is one shorter (3.14 Å) and one longer (3.18 Å) Mg(3)-Mg(4) bond length. There is one shorter (3.14 Å) and one longer (3.18 Å) Mg(3)-Hf(1) bond length. Both Mg(3)-Sb(1) bond lengths are 3.20 Å. In the fifth Mg site, Mg(4) is bonded to two equivalent Mg(2); four Mg(1,1); four Mg(3,3,3); and two equivalent Hf(1) atoms to form MgHf2Mg10 cuboctahedra that share corners with four equivalent Hf(1)Mg10Sb2 cuboctahedra; corners with six equivalent Mg(4)Hf2Mg10 cuboctahedra; corners with eight Mg(3,3,3)Hf2Mg8Sb2 cuboctahedra; edges with two equivalent Hf(1)Mg10Sb2 cuboctahedra; edges with four Mg(3,3,3)Hf2Mg8Sb2 cuboctahedra; edges with four equivalent Mg(2)Mg10Sb2 cuboctahedra; edges with eight Mg(1,1,1)Hf2Mg8Sb2 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Mg10Sb2 cuboctahedra; faces with two equivalent Hf(1)Mg10Sb2 cuboctahedra; faces with four Mg(1,1)Hf2Mg8Sb2 cuboctahedra; faces with four Mg(3,3,3)Hf2Mg8Sb2 cuboctahedra; and faces with six equivalent Sb(1)Hf2Mg10 cuboctahedra. All Mg(4)-Mg(1,1) bond lengths are 3.15 Å. The Mg(4)-Mg(3) bond length is 3.14 Å. Both Mg(4)-Hf(1) bond lengths are 3.24 Å. In the sixth Mg site, Mg(1) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Hf(1), and two equivalent Sb(1) atoms to form distorted MgHf2Mg8Sb2 cuboctahedra that share corners with four equivalent Mg(2)Mg10Sb2 cuboctahedra; corners with four equivalent Sb(1)Hf2Mg10 cuboctahedra; corners with ten Mg(1,1,1)Hf2Mg8Sb2 cuboctahedra; edges with two equivalent Mg(1)Hf2Mg8Sb2 cuboctahedra; edges with two equivalent Mg(2)Mg10Sb2 cuboctahedra; edges with two equivalent Sb(1)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(3)Hf2Mg8Sb2 cuboctahedra; edges with four equivalent Hf(1)Mg10Sb2 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Mg10Sb2 cuboctahedra; faces with two equivalent Hf(1)Mg10Sb2 cuboctahedra; faces with two equivalent Sb(1)Hf2Mg10 cuboctahedra; faces with four Mg(1,1)Hf2Mg8Sb2 cuboctahedra; and faces with eight Mg(3,3)Hf2Mg8Sb2 cuboctahedra. There is one shorter (3.22 Å) and one longer (3.26 Å) Mg(1)-Mg(1) bond length. Both Mg(1)-Mg(3) bond lengths are 3.11 Å. Both Mg(1)-Hf(1) bond lengths are 3.17 Å. There is one shorter (3.13 Å) and one longer (3.20 Å) Mg(1)-Sb(1) bond length. In the seventh Mg site, Mg(1) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Hf(1), and two equivalent Sb(1) atoms to form distorted MgHf2Mg8Sb2 cuboctahedra that share corners with four equivalent Mg(2)Mg10Sb2 cuboctahedra; corners with four equivalent Sb(1)Hf2Mg10 cuboctahedra; corners with ten Mg(1,1,1)Hf2Mg8Sb2 cuboctahedra; edges with two equivalent Mg(1)Hf2Mg8Sb2 cuboctahedra; edges with two equivalent Mg(2)Mg10Sb2 cuboctahedra; edges with two equivalent Sb(1)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(3)Hf2Mg8Sb2 cuboctahedra; edges with four equivalent Hf(1)Mg10Sb2 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Mg10Sb2 cuboctahedra; faces with two equivalent Hf(1)Mg10Sb2 cuboctahedra; faces with two equivalent Sb(1)Hf2Mg10 cuboctahedra; faces with four Mg(1,1)Hf2Mg8Sb2 cuboctahedra; and faces with eight Mg(3,3,3)Hf2Mg8Sb2 cuboctahedra. Both Mg(1)-Mg(3) bond lengths are 3.11 Å. Both Mg(1)-Hf(1) bond lengths are 3.17 Å. There is one shorter (3.13 Å) and one longer (3.20 Å) Mg(1)-Sb(1) bond length. In the eighth Mg site, Mg(3) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Hf(1), and two equivalent Sb(1) atoms to form distorted MgHf2Mg8Sb2 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra; corners with four equivalent Hf(1)Mg10Sb2 cuboctahedra; corners with ten Mg(3,3)Hf2Mg8Sb2 cuboctahedra; edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)Hf2Mg8Sb2 cuboctahedra; edges with two equivalent Hf(1)Mg10Sb2 cuboctahedra; edges with four equivalent Mg(1)Hf2Mg8Sb2 cuboctahedra; edges with four equivalent Mg(2)Mg10Sb2 cuboctahedra; edges with four equivalent Sb(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Mg10Sb2 cuboctahedra; faces with two equivalent Hf(1)Mg10Sb2 cuboctahedra; faces with two equivalent Sb(1)Hf2Mg10 cuboctahedra; faces with four Mg(3,3)Hf2Mg8Sb2 cuboctahedra; and faces with eight Mg(1,1,1)Hf2Mg8Sb2 cuboctahedra. Both Mg(3)-Mg(2) bond lengths are 3.14 Å. There is one shorter (3.16 Å) and one longer (3.31 Å) Mg(3)-Mg(3) bond length. There is one shorter (3.14 Å) and one longer (3.18 Å) Mg(3)-Hf(1) bond length. Both Mg(3)-Sb(1) bond lengths are 3.20 Å. Hf(1) is bonded to two equivalent Mg(4); four equivalent Mg(1); four Mg(3,3,3); and two equivalent Sb(1) atoms to form distorted HfMg10Sb2 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra; corners with six equivalent Hf(1)Mg10Sb2 cuboctahedra; corners with eight Mg(3,3,3)Hf2Mg8Sb2 cuboctahedra; edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with four Mg(3,3,3)Hf2Mg8Sb2 cuboctahedra; edges with four equivalent Sb(1)Hf2Mg10 cuboctahedra; edges with eight Mg(1,1,1)Hf2Mg8Sb2 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Hf(1)Mg10Sb2 cuboctahedra; faces with two equivalent Sb(1)Hf2Mg10 cuboctahedra; faces with four equivalent Mg(1)Hf2Mg8Sb2 cuboctahedra; faces with four Mg(3,3,3)Hf2Mg8Sb2 cuboctahedra; and faces with six equivalent Mg(2)Mg10Sb2 cuboctahedra. Both Hf(1)-Sb(1) bond lengths are 3.08 Å. Sb(1) is bonded to two equivalent Mg(2); four Mg(1,1,1); four Mg(3,3); and two equivalent Hf(1) atoms to form SbHf2Mg10 cuboctahedra that share corners with four equivalent Mg(2)Mg10Sb2 cuboctahedra; corners with six equivalent Sb(1)Hf2Mg10 cuboctahedra; corners with eight Mg(1,1,1)Hf2Mg8Sb2 cuboctahedra; edges with two equivalent Mg(2)Mg10Sb2 cuboctahedra; edges with four Mg(1,1,1)Hf2Mg8Sb2 cuboctahedra; edges with four equivalent Hf(1)Mg10Sb2 cuboctahedra; edges with eight Mg(3,3,3)Hf2Mg8Sb2 cuboctahedra; faces with two equivalent Mg(2)Mg10Sb2 cuboctahedra; faces with two equivalent Hf(1)Mg10Sb2 cuboctahedra; faces with two equivalent Sb(1)Hf2Mg10 cuboctahedra; faces with four Mg(1,1,1)Hf2Mg8Sb2 cuboctahedra; faces with four Mg(3,3)Hf2Mg8Sb2 cuboctahedra; and faces with six equivalent Mg(4)Hf2Mg10 cuboctahedra.