Mg6HfBi crystallizes in the orthorhombic Amm2 space group. There are seven 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 Bi(1) atoms to form distorted MgHf2Mg8Bi2 cuboctahedra that share corners with four equivalent Mg(2)Mg10Bi2 cuboctahedra; corners with four equivalent Bi(1)Hf2Mg10 cuboctahedra; corners with ten Mg(1,1)Hf2Mg8Bi2 cuboctahedra; edges with two equivalent Mg(1)Hf2Mg8Bi2 cuboctahedra; edges with two equivalent Mg(2)Mg10Bi2 cuboctahedra; edges with two equivalent Bi(1)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(3)Hf2Mg8Bi2 cuboctahedra; edges with four equivalent Hf(1)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Mg10Bi2 cuboctahedra; faces with two equivalent Hf(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Hf2Mg10 cuboctahedra; faces with four Mg(1,1)Hf2Mg8Bi2 cuboctahedra; and faces with eight Mg(3,3,3)Hf2Mg8Bi2 cuboctahedra. In the second 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 Bi(1) atoms to form distorted MgHf2Mg8Bi2 cuboctahedra that share corners with four equivalent Mg(2)Mg10Bi2 cuboctahedra; corners with four equivalent Bi(1)Hf2Mg10 cuboctahedra; corners with ten Mg(1,1)Hf2Mg8Bi2 cuboctahedra; edges with two equivalent Mg(1)Hf2Mg8Bi2 cuboctahedra; edges with two equivalent Mg(2)Mg10Bi2 cuboctahedra; edges with two equivalent Bi(1)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(3)Hf2Mg8Bi2 cuboctahedra; edges with four equivalent Hf(1)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Mg10Bi2 cuboctahedra; faces with two equivalent Hf(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Hf2Mg10 cuboctahedra; faces with four Mg(1,1)Hf2Mg8Bi2 cuboctahedra; and faces with eight Mg(3,3)Hf2Mg8Bi2 cuboctahedra. In the third Mg site, Mg(2) is bonded to two equivalent Mg(4); four Mg(1,1); four Mg(3,3); and two equivalent Bi(1) atoms to form distorted MgMg10Bi2 cuboctahedra that share corners with four equivalent Bi(1)Hf2Mg10 cuboctahedra; corners with six equivalent Mg(2)Mg10Bi2 cuboctahedra; corners with eight Mg(1,1)Hf2Mg8Bi2 cuboctahedra; edges with two equivalent Bi(1)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with four Mg(1,1)Hf2Mg8Bi2 cuboctahedra; edges with eight Mg(3,3,3)Hf2Mg8Bi2 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Hf2Mg10 cuboctahedra; faces with four Mg(1,1)Hf2Mg8Bi2 cuboctahedra; faces with four Mg(3,3)Hf2Mg8Bi2 cuboctahedra; and faces with six equivalent Hf(1)Mg10Bi2 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 Bi(1) atoms to form distorted MgHf2Mg8Bi2 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra; corners with four equivalent Hf(1)Mg10Bi2 cuboctahedra; corners with ten Mg(3,3)Hf2Mg8Bi2 cuboctahedra; edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)Hf2Mg8Bi2 cuboctahedra; edges with two equivalent Hf(1)Mg10Bi2 cuboctahedra; edges with four equivalent Mg(1)Hf2Mg8Bi2 cuboctahedra; edges with four equivalent Mg(2)Mg10Bi2 cuboctahedra; edges with four equivalent Bi(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Mg10Bi2 cuboctahedra; faces with two equivalent Hf(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Hf2Mg10 cuboctahedra; faces with four Mg(3,3)Hf2Mg8Bi2 cuboctahedra; and faces with eight Mg(1,1)Hf2Mg8Bi2 cuboctahedra. In the fifth 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 Bi(1) atoms to form distorted MgHf2Mg8Bi2 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra; corners with four equivalent Hf(1)Mg10Bi2 cuboctahedra; corners with ten Mg(3,3,3)Hf2Mg8Bi2 cuboctahedra; edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)Hf2Mg8Bi2 cuboctahedra; edges with two equivalent Hf(1)Mg10Bi2 cuboctahedra; edges with four equivalent Mg(1)Hf2Mg8Bi2 cuboctahedra; edges with four equivalent Mg(2)Mg10Bi2 cuboctahedra; edges with four equivalent Bi(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Mg10Bi2 cuboctahedra; faces with two equivalent Hf(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Hf2Mg10 cuboctahedra; faces with four Mg(3,3)Hf2Mg8Bi2 cuboctahedra; and faces with eight Mg(1,1)Hf2Mg8Bi2 cuboctahedra. In the sixth 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)Mg10Bi2 cuboctahedra; corners with six equivalent Mg(4)Hf2Mg10 cuboctahedra; corners with eight Mg(3,3,3)Hf2Mg8Bi2 cuboctahedra; edges with two equivalent Hf(1)Mg10Bi2 cuboctahedra; edges with four Mg(3,3,3)Hf2Mg8Bi2 cuboctahedra; edges with four equivalent Mg(2)Mg10Bi2 cuboctahedra; edges with eight Mg(1,1)Hf2Mg8Bi2 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Mg10Bi2 cuboctahedra; faces with two equivalent Hf(1)Mg10Bi2 cuboctahedra; faces with four Mg(1,1)Hf2Mg8Bi2 cuboctahedra; faces with four Mg(3,3,3)Hf2Mg8Bi2 cuboctahedra; and faces with six equivalent Bi(1)Hf2Mg10 cuboctahedra. In the seventh 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 Bi(1) atoms to form distorted MgHf2Mg8Bi2 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra; corners with four equivalent Hf(1)Mg10Bi2 cuboctahedra; corners with ten Mg(3,3)Hf2Mg8Bi2 cuboctahedra; edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)Hf2Mg8Bi2 cuboctahedra; edges with two equivalent Hf(1)Mg10Bi2 cuboctahedra; edges with four equivalent Mg(1)Hf2Mg8Bi2 cuboctahedra; edges with four equivalent Mg(2)Mg10Bi2 cuboctahedra; edges with four equivalent Bi(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Mg10Bi2 cuboctahedra; faces with two equivalent Hf(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Hf2Mg10 cuboctahedra; faces with four Mg(3,3)Hf2Mg8Bi2 cuboctahedra; and faces with eight Mg(1,1)Hf2Mg8Bi2 cuboctahedra. Hf(1) is bonded to two equivalent Mg(4); four Mg(1,1); four Mg(3,3,3); and two equivalent Bi(1) atoms to form distorted HfMg10Bi2 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra; corners with six equivalent Hf(1)Mg10Bi2 cuboctahedra; corners with eight Mg(3,3,3)Hf2Mg8Bi2 cuboctahedra; edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with four Mg(3,3,3)Hf2Mg8Bi2 cuboctahedra; edges with four equivalent Bi(1)Hf2Mg10 cuboctahedra; edges with eight Mg(1,1)Hf2Mg8Bi2 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Hf(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Hf2Mg10 cuboctahedra; faces with four Mg(1,1)Hf2Mg8Bi2 cuboctahedra; faces with four Mg(3,3,3)Hf2Mg8Bi2 cuboctahedra; and faces with six equivalent Mg(2)Mg10Bi2 cuboctahedra. Bi(1) is bonded to two equivalent Mg(2); four Mg(1,1); four Mg(3,3); and two equivalent Hf(1) atoms to form BiHf2Mg10 cuboctahedra that share corners with four equivalent Mg(2)Mg10Bi2 cuboctahedra; corners with six equivalent Bi(1)Hf2Mg10 cuboctahedra; corners with eight Mg(1,1)Hf2Mg8Bi2 cuboctahedra; edges with two equivalent Mg(2)Mg10Bi2 cuboctahedra; edges with four Mg(1,1)Hf2Mg8Bi2 cuboctahedra; edges with four equivalent Hf(1)Mg10Bi2 cuboctahedra; edges with eight Mg(3,3,3)Hf2Mg8Bi2 cuboctahedra; faces with two equivalent Mg(2)Mg10Bi2 cuboctahedra; faces with two equivalent Hf(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Hf2Mg10 cuboctahedra; faces with four Mg(1,1)Hf2Mg8Bi2 cuboctahedra; faces with four Mg(3,3)Hf2Mg8Bi2 cuboctahedra; and faces with six equivalent Mg(4)Hf2Mg10 cuboctahedra.
Mg6HfBi crystallizes in the orthorhombic Amm2 space group. There are seven 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 Bi(1) atoms to form distorted MgHf2Mg8Bi2 cuboctahedra that share corners with four equivalent Mg(2)Mg10Bi2 cuboctahedra; corners with four equivalent Bi(1)Hf2Mg10 cuboctahedra; corners with ten Mg(1,1)Hf2Mg8Bi2 cuboctahedra; edges with two equivalent Mg(1)Hf2Mg8Bi2 cuboctahedra; edges with two equivalent Mg(2)Mg10Bi2 cuboctahedra; edges with two equivalent Bi(1)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(3)Hf2Mg8Bi2 cuboctahedra; edges with four equivalent Hf(1)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Mg10Bi2 cuboctahedra; faces with two equivalent Hf(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Hf2Mg10 cuboctahedra; faces with four Mg(1,1)Hf2Mg8Bi2 cuboctahedra; and faces with eight Mg(3,3,3)Hf2Mg8Bi2 cuboctahedra. Both Mg(1)-Mg(1) bond lengths are 3.26 Å. There is one shorter (3.18 Å) and one longer (3.21 Å) Mg(1)-Mg(2) bond length. Both Mg(1)-Mg(3) bond lengths are 3.16 Å. Both Mg(1)-Mg(4) bond lengths are 3.20 Å. Both Mg(1)-Hf(1) bond lengths are 3.20 Å. There is one shorter (3.16 Å) and one longer (3.23 Å) Mg(1)-Bi(1) bond length. In the second 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 Bi(1) atoms to form distorted MgHf2Mg8Bi2 cuboctahedra that share corners with four equivalent Mg(2)Mg10Bi2 cuboctahedra; corners with four equivalent Bi(1)Hf2Mg10 cuboctahedra; corners with ten Mg(1,1)Hf2Mg8Bi2 cuboctahedra; edges with two equivalent Mg(1)Hf2Mg8Bi2 cuboctahedra; edges with two equivalent Mg(2)Mg10Bi2 cuboctahedra; edges with two equivalent Bi(1)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(3)Hf2Mg8Bi2 cuboctahedra; edges with four equivalent Hf(1)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Mg10Bi2 cuboctahedra; faces with two equivalent Hf(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Hf2Mg10 cuboctahedra; faces with four Mg(1,1)Hf2Mg8Bi2 cuboctahedra; and faces with eight Mg(3,3)Hf2Mg8Bi2 cuboctahedra. There is one shorter (3.18 Å) and one longer (3.21 Å) Mg(1)-Mg(2) bond length. Both Mg(1)-Mg(3) bond lengths are 3.16 Å. Both Mg(1)-Mg(4) bond lengths are 3.20 Å. Both Mg(1)-Hf(1) bond lengths are 3.20 Å. There is one shorter (3.16 Å) and one longer (3.23 Å) Mg(1)-Bi(1) bond length. In the third Mg site, Mg(2) is bonded to two equivalent Mg(4); four Mg(1,1); four Mg(3,3); and two equivalent Bi(1) atoms to form distorted MgMg10Bi2 cuboctahedra that share corners with four equivalent Bi(1)Hf2Mg10 cuboctahedra; corners with six equivalent Mg(2)Mg10Bi2 cuboctahedra; corners with eight Mg(1,1)Hf2Mg8Bi2 cuboctahedra; edges with two equivalent Bi(1)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with four Mg(1,1)Hf2Mg8Bi2 cuboctahedra; edges with eight Mg(3,3,3)Hf2Mg8Bi2 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Hf2Mg10 cuboctahedra; faces with four Mg(1,1)Hf2Mg8Bi2 cuboctahedra; faces with four Mg(3,3)Hf2Mg8Bi2 cuboctahedra; and faces with six equivalent Hf(1)Mg10Bi2 cuboctahedra. Both Mg(2)-Mg(4) bond lengths are 3.20 Å. All Mg(2)-Mg(3,3) bond lengths are 3.18 Å. Both Mg(2)-Bi(1) bond lengths are 3.26 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 Bi(1) atoms to form distorted MgHf2Mg8Bi2 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra; corners with four equivalent Hf(1)Mg10Bi2 cuboctahedra; corners with ten Mg(3,3)Hf2Mg8Bi2 cuboctahedra; edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)Hf2Mg8Bi2 cuboctahedra; edges with two equivalent Hf(1)Mg10Bi2 cuboctahedra; edges with four equivalent Mg(1)Hf2Mg8Bi2 cuboctahedra; edges with four equivalent Mg(2)Mg10Bi2 cuboctahedra; edges with four equivalent Bi(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Mg10Bi2 cuboctahedra; faces with two equivalent Hf(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Hf2Mg10 cuboctahedra; faces with four Mg(3,3)Hf2Mg8Bi2 cuboctahedra; and faces with eight Mg(1,1)Hf2Mg8Bi2 cuboctahedra. There is one shorter (3.15 Å) and one longer (3.38 Å) Mg(3)-Mg(3) bond length. There is one shorter (3.17 Å) and one longer (3.22 Å) Mg(3)-Mg(4) bond length. There is one shorter (3.13 Å) and one longer (3.26 Å) Mg(3)-Hf(1) bond length. Both Mg(3)-Bi(1) bond lengths are 3.26 Å. In the fifth 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 Bi(1) atoms to form distorted MgHf2Mg8Bi2 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra; corners with four equivalent Hf(1)Mg10Bi2 cuboctahedra; corners with ten Mg(3,3,3)Hf2Mg8Bi2 cuboctahedra; edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)Hf2Mg8Bi2 cuboctahedra; edges with two equivalent Hf(1)Mg10Bi2 cuboctahedra; edges with four equivalent Mg(1)Hf2Mg8Bi2 cuboctahedra; edges with four equivalent Mg(2)Mg10Bi2 cuboctahedra; edges with four equivalent Bi(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Mg10Bi2 cuboctahedra; faces with two equivalent Hf(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Hf2Mg10 cuboctahedra; faces with four Mg(3,3)Hf2Mg8Bi2 cuboctahedra; and faces with eight Mg(1,1)Hf2Mg8Bi2 cuboctahedra. There is one shorter (3.17 Å) and one longer (3.22 Å) Mg(3)-Mg(4) bond length. There is one shorter (3.13 Å) and one longer (3.26 Å) Mg(3)-Hf(1) bond length. Both Mg(3)-Bi(1) bond lengths are 3.26 Å. In the sixth 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)Mg10Bi2 cuboctahedra; corners with six equivalent Mg(4)Hf2Mg10 cuboctahedra; corners with eight Mg(3,3,3)Hf2Mg8Bi2 cuboctahedra; edges with two equivalent Hf(1)Mg10Bi2 cuboctahedra; edges with four Mg(3,3,3)Hf2Mg8Bi2 cuboctahedra; edges with four equivalent Mg(2)Mg10Bi2 cuboctahedra; edges with eight Mg(1,1)Hf2Mg8Bi2 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Mg10Bi2 cuboctahedra; faces with two equivalent Hf(1)Mg10Bi2 cuboctahedra; faces with four Mg(1,1)Hf2Mg8Bi2 cuboctahedra; faces with four Mg(3,3,3)Hf2Mg8Bi2 cuboctahedra; and faces with six equivalent Bi(1)Hf2Mg10 cuboctahedra. The Mg(4)-Mg(3) bond length is 3.17 Å. Both Mg(4)-Hf(1) bond lengths are 3.26 Å. In the seventh 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 Bi(1) atoms to form distorted MgHf2Mg8Bi2 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra; corners with four equivalent Hf(1)Mg10Bi2 cuboctahedra; corners with ten Mg(3,3)Hf2Mg8Bi2 cuboctahedra; edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)Hf2Mg8Bi2 cuboctahedra; edges with two equivalent Hf(1)Mg10Bi2 cuboctahedra; edges with four equivalent Mg(1)Hf2Mg8Bi2 cuboctahedra; edges with four equivalent Mg(2)Mg10Bi2 cuboctahedra; edges with four equivalent Bi(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Mg10Bi2 cuboctahedra; faces with two equivalent Hf(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Hf2Mg10 cuboctahedra; faces with four Mg(3,3)Hf2Mg8Bi2 cuboctahedra; and faces with eight Mg(1,1)Hf2Mg8Bi2 cuboctahedra. Both Mg(3)-Mg(1) bond lengths are 3.16 Å. Both Mg(3)-Mg(2) bond lengths are 3.18 Å. There is one shorter (3.15 Å) and one longer (3.38 Å) Mg(3)-Mg(3) bond length. There is one shorter (3.13 Å) and one longer (3.26 Å) Mg(3)-Hf(1) bond length. Both Mg(3)-Bi(1) bond lengths are 3.26 Å. Hf(1) is bonded to two equivalent Mg(4); four Mg(1,1); four Mg(3,3,3); and two equivalent Bi(1) atoms to form distorted HfMg10Bi2 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra; corners with six equivalent Hf(1)Mg10Bi2 cuboctahedra; corners with eight Mg(3,3,3)Hf2Mg8Bi2 cuboctahedra; edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with four Mg(3,3,3)Hf2Mg8Bi2 cuboctahedra; edges with four equivalent Bi(1)Hf2Mg10 cuboctahedra; edges with eight Mg(1,1)Hf2Mg8Bi2 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Hf(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Hf2Mg10 cuboctahedra; faces with four Mg(1,1)Hf2Mg8Bi2 cuboctahedra; faces with four Mg(3,3,3)Hf2Mg8Bi2 cuboctahedra; and faces with six equivalent Mg(2)Mg10Bi2 cuboctahedra. Both Hf(1)-Bi(1) bond lengths are 3.16 Å. Bi(1) is bonded to two equivalent Mg(2); four Mg(1,1); four Mg(3,3); and two equivalent Hf(1) atoms to form BiHf2Mg10 cuboctahedra that share corners with four equivalent Mg(2)Mg10Bi2 cuboctahedra; corners with six equivalent Bi(1)Hf2Mg10 cuboctahedra; corners with eight Mg(1,1)Hf2Mg8Bi2 cuboctahedra; edges with two equivalent Mg(2)Mg10Bi2 cuboctahedra; edges with four Mg(1,1)Hf2Mg8Bi2 cuboctahedra; edges with four equivalent Hf(1)Mg10Bi2 cuboctahedra; edges with eight Mg(3,3,3)Hf2Mg8Bi2 cuboctahedra; faces with two equivalent Mg(2)Mg10Bi2 cuboctahedra; faces with two equivalent Hf(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Hf2Mg10 cuboctahedra; faces with four Mg(1,1)Hf2Mg8Bi2 cuboctahedra; faces with four Mg(3,3)Hf2Mg8Bi2 cuboctahedra; and faces with six equivalent Mg(4)Hf2Mg10 cuboctahedra.