Mg6YHf 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 Y(1), and two equivalent Hf(1) atoms to form MgY2Hf2Mg8 cuboctahedra that share corners with four equivalent Mg(2)Y2Mg10 cuboctahedra; corners with four equivalent Y(1)Hf2Mg10 cuboctahedra; corners with ten Mg(1,1,1)Y2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(1)Y2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(2)Y2Mg10 cuboctahedra; edges with two equivalent Y(1)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(3)Y2Hf2Mg8 cuboctahedra; edges with four equivalent Hf(1)Y2Mg10 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Y2Mg10 cuboctahedra; faces with two equivalent Y(1)Hf2Mg10 cuboctahedra; faces with two equivalent Hf(1)Y2Mg10 cuboctahedra; faces with four Mg(1,1)Y2Hf2Mg8 cuboctahedra; and faces with eight equivalent Mg(3)Y2Hf2Mg8 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 Y(1), and two equivalent Hf(1) atoms to form MgY2Hf2Mg8 cuboctahedra that share corners with four equivalent Mg(2)Y2Mg10 cuboctahedra; corners with four equivalent Y(1)Hf2Mg10 cuboctahedra; corners with ten Mg(1,1,1)Y2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(1)Y2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(2)Y2Mg10 cuboctahedra; edges with two equivalent Y(1)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(3)Y2Hf2Mg8 cuboctahedra; edges with four equivalent Hf(1)Y2Mg10 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Y2Mg10 cuboctahedra; faces with two equivalent Y(1)Hf2Mg10 cuboctahedra; faces with two equivalent Hf(1)Y2Mg10 cuboctahedra; faces with four Mg(1,1)Y2Hf2Mg8 cuboctahedra; and faces with eight Mg(3,3)Y2Hf2Mg8 cuboctahedra. In the third Mg site, Mg(2) is bonded to two equivalent Mg(4); four Mg(1,1,1); four Mg(3,3); and two equivalent Y(1) atoms to form MgY2Mg10 cuboctahedra that share corners with four equivalent Y(1)Hf2Mg10 cuboctahedra; corners with six equivalent Mg(2)Y2Mg10 cuboctahedra; corners with eight Mg(1,1,1)Y2Hf2Mg8 cuboctahedra; edges with two equivalent Y(1)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with four Mg(1,1,1)Y2Hf2Mg8 cuboctahedra; edges with eight Mg(3,3)Y2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Y2Mg10 cuboctahedra; faces with two equivalent Y(1)Hf2Mg10 cuboctahedra; faces with four Mg(1,1,1)Y2Hf2Mg8 cuboctahedra; faces with four Mg(3,3)Y2Hf2Mg8 cuboctahedra; and faces with six equivalent Hf(1)Y2Mg10 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 Y(1), and two equivalent Hf(1) atoms to form MgY2Hf2Mg8 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra; corners with four equivalent Hf(1)Y2Mg10 cuboctahedra; corners with ten Mg(3,3)Y2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)Y2Hf2Mg8 cuboctahedra; edges with two equivalent Hf(1)Y2Mg10 cuboctahedra; edges with four equivalent Mg(1)Y2Hf2Mg8 cuboctahedra; edges with four equivalent Mg(2)Y2Mg10 cuboctahedra; edges with four equivalent Y(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Y2Mg10 cuboctahedra; faces with two equivalent Y(1)Hf2Mg10 cuboctahedra; faces with two equivalent Hf(1)Y2Mg10 cuboctahedra; faces with four Mg(3,3)Y2Hf2Mg8 cuboctahedra; and faces with eight Mg(1,1)Y2Hf2Mg8 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 Y(1), and two equivalent Hf(1) atoms to form MgY2Hf2Mg8 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra; corners with four equivalent Hf(1)Y2Mg10 cuboctahedra; corners with ten Mg(3,3)Y2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)Y2Hf2Mg8 cuboctahedra; edges with two equivalent Hf(1)Y2Mg10 cuboctahedra; edges with four equivalent Mg(1)Y2Hf2Mg8 cuboctahedra; edges with four equivalent Mg(2)Y2Mg10 cuboctahedra; edges with four equivalent Y(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Y2Mg10 cuboctahedra; faces with two equivalent Y(1)Hf2Mg10 cuboctahedra; faces with two equivalent Hf(1)Y2Mg10 cuboctahedra; faces with four Mg(3,3)Y2Hf2Mg8 cuboctahedra; and faces with eight Mg(1,1)Y2Hf2Mg8 cuboctahedra. In the sixth Mg site, Mg(4) is bonded to two equivalent Mg(2); four Mg(1,1); four Mg(3,3); and two equivalent Hf(1) atoms to form MgHf2Mg10 cuboctahedra that share corners with four equivalent Hf(1)Y2Mg10 cuboctahedra; corners with six equivalent Mg(4)Hf2Mg10 cuboctahedra; corners with eight Mg(3,3)Y2Hf2Mg8 cuboctahedra; edges with two equivalent Hf(1)Y2Mg10 cuboctahedra; edges with four Mg(3,3)Y2Hf2Mg8 cuboctahedra; edges with four equivalent Mg(2)Y2Mg10 cuboctahedra; edges with eight Mg(1,1,1)Y2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Y2Mg10 cuboctahedra; faces with two equivalent Hf(1)Y2Mg10 cuboctahedra; faces with four Mg(1,1)Y2Hf2Mg8 cuboctahedra; faces with four Mg(3,3)Y2Hf2Mg8 cuboctahedra; and faces with six equivalent Y(1)Hf2Mg10 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 Y(1), and two equivalent Hf(1) atoms to form MgY2Hf2Mg8 cuboctahedra that share corners with four equivalent Mg(2)Y2Mg10 cuboctahedra; corners with four equivalent Y(1)Hf2Mg10 cuboctahedra; corners with ten Mg(1,1)Y2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(1)Y2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(2)Y2Mg10 cuboctahedra; edges with two equivalent Y(1)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(3)Y2Hf2Mg8 cuboctahedra; edges with four equivalent Hf(1)Y2Mg10 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Y2Mg10 cuboctahedra; faces with two equivalent Y(1)Hf2Mg10 cuboctahedra; faces with two equivalent Hf(1)Y2Mg10 cuboctahedra; faces with four equivalent Mg(1)Y2Hf2Mg8 cuboctahedra; and faces with eight Mg(3,3)Y2Hf2Mg8 cuboctahedra. Y(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 YHf2Mg10 cuboctahedra that share corners with four equivalent Mg(2)Y2Mg10 cuboctahedra; corners with six equivalent Y(1)Hf2Mg10 cuboctahedra; corners with eight Mg(1,1,1)Y2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(2)Y2Mg10 cuboctahedra; edges with four Mg(1,1,1)Y2Hf2Mg8 cuboctahedra; edges with four equivalent Hf(1)Y2Mg10 cuboctahedra; edges with eight Mg(3,3)Y2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(2)Y2Mg10 cuboctahedra; faces with two equivalent Y(1)Hf2Mg10 cuboctahedra; faces with two equivalent Hf(1)Y2Mg10 cuboctahedra; faces with four Mg(1,1,1)Y2Hf2Mg8 cuboctahedra; faces with four Mg(3,3)Y2Hf2Mg8 cuboctahedra; and faces with six equivalent Mg(4)Hf2Mg10 cuboctahedra. Hf(1) is bonded to two equivalent Mg(4); four Mg(1,1); four Mg(3,3); and two equivalent Y(1) atoms to form HfY2Mg10 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra; corners with six equivalent Hf(1)Y2Mg10 cuboctahedra; corners with eight Mg(3,3)Y2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with four Mg(3,3)Y2Hf2Mg8 cuboctahedra; edges with four equivalent Y(1)Hf2Mg10 cuboctahedra; edges with eight Mg(1,1,1)Y2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Y(1)Hf2Mg10 cuboctahedra; faces with two equivalent Hf(1)Y2Mg10 cuboctahedra; faces with four Mg(1,1)Y2Hf2Mg8 cuboctahedra; faces with four Mg(3,3)Y2Hf2Mg8 cuboctahedra; and faces with six equivalent Mg(2)Y2Mg10 cuboctahedra.
Mg6YHf 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 Y(1), and two equivalent Hf(1) atoms to form MgY2Hf2Mg8 cuboctahedra that share corners with four equivalent Mg(2)Y2Mg10 cuboctahedra; corners with four equivalent Y(1)Hf2Mg10 cuboctahedra; corners with ten Mg(1,1,1)Y2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(1)Y2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(2)Y2Mg10 cuboctahedra; edges with two equivalent Y(1)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(3)Y2Hf2Mg8 cuboctahedra; edges with four equivalent Hf(1)Y2Mg10 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Y2Mg10 cuboctahedra; faces with two equivalent Y(1)Hf2Mg10 cuboctahedra; faces with two equivalent Hf(1)Y2Mg10 cuboctahedra; faces with four Mg(1,1)Y2Hf2Mg8 cuboctahedra; and faces with eight equivalent Mg(3)Y2Hf2Mg8 cuboctahedra. There is one shorter (3.17 Å) and one longer (3.36 Å) Mg(1)-Mg(1) bond length. There is one shorter (3.25 Å) and one longer (3.30 Å) Mg(1)-Mg(2) bond length. Both Mg(1)-Mg(3) bond lengths are 3.21 Å. Both Mg(1)-Mg(4) bond lengths are 3.22 Å. There is one shorter (3.21 Å) and one longer (3.33 Å) Mg(1)-Y(1) bond length. Both Mg(1)-Hf(1) bond lengths are 3.17 Å. 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 Y(1), and two equivalent Hf(1) atoms to form MgY2Hf2Mg8 cuboctahedra that share corners with four equivalent Mg(2)Y2Mg10 cuboctahedra; corners with four equivalent Y(1)Hf2Mg10 cuboctahedra; corners with ten Mg(1,1,1)Y2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(1)Y2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(2)Y2Mg10 cuboctahedra; edges with two equivalent Y(1)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(3)Y2Hf2Mg8 cuboctahedra; edges with four equivalent Hf(1)Y2Mg10 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Y2Mg10 cuboctahedra; faces with two equivalent Y(1)Hf2Mg10 cuboctahedra; faces with two equivalent Hf(1)Y2Mg10 cuboctahedra; faces with four Mg(1,1)Y2Hf2Mg8 cuboctahedra; and faces with eight Mg(3,3)Y2Hf2Mg8 cuboctahedra. There is one shorter (3.25 Å) and one longer (3.30 Å) Mg(1)-Mg(2) bond length. Both Mg(1)-Mg(3) bond lengths are 3.21 Å. Both Mg(1)-Mg(4) bond lengths are 3.22 Å. There is one shorter (3.21 Å) and one longer (3.33 Å) Mg(1)-Y(1) bond length. Both Mg(1)-Hf(1) bond lengths are 3.17 Å. In the third Mg site, Mg(2) is bonded to two equivalent Mg(4); four Mg(1,1,1); four Mg(3,3); and two equivalent Y(1) atoms to form MgY2Mg10 cuboctahedra that share corners with four equivalent Y(1)Hf2Mg10 cuboctahedra; corners with six equivalent Mg(2)Y2Mg10 cuboctahedra; corners with eight Mg(1,1,1)Y2Hf2Mg8 cuboctahedra; edges with two equivalent Y(1)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with four Mg(1,1,1)Y2Hf2Mg8 cuboctahedra; edges with eight Mg(3,3)Y2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Y2Mg10 cuboctahedra; faces with two equivalent Y(1)Hf2Mg10 cuboctahedra; faces with four Mg(1,1,1)Y2Hf2Mg8 cuboctahedra; faces with four Mg(3,3)Y2Hf2Mg8 cuboctahedra; and faces with six equivalent Hf(1)Y2Mg10 cuboctahedra. Both Mg(2)-Mg(4) bond lengths are 3.23 Å. Both Mg(2)-Mg(1) bond lengths are 3.25 Å. All Mg(2)-Mg(3,3) bond lengths are 3.20 Å. Both Mg(2)-Y(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 Y(1), and two equivalent Hf(1) atoms to form MgY2Hf2Mg8 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra; corners with four equivalent Hf(1)Y2Mg10 cuboctahedra; corners with ten Mg(3,3)Y2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)Y2Hf2Mg8 cuboctahedra; edges with two equivalent Hf(1)Y2Mg10 cuboctahedra; edges with four equivalent Mg(1)Y2Hf2Mg8 cuboctahedra; edges with four equivalent Mg(2)Y2Mg10 cuboctahedra; edges with four equivalent Y(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Y2Mg10 cuboctahedra; faces with two equivalent Y(1)Hf2Mg10 cuboctahedra; faces with two equivalent Hf(1)Y2Mg10 cuboctahedra; faces with four Mg(3,3)Y2Hf2Mg8 cuboctahedra; and faces with eight Mg(1,1)Y2Hf2Mg8 cuboctahedra. Both Mg(3)-Mg(1) bond lengths are 3.21 Å. There is one shorter (3.24 Å) and one longer (3.29 Å) Mg(3)-Mg(3) bond length. There is one shorter (3.25 Å) and one longer (3.29 Å) Mg(3)-Mg(4) bond length. Both Mg(3)-Y(1) bond lengths are 3.22 Å. There is one shorter (3.23 Å) and one longer (3.31 Å) Mg(3)-Hf(1) bond length. 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 Y(1), and two equivalent Hf(1) atoms to form MgY2Hf2Mg8 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra; corners with four equivalent Hf(1)Y2Mg10 cuboctahedra; corners with ten Mg(3,3)Y2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)Y2Hf2Mg8 cuboctahedra; edges with two equivalent Hf(1)Y2Mg10 cuboctahedra; edges with four equivalent Mg(1)Y2Hf2Mg8 cuboctahedra; edges with four equivalent Mg(2)Y2Mg10 cuboctahedra; edges with four equivalent Y(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Y2Mg10 cuboctahedra; faces with two equivalent Y(1)Hf2Mg10 cuboctahedra; faces with two equivalent Hf(1)Y2Mg10 cuboctahedra; faces with four Mg(3,3)Y2Hf2Mg8 cuboctahedra; and faces with eight Mg(1,1)Y2Hf2Mg8 cuboctahedra. Both Mg(3)-Mg(1) bond lengths are 3.21 Å. There is one shorter (3.25 Å) and one longer (3.29 Å) Mg(3)-Mg(4) bond length. Both Mg(3)-Y(1) bond lengths are 3.22 Å. There is one shorter (3.23 Å) and one longer (3.31 Å) Mg(3)-Hf(1) bond length. In the sixth Mg site, Mg(4) is bonded to two equivalent Mg(2); four Mg(1,1); four Mg(3,3); and two equivalent Hf(1) atoms to form MgHf2Mg10 cuboctahedra that share corners with four equivalent Hf(1)Y2Mg10 cuboctahedra; corners with six equivalent Mg(4)Hf2Mg10 cuboctahedra; corners with eight Mg(3,3)Y2Hf2Mg8 cuboctahedra; edges with two equivalent Hf(1)Y2Mg10 cuboctahedra; edges with four Mg(3,3)Y2Hf2Mg8 cuboctahedra; edges with four equivalent Mg(2)Y2Mg10 cuboctahedra; edges with eight Mg(1,1,1)Y2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Y2Mg10 cuboctahedra; faces with two equivalent Hf(1)Y2Mg10 cuboctahedra; faces with four Mg(1,1)Y2Hf2Mg8 cuboctahedra; faces with four Mg(3,3)Y2Hf2Mg8 cuboctahedra; and faces with six equivalent Y(1)Hf2Mg10 cuboctahedra. Both Mg(4)-Hf(1) bond lengths are 3.26 Å. 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 Y(1), and two equivalent Hf(1) atoms to form MgY2Hf2Mg8 cuboctahedra that share corners with four equivalent Mg(2)Y2Mg10 cuboctahedra; corners with four equivalent Y(1)Hf2Mg10 cuboctahedra; corners with ten Mg(1,1)Y2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(1)Y2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(2)Y2Mg10 cuboctahedra; edges with two equivalent Y(1)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(3)Y2Hf2Mg8 cuboctahedra; edges with four equivalent Hf(1)Y2Mg10 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Y2Mg10 cuboctahedra; faces with two equivalent Y(1)Hf2Mg10 cuboctahedra; faces with two equivalent Hf(1)Y2Mg10 cuboctahedra; faces with four equivalent Mg(1)Y2Hf2Mg8 cuboctahedra; and faces with eight Mg(3,3)Y2Hf2Mg8 cuboctahedra. There is one shorter (3.17 Å) and one longer (3.36 Å) Mg(1)-Mg(1) bond length. Both Mg(1)-Mg(4) bond lengths are 3.22 Å. There is one shorter (3.21 Å) and one longer (3.33 Å) Mg(1)-Y(1) bond length. Both Mg(1)-Hf(1) bond lengths are 3.17 Å. Y(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 YHf2Mg10 cuboctahedra that share corners with four equivalent Mg(2)Y2Mg10 cuboctahedra; corners with six equivalent Y(1)Hf2Mg10 cuboctahedra; corners with eight Mg(1,1,1)Y2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(2)Y2Mg10 cuboctahedra; edges with four Mg(1,1,1)Y2Hf2Mg8 cuboctahedra; edges with four equivalent Hf(1)Y2Mg10 cuboctahedra; edges with eight Mg(3,3)Y2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(2)Y2Mg10 cuboctahedra; faces with two equivalent Y(1)Hf2Mg10 cuboctahedra; faces with two equivalent Hf(1)Y2Mg10 cuboctahedra; faces with four Mg(1,1,1)Y2Hf2Mg8 cuboctahedra; faces with four Mg(3,3)Y2Hf2Mg8 cuboctahedra; and faces with six equivalent Mg(4)Hf2Mg10 cuboctahedra. Both Y(1)-Hf(1) bond lengths are 3.22 Å. Hf(1) is bonded to two equivalent Mg(4); four Mg(1,1); four Mg(3,3); and two equivalent Y(1) atoms to form HfY2Mg10 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra; corners with six equivalent Hf(1)Y2Mg10 cuboctahedra; corners with eight Mg(3,3)Y2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with four Mg(3,3)Y2Hf2Mg8 cuboctahedra; edges with four equivalent Y(1)Hf2Mg10 cuboctahedra; edges with eight Mg(1,1,1)Y2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Y(1)Hf2Mg10 cuboctahedra; faces with two equivalent Hf(1)Y2Mg10 cuboctahedra; faces with four Mg(1,1)Y2Hf2Mg8 cuboctahedra; faces with four Mg(3,3)Y2Hf2Mg8 cuboctahedra; and faces with six equivalent Mg(2)Y2Mg10 cuboctahedra.