Mg6CuZn is beta Cu3Ti-derived structured and 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 Cu(1), and two equivalent Zn(1) atoms to form distorted MgMg8Zn2Cu2 cuboctahedra that share corners with four equivalent Mg(2)Mg10Zn2 cuboctahedra; corners with four equivalent Zn(1)Mg10Cu2 cuboctahedra; corners with ten Mg(1,1)Mg8Zn2Cu2 cuboctahedra; edges with two equivalent Mg(2)Mg10Zn2 cuboctahedra; edges with two equivalent Mg(1)Mg8Zn2Cu2 cuboctahedra; edges with two equivalent Zn(1)Mg10Cu2 cuboctahedra; edges with four equivalent Mg(4)Mg10Cu2 cuboctahedra; edges with four equivalent Mg(3)Mg8Zn2Cu2 cuboctahedra; edges with four equivalent Cu(1)Mg10Zn2 cuboctahedra; faces with two equivalent Mg(4)Mg10Cu2 cuboctahedra; faces with two equivalent Mg(2)Mg10Zn2 cuboctahedra; faces with two equivalent Cu(1)Mg10Zn2 cuboctahedra; faces with two equivalent Zn(1)Mg10Cu2 cuboctahedra; faces with four equivalent Mg(1)Mg8Zn2Cu2 cuboctahedra; and faces with eight Mg(3,3,3)Mg8Zn2Cu2 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 Zn(1) atoms to form distorted MgMg10Zn2 cuboctahedra that share corners with four equivalent Zn(1)Mg10Cu2 cuboctahedra; corners with six equivalent Mg(2)Mg10Zn2 cuboctahedra; corners with eight Mg(1,1,1)Mg8Zn2Cu2 cuboctahedra; edges with two equivalent Zn(1)Mg10Cu2 cuboctahedra; edges with four equivalent Mg(4)Mg10Cu2 cuboctahedra; edges with four Mg(1,1,1)Mg8Zn2Cu2 cuboctahedra; edges with eight Mg(3,3,3)Mg8Zn2Cu2 cuboctahedra; faces with two equivalent Mg(4)Mg10Cu2 cuboctahedra; faces with two equivalent Mg(2)Mg10Zn2 cuboctahedra; faces with two equivalent Zn(1)Mg10Cu2 cuboctahedra; faces with four Mg(1,1,1)Mg8Zn2Cu2 cuboctahedra; faces with four Mg(3,3)Mg8Zn2Cu2 cuboctahedra; and faces with six equivalent Cu(1)Mg10Zn2 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 Cu(1), and two equivalent Zn(1) atoms to form distorted MgMg8Zn2Cu2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Cu2 cuboctahedra; corners with four equivalent Cu(1)Mg10Zn2 cuboctahedra; corners with ten Mg(3,3)Mg8Zn2Cu2 cuboctahedra; edges with two equivalent Mg(4)Mg10Cu2 cuboctahedra; edges with two equivalent Mg(3)Mg8Zn2Cu2 cuboctahedra; edges with two equivalent Cu(1)Mg10Zn2 cuboctahedra; edges with four equivalent Mg(2)Mg10Zn2 cuboctahedra; edges with four equivalent Mg(1)Mg8Zn2Cu2 cuboctahedra; edges with four equivalent Zn(1)Mg10Cu2 cuboctahedra; faces with two equivalent Mg(4)Mg10Cu2 cuboctahedra; faces with two equivalent Mg(2)Mg10Zn2 cuboctahedra; faces with two equivalent Cu(1)Mg10Zn2 cuboctahedra; faces with two equivalent Zn(1)Mg10Cu2 cuboctahedra; faces with four Mg(3,3)Mg8Zn2Cu2 cuboctahedra; and faces with eight Mg(1,1,1)Mg8Zn2Cu2 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 Cu(1), and two equivalent Zn(1) atoms to form distorted MgMg8Zn2Cu2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Cu2 cuboctahedra; corners with four equivalent Cu(1)Mg10Zn2 cuboctahedra; corners with ten Mg(3,3,3)Mg8Zn2Cu2 cuboctahedra; edges with two equivalent Mg(4)Mg10Cu2 cuboctahedra; edges with two equivalent Mg(3)Mg8Zn2Cu2 cuboctahedra; edges with two equivalent Cu(1)Mg10Zn2 cuboctahedra; edges with four equivalent Mg(2)Mg10Zn2 cuboctahedra; edges with four equivalent Mg(1)Mg8Zn2Cu2 cuboctahedra; edges with four equivalent Zn(1)Mg10Cu2 cuboctahedra; faces with two equivalent Mg(4)Mg10Cu2 cuboctahedra; faces with two equivalent Mg(2)Mg10Zn2 cuboctahedra; faces with two equivalent Cu(1)Mg10Zn2 cuboctahedra; faces with two equivalent Zn(1)Mg10Cu2 cuboctahedra; faces with four Mg(3,3)Mg8Zn2Cu2 cuboctahedra; and faces with eight Mg(1,1,1)Mg8Zn2Cu2 cuboctahedra. In the fifth Mg site, Mg(4) is bonded to two equivalent Mg(2); four equivalent Mg(1); four Mg(3,3,3); and two equivalent Cu(1) atoms to form distorted MgMg10Cu2 cuboctahedra that share corners with four equivalent Cu(1)Mg10Zn2 cuboctahedra; corners with six equivalent Mg(4)Mg10Cu2 cuboctahedra; corners with eight Mg(3,3,3)Mg8Zn2Cu2 cuboctahedra; edges with two equivalent Cu(1)Mg10Zn2 cuboctahedra; edges with four equivalent Mg(2)Mg10Zn2 cuboctahedra; edges with four Mg(3,3,3)Mg8Zn2Cu2 cuboctahedra; edges with eight Mg(1,1,1)Mg8Zn2Cu2 cuboctahedra; faces with two equivalent Mg(4)Mg10Cu2 cuboctahedra; faces with two equivalent Mg(2)Mg10Zn2 cuboctahedra; faces with two equivalent Cu(1)Mg10Zn2 cuboctahedra; faces with four equivalent Mg(1)Mg8Zn2Cu2 cuboctahedra; faces with four Mg(3,3,3)Mg8Zn2Cu2 cuboctahedra; and faces with six equivalent Zn(1)Mg10Cu2 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 Cu(1), and two equivalent Zn(1) atoms to form distorted MgMg8Zn2Cu2 cuboctahedra that share corners with four equivalent Mg(2)Mg10Zn2 cuboctahedra; corners with four equivalent Zn(1)Mg10Cu2 cuboctahedra; corners with ten Mg(1,1,1)Mg8Zn2Cu2 cuboctahedra; edges with two equivalent Mg(2)Mg10Zn2 cuboctahedra; edges with two equivalent Mg(1)Mg8Zn2Cu2 cuboctahedra; edges with two equivalent Zn(1)Mg10Cu2 cuboctahedra; edges with four equivalent Mg(4)Mg10Cu2 cuboctahedra; edges with four equivalent Mg(3)Mg8Zn2Cu2 cuboctahedra; edges with four equivalent Cu(1)Mg10Zn2 cuboctahedra; faces with two equivalent Mg(4)Mg10Cu2 cuboctahedra; faces with two equivalent Mg(2)Mg10Zn2 cuboctahedra; faces with two equivalent Cu(1)Mg10Zn2 cuboctahedra; faces with two equivalent Zn(1)Mg10Cu2 cuboctahedra; faces with four Mg(1,1)Mg8Zn2Cu2 cuboctahedra; and faces with eight Mg(3,3,3)Mg8Zn2Cu2 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 Cu(1), and two equivalent Zn(1) atoms to form distorted MgMg8Zn2Cu2 cuboctahedra that share corners with four equivalent Mg(2)Mg10Zn2 cuboctahedra; corners with four equivalent Zn(1)Mg10Cu2 cuboctahedra; corners with ten Mg(1,1,1)Mg8Zn2Cu2 cuboctahedra; edges with two equivalent Mg(2)Mg10Zn2 cuboctahedra; edges with two equivalent Mg(1)Mg8Zn2Cu2 cuboctahedra; edges with two equivalent Zn(1)Mg10Cu2 cuboctahedra; edges with four equivalent Mg(4)Mg10Cu2 cuboctahedra; edges with four equivalent Mg(3)Mg8Zn2Cu2 cuboctahedra; edges with four equivalent Cu(1)Mg10Zn2 cuboctahedra; faces with two equivalent Mg(4)Mg10Cu2 cuboctahedra; faces with two equivalent Mg(2)Mg10Zn2 cuboctahedra; faces with two equivalent Cu(1)Mg10Zn2 cuboctahedra; faces with two equivalent Zn(1)Mg10Cu2 cuboctahedra; faces with four Mg(1,1)Mg8Zn2Cu2 cuboctahedra; and faces with eight Mg(3,3)Mg8Zn2Cu2 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 Cu(1), and two equivalent Zn(1) atoms to form distorted MgMg8Zn2Cu2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Cu2 cuboctahedra; corners with four equivalent Cu(1)Mg10Zn2 cuboctahedra; corners with ten Mg(3,3,3)Mg8Zn2Cu2 cuboctahedra; edges with two equivalent Mg(4)Mg10Cu2 cuboctahedra; edges with two equivalent Mg(3)Mg8Zn2Cu2 cuboctahedra; edges with two equivalent Cu(1)Mg10Zn2 cuboctahedra; edges with four equivalent Mg(2)Mg10Zn2 cuboctahedra; edges with four equivalent Mg(1)Mg8Zn2Cu2 cuboctahedra; edges with four equivalent Zn(1)Mg10Cu2 cuboctahedra; faces with two equivalent Mg(4)Mg10Cu2 cuboctahedra; faces with two equivalent Mg(2)Mg10Zn2 cuboctahedra; faces with two equivalent Cu(1)Mg10Zn2 cuboctahedra; faces with two equivalent Zn(1)Mg10Cu2 cuboctahedra; faces with four Mg(3,3)Mg8Zn2Cu2 cuboctahedra; and faces with eight Mg(1,1)Mg8Zn2Cu2 cuboctahedra. Cu(1) is bonded to two equivalent Mg(4); four equivalent Mg(1); four Mg(3,3,3); and two equivalent Zn(1) atoms to form CuMg10Zn2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Cu2 cuboctahedra; corners with six equivalent Cu(1)Mg10Zn2 cuboctahedra; corners with eight Mg(3,3,3)Mg8Zn2Cu2 cuboctahedra; edges with two equivalent Mg(4)Mg10Cu2 cuboctahedra; edges with four Mg(3,3,3)Mg8Zn2Cu2 cuboctahedra; edges with four equivalent Zn(1)Mg10Cu2 cuboctahedra; edges with eight Mg(1,1,1)Mg8Zn2Cu2 cuboctahedra; faces with two equivalent Mg(4)Mg10Cu2 cuboctahedra; faces with two equivalent Cu(1)Mg10Zn2 cuboctahedra; faces with two equivalent Zn(1)Mg10Cu2 cuboctahedra; faces with four equivalent Mg(1)Mg8Zn2Cu2 cuboctahedra; faces with four Mg(3,3,3)Mg8Zn2Cu2 cuboctahedra; and faces with six equivalent Mg(2)Mg10Zn2 cuboctahedra. Zn(1) is bonded to two equivalent Mg(2); four Mg(1,1,1); four Mg(3,3); and two equivalent Cu(1) atoms to form ZnMg10Cu2 cuboctahedra that share corners with four equivalent Mg(2)Mg10Zn2 cuboctahedra; corners with six equivalent Zn(1)Mg10Cu2 cuboctahedra; corners with eight Mg(1,1,1)Mg8Zn2Cu2 cuboctahedra; edges with two equivalent Mg(2)Mg10Zn2 cuboctahedra; edges with four Mg(1,1,1)Mg8Zn2Cu2 cuboctahedra; edges with four equivalent Cu(1)Mg10Zn2 cuboctahedra; edges with eight Mg(3,3,3)Mg8Zn2Cu2 cuboctahedra; faces with two equivalent Mg(2)Mg10Zn2 cuboctahedra; faces with two equivalent Cu(1)Mg10Zn2 cuboctahedra; faces with two equivalent Zn(1)Mg10Cu2 cuboctahedra; faces with four Mg(1,1,1)Mg8Zn2Cu2 cuboctahedra; faces with four Mg(3,3)Mg8Zn2Cu2 cuboctahedra; and faces with six equivalent Mg(4)Mg10Cu2 cuboctahedra.
Mg6CuZn is beta Cu3Ti-derived structured and 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 Cu(1), and two equivalent Zn(1) atoms to form distorted MgMg8Zn2Cu2 cuboctahedra that share corners with four equivalent Mg(2)Mg10Zn2 cuboctahedra; corners with four equivalent Zn(1)Mg10Cu2 cuboctahedra; corners with ten Mg(1,1)Mg8Zn2Cu2 cuboctahedra; edges with two equivalent Mg(2)Mg10Zn2 cuboctahedra; edges with two equivalent Mg(1)Mg8Zn2Cu2 cuboctahedra; edges with two equivalent Zn(1)Mg10Cu2 cuboctahedra; edges with four equivalent Mg(4)Mg10Cu2 cuboctahedra; edges with four equivalent Mg(3)Mg8Zn2Cu2 cuboctahedra; edges with four equivalent Cu(1)Mg10Zn2 cuboctahedra; faces with two equivalent Mg(4)Mg10Cu2 cuboctahedra; faces with two equivalent Mg(2)Mg10Zn2 cuboctahedra; faces with two equivalent Cu(1)Mg10Zn2 cuboctahedra; faces with two equivalent Zn(1)Mg10Cu2 cuboctahedra; faces with four equivalent Mg(1)Mg8Zn2Cu2 cuboctahedra; and faces with eight Mg(3,3,3)Mg8Zn2Cu2 cuboctahedra. There is one shorter (2.89 Å) and one longer (3.11 Å) Mg(1)-Mg(1) bond length. There is one shorter (3.00 Å) and one longer (3.07 Å) Mg(1)-Mg(2) bond length. Both Mg(1)-Mg(3) bond lengths are 3.09 Å. Both Mg(1)-Mg(4) bond lengths are 3.04 Å. Both Mg(1)-Cu(1) bond lengths are 2.98 Å. There is one shorter (2.94 Å) and one longer (3.13 Å) Mg(1)-Zn(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 Zn(1) atoms to form distorted MgMg10Zn2 cuboctahedra that share corners with four equivalent Zn(1)Mg10Cu2 cuboctahedra; corners with six equivalent Mg(2)Mg10Zn2 cuboctahedra; corners with eight Mg(1,1,1)Mg8Zn2Cu2 cuboctahedra; edges with two equivalent Zn(1)Mg10Cu2 cuboctahedra; edges with four equivalent Mg(4)Mg10Cu2 cuboctahedra; edges with four Mg(1,1,1)Mg8Zn2Cu2 cuboctahedra; edges with eight Mg(3,3,3)Mg8Zn2Cu2 cuboctahedra; faces with two equivalent Mg(4)Mg10Cu2 cuboctahedra; faces with two equivalent Mg(2)Mg10Zn2 cuboctahedra; faces with two equivalent Zn(1)Mg10Cu2 cuboctahedra; faces with four Mg(1,1,1)Mg8Zn2Cu2 cuboctahedra; faces with four Mg(3,3)Mg8Zn2Cu2 cuboctahedra; and faces with six equivalent Cu(1)Mg10Zn2 cuboctahedra. Both Mg(2)-Mg(4) bond lengths are 3.02 Å. Both Mg(2)-Mg(1,1) bond lengths are 3.07 Å. All Mg(2)-Mg(3,3) bond lengths are 3.03 Å. Both Mg(2)-Zn(1) bond lengths are 3.00 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 Cu(1), and two equivalent Zn(1) atoms to form distorted MgMg8Zn2Cu2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Cu2 cuboctahedra; corners with four equivalent Cu(1)Mg10Zn2 cuboctahedra; corners with ten Mg(3,3)Mg8Zn2Cu2 cuboctahedra; edges with two equivalent Mg(4)Mg10Cu2 cuboctahedra; edges with two equivalent Mg(3)Mg8Zn2Cu2 cuboctahedra; edges with two equivalent Cu(1)Mg10Zn2 cuboctahedra; edges with four equivalent Mg(2)Mg10Zn2 cuboctahedra; edges with four equivalent Mg(1)Mg8Zn2Cu2 cuboctahedra; edges with four equivalent Zn(1)Mg10Cu2 cuboctahedra; faces with two equivalent Mg(4)Mg10Cu2 cuboctahedra; faces with two equivalent Mg(2)Mg10Zn2 cuboctahedra; faces with two equivalent Cu(1)Mg10Zn2 cuboctahedra; faces with two equivalent Zn(1)Mg10Cu2 cuboctahedra; faces with four Mg(3,3)Mg8Zn2Cu2 cuboctahedra; and faces with eight Mg(1,1,1)Mg8Zn2Cu2 cuboctahedra. Both Mg(3)-Mg(1) bond lengths are 3.09 Å. There is one shorter (2.94 Å) and one longer (3.06 Å) Mg(3)-Mg(3) bond length. There is one shorter (3.01 Å) and one longer (3.06 Å) Mg(3)-Mg(4) bond length. There is one shorter (2.99 Å) and one longer (3.07 Å) Mg(3)-Cu(1) bond length. Both Mg(3)-Zn(1) bond lengths are 3.00 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 Cu(1), and two equivalent Zn(1) atoms to form distorted MgMg8Zn2Cu2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Cu2 cuboctahedra; corners with four equivalent Cu(1)Mg10Zn2 cuboctahedra; corners with ten Mg(3,3,3)Mg8Zn2Cu2 cuboctahedra; edges with two equivalent Mg(4)Mg10Cu2 cuboctahedra; edges with two equivalent Mg(3)Mg8Zn2Cu2 cuboctahedra; edges with two equivalent Cu(1)Mg10Zn2 cuboctahedra; edges with four equivalent Mg(2)Mg10Zn2 cuboctahedra; edges with four equivalent Mg(1)Mg8Zn2Cu2 cuboctahedra; edges with four equivalent Zn(1)Mg10Cu2 cuboctahedra; faces with two equivalent Mg(4)Mg10Cu2 cuboctahedra; faces with two equivalent Mg(2)Mg10Zn2 cuboctahedra; faces with two equivalent Cu(1)Mg10Zn2 cuboctahedra; faces with two equivalent Zn(1)Mg10Cu2 cuboctahedra; faces with four Mg(3,3)Mg8Zn2Cu2 cuboctahedra; and faces with eight Mg(1,1,1)Mg8Zn2Cu2 cuboctahedra. Both Mg(3)-Mg(1) bond lengths are 3.09 Å. There is one shorter (3.01 Å) and one longer (3.06 Å) Mg(3)-Mg(4) bond length. There is one shorter (2.99 Å) and one longer (3.07 Å) Mg(3)-Cu(1) bond length. Both Mg(3)-Zn(1) bond lengths are 3.00 Å. In the fifth Mg site, Mg(4) is bonded to two equivalent Mg(2); four equivalent Mg(1); four Mg(3,3,3); and two equivalent Cu(1) atoms to form distorted MgMg10Cu2 cuboctahedra that share corners with four equivalent Cu(1)Mg10Zn2 cuboctahedra; corners with six equivalent Mg(4)Mg10Cu2 cuboctahedra; corners with eight Mg(3,3,3)Mg8Zn2Cu2 cuboctahedra; edges with two equivalent Cu(1)Mg10Zn2 cuboctahedra; edges with four equivalent Mg(2)Mg10Zn2 cuboctahedra; edges with four Mg(3,3,3)Mg8Zn2Cu2 cuboctahedra; edges with eight Mg(1,1,1)Mg8Zn2Cu2 cuboctahedra; faces with two equivalent Mg(4)Mg10Cu2 cuboctahedra; faces with two equivalent Mg(2)Mg10Zn2 cuboctahedra; faces with two equivalent Cu(1)Mg10Zn2 cuboctahedra; faces with four equivalent Mg(1)Mg8Zn2Cu2 cuboctahedra; faces with four Mg(3,3,3)Mg8Zn2Cu2 cuboctahedra; and faces with six equivalent Zn(1)Mg10Cu2 cuboctahedra. The Mg(4)-Mg(3) bond length is 3.06 Å. Both Mg(4)-Cu(1) bond lengths are 3.00 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 Cu(1), and two equivalent Zn(1) atoms to form distorted MgMg8Zn2Cu2 cuboctahedra that share corners with four equivalent Mg(2)Mg10Zn2 cuboctahedra; corners with four equivalent Zn(1)Mg10Cu2 cuboctahedra; corners with ten Mg(1,1,1)Mg8Zn2Cu2 cuboctahedra; edges with two equivalent Mg(2)Mg10Zn2 cuboctahedra; edges with two equivalent Mg(1)Mg8Zn2Cu2 cuboctahedra; edges with two equivalent Zn(1)Mg10Cu2 cuboctahedra; edges with four equivalent Mg(4)Mg10Cu2 cuboctahedra; edges with four equivalent Mg(3)Mg8Zn2Cu2 cuboctahedra; edges with four equivalent Cu(1)Mg10Zn2 cuboctahedra; faces with two equivalent Mg(4)Mg10Cu2 cuboctahedra; faces with two equivalent Mg(2)Mg10Zn2 cuboctahedra; faces with two equivalent Cu(1)Mg10Zn2 cuboctahedra; faces with two equivalent Zn(1)Mg10Cu2 cuboctahedra; faces with four Mg(1,1)Mg8Zn2Cu2 cuboctahedra; and faces with eight Mg(3,3,3)Mg8Zn2Cu2 cuboctahedra. There is one shorter (2.89 Å) and one longer (3.11 Å) Mg(1)-Mg(1) bond length. Both Mg(1)-Mg(4) bond lengths are 3.04 Å. Both Mg(1)-Cu(1) bond lengths are 2.98 Å. There is one shorter (2.94 Å) and one longer (3.13 Å) Mg(1)-Zn(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 Cu(1), and two equivalent Zn(1) atoms to form distorted MgMg8Zn2Cu2 cuboctahedra that share corners with four equivalent Mg(2)Mg10Zn2 cuboctahedra; corners with four equivalent Zn(1)Mg10Cu2 cuboctahedra; corners with ten Mg(1,1,1)Mg8Zn2Cu2 cuboctahedra; edges with two equivalent Mg(2)Mg10Zn2 cuboctahedra; edges with two equivalent Mg(1)Mg8Zn2Cu2 cuboctahedra; edges with two equivalent Zn(1)Mg10Cu2 cuboctahedra; edges with four equivalent Mg(4)Mg10Cu2 cuboctahedra; edges with four equivalent Mg(3)Mg8Zn2Cu2 cuboctahedra; edges with four equivalent Cu(1)Mg10Zn2 cuboctahedra; faces with two equivalent Mg(4)Mg10Cu2 cuboctahedra; faces with two equivalent Mg(2)Mg10Zn2 cuboctahedra; faces with two equivalent Cu(1)Mg10Zn2 cuboctahedra; faces with two equivalent Zn(1)Mg10Cu2 cuboctahedra; faces with four Mg(1,1)Mg8Zn2Cu2 cuboctahedra; and faces with eight Mg(3,3)Mg8Zn2Cu2 cuboctahedra. Both Mg(1)-Mg(4) bond lengths are 3.04 Å. Both Mg(1)-Cu(1) bond lengths are 2.98 Å. There is one shorter (2.94 Å) and one longer (3.13 Å) Mg(1)-Zn(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 Cu(1), and two equivalent Zn(1) atoms to form distorted MgMg8Zn2Cu2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Cu2 cuboctahedra; corners with four equivalent Cu(1)Mg10Zn2 cuboctahedra; corners with ten Mg(3,3,3)Mg8Zn2Cu2 cuboctahedra; edges with two equivalent Mg(4)Mg10Cu2 cuboctahedra; edges with two equivalent Mg(3)Mg8Zn2Cu2 cuboctahedra; edges with two equivalent Cu(1)Mg10Zn2 cuboctahedra; edges with four equivalent Mg(2)Mg10Zn2 cuboctahedra; edges with four equivalent Mg(1)Mg8Zn2Cu2 cuboctahedra; edges with four equivalent Zn(1)Mg10Cu2 cuboctahedra; faces with two equivalent Mg(4)Mg10Cu2 cuboctahedra; faces with two equivalent Mg(2)Mg10Zn2 cuboctahedra; faces with two equivalent Cu(1)Mg10Zn2 cuboctahedra; faces with two equivalent Zn(1)Mg10Cu2 cuboctahedra; faces with four Mg(3,3)Mg8Zn2Cu2 cuboctahedra; and faces with eight Mg(1,1)Mg8Zn2Cu2 cuboctahedra. Both Mg(3)-Mg(1) bond lengths are 3.09 Å. Both Mg(3)-Mg(2) bond lengths are 3.03 Å. There is one shorter (2.94 Å) and one longer (3.06 Å) Mg(3)-Mg(3) bond length. There is one shorter (2.99 Å) and one longer (3.07 Å) Mg(3)-Cu(1) bond length. Both Mg(3)-Zn(1) bond lengths are 3.00 Å. Cu(1) is bonded to two equivalent Mg(4); four equivalent Mg(1); four Mg(3,3,3); and two equivalent Zn(1) atoms to form CuMg10Zn2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Cu2 cuboctahedra; corners with six equivalent Cu(1)Mg10Zn2 cuboctahedra; corners with eight Mg(3,3,3)Mg8Zn2Cu2 cuboctahedra; edges with two equivalent Mg(4)Mg10Cu2 cuboctahedra; edges with four Mg(3,3,3)Mg8Zn2Cu2 cuboctahedra; edges with four equivalent Zn(1)Mg10Cu2 cuboctahedra; edges with eight Mg(1,1,1)Mg8Zn2Cu2 cuboctahedra; faces with two equivalent Mg(4)Mg10Cu2 cuboctahedra; faces with two equivalent Cu(1)Mg10Zn2 cuboctahedra; faces with two equivalent Zn(1)Mg10Cu2 cuboctahedra; faces with four equivalent Mg(1)Mg8Zn2Cu2 cuboctahedra; faces with four Mg(3,3,3)Mg8Zn2Cu2 cuboctahedra; and faces with six equivalent Mg(2)Mg10Zn2 cuboctahedra. Both Cu(1)-Zn(1) bond lengths are 3.03 Å. Zn(1) is bonded to two equivalent Mg(2); four Mg(1,1,1); four Mg(3,3); and two equivalent Cu(1) atoms to form ZnMg10Cu2 cuboctahedra that share corners with four equivalent Mg(2)Mg10Zn2 cuboctahedra; corners with six equivalent Zn(1)Mg10Cu2 cuboctahedra; corners with eight Mg(1,1,1)Mg8Zn2Cu2 cuboctahedra; edges with two equivalent Mg(2)Mg10Zn2 cuboctahedra; edges with four Mg(1,1,1)Mg8Zn2Cu2 cuboctahedra; edges with four equivalent Cu(1)Mg10Zn2 cuboctahedra; edges with eight Mg(3,3,3)Mg8Zn2Cu2 cuboctahedra; faces with two equivalent Mg(2)Mg10Zn2 cuboctahedra; faces with two equivalent Cu(1)Mg10Zn2 cuboctahedra; faces with two equivalent Zn(1)Mg10Cu2 cuboctahedra; faces with four Mg(1,1,1)Mg8Zn2Cu2 cuboctahedra; faces with four Mg(3,3)Mg8Zn2Cu2 cuboctahedra; and faces with six equivalent Mg(4)Mg10Cu2 cuboctahedra.