Mg7Sc is alpha La-derived structured and crystallizes in the cubic Fm-3m space group. There are twenty-five inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to twelve Mg(2,2,2,2,2,2,2,2,2,2,2,2) atoms to form MgMg12 cuboctahedra that share corners with twelve equivalent Mg(1)Mg12 cuboctahedra; edges with twenty-four Mg(2,2,2,2,2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra; faces with six equivalent Sc(1)Mg12 cuboctahedra; and faces with twelve Mg(2,2,2,2,2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(1); eight Mg(2,2,2,2,2,2,2,2); and two equivalent Sc(1) atoms to form MgMg10Sc2 cuboctahedra that share corners with twelve Mg(2,2,2)Mg10Sc2 cuboctahedra; edges with four equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Sc(1)Mg12 cuboctahedra; edges with sixteen Mg(2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Sc(1)Mg12 cuboctahedra; and faces with fourteen Mg(2,2,2,2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra. In the third Mg site, Mg(2) is bonded to two equivalent Mg(1); eight Mg(2,2,2,2,2,2,2,2); and two equivalent Sc(1) atoms to form MgMg10Sc2 cuboctahedra that share corners with twelve Mg(2,2,2)Mg10Sc2 cuboctahedra; edges with four equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Sc(1)Mg12 cuboctahedra; edges with sixteen Mg(2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Sc(1)Mg12 cuboctahedra; and faces with fourteen Mg(2,2,2,2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra. In the fourth Mg site, Mg(2) is bonded to two equivalent Mg(1); eight Mg(2,2,2,2,2,2,2,2); and two equivalent Sc(1) atoms to form MgMg10Sc2 cuboctahedra that share corners with twelve Mg(2,2,2)Mg10Sc2 cuboctahedra; edges with four equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Sc(1)Mg12 cuboctahedra; edges with sixteen Mg(2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Sc(1)Mg12 cuboctahedra; and faces with fourteen Mg(2,2,2,2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra. In the fifth Mg site, Mg(2) is bonded to two equivalent Mg(1); eight Mg(2,2,2,2,2,2,2,2); and two equivalent Sc(1) atoms to form MgMg10Sc2 cuboctahedra that share corners with twelve Mg(2,2,2)Mg10Sc2 cuboctahedra; edges with four equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Sc(1)Mg12 cuboctahedra; edges with sixteen Mg(2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Sc(1)Mg12 cuboctahedra; and faces with fourteen Mg(2,2,2,2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra. In the sixth Mg site, Mg(2) is bonded to two equivalent Mg(1); eight Mg(2,2,2,2,2,2,2,2); and two equivalent Sc(1) atoms to form MgMg10Sc2 cuboctahedra that share corners with twelve Mg(2,2,2)Mg10Sc2 cuboctahedra; edges with four equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Sc(1)Mg12 cuboctahedra; edges with sixteen Mg(2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Sc(1)Mg12 cuboctahedra; and faces with fourteen Mg(2,2,2,2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra. In the seventh Mg site, Mg(2) is bonded to two equivalent Mg(1); eight Mg(2,2,2,2,2,2,2,2); and two equivalent Sc(1) atoms to form MgMg10Sc2 cuboctahedra that share corners with twelve Mg(2,2,2)Mg10Sc2 cuboctahedra; edges with four equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Sc(1)Mg12 cuboctahedra; edges with sixteen Mg(2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Sc(1)Mg12 cuboctahedra; and faces with fourteen Mg(2,2,2,2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra. In the eighth Mg site, Mg(2) is bonded to two equivalent Mg(1); eight Mg(2,2,2,2,2,2,2,2); and two equivalent Sc(1) atoms to form MgMg10Sc2 cuboctahedra that share corners with twelve Mg(2,2,2)Mg10Sc2 cuboctahedra; edges with four equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Sc(1)Mg12 cuboctahedra; edges with sixteen Mg(2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Sc(1)Mg12 cuboctahedra; and faces with fourteen Mg(2,2,2,2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra. In the ninth Mg site, Mg(2) is bonded to two equivalent Mg(1); eight Mg(2,2,2,2,2,2,2,2); and two equivalent Sc(1) atoms to form MgMg10Sc2 cuboctahedra that share corners with twelve Mg(2,2,2)Mg10Sc2 cuboctahedra; edges with four equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Sc(1)Mg12 cuboctahedra; edges with sixteen Mg(2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Sc(1)Mg12 cuboctahedra; and faces with fourteen Mg(2,2,2,2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra. In the tenth Mg site, Mg(2) is bonded to two equivalent Mg(1); eight Mg(2,2,2,2,2,2,2,2); and two equivalent Sc(1) atoms to form MgMg10Sc2 cuboctahedra that share corners with twelve Mg(2,2,2)Mg10Sc2 cuboctahedra; edges with four equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Sc(1)Mg12 cuboctahedra; edges with sixteen Mg(2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Sc(1)Mg12 cuboctahedra; and faces with fourteen Mg(2,2,2,2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra. In the eleventh Mg site, Mg(2) is bonded to two equivalent Mg(1); eight Mg(2,2,2,2,2,2,2,2); and two equivalent Sc(1) atoms to form MgMg10Sc2 cuboctahedra that share corners with twelve Mg(2,2,2)Mg10Sc2 cuboctahedra; edges with four equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Sc(1)Mg12 cuboctahedra; edges with sixteen Mg(2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Sc(1)Mg12 cuboctahedra; and faces with fourteen Mg(2,2,2,2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra. In the twelfth Mg site, Mg(2) is bonded to two equivalent Mg(1); eight Mg(2,2,2,2,2,2,2,2); and two equivalent Sc(1) atoms to form MgMg10Sc2 cuboctahedra that share corners with twelve Mg(2,2,2)Mg10Sc2 cuboctahedra; edges with four equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Sc(1)Mg12 cuboctahedra; edges with sixteen Mg(2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Sc(1)Mg12 cuboctahedra; and faces with fourteen Mg(2,2,2,2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra. In the thirteenth Mg site, Mg(2) is bonded to two equivalent Mg(1); eight Mg(2,2,2,2,2,2,2,2); and two equivalent Sc(1) atoms to form MgMg10Sc2 cuboctahedra that share corners with twelve Mg(2,2,2)Mg10Sc2 cuboctahedra; edges with four equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Sc(1)Mg12 cuboctahedra; edges with sixteen Mg(2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Sc(1)Mg12 cuboctahedra; and faces with fourteen Mg(2,2,2,2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra. In the fourteenth Mg site, Mg(2) is bonded to two equivalent Mg(1); eight Mg(2,2,2,2,2,2,2,2); and two equivalent Sc(1) atoms to form MgMg10Sc2 cuboctahedra that share corners with twelve Mg(2,2,2)Mg10Sc2 cuboctahedra; edges with four equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Sc(1)Mg12 cuboctahedra; edges with sixteen Mg(2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Sc(1)Mg12 cuboctahedra; and faces with fourteen Mg(2,2,2,2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra. In the fifteenth Mg site, Mg(2) is bonded to two equivalent Mg(1); eight Mg(2,2,2,2,2,2,2,2); and two equivalent Sc(1) atoms to form MgMg10Sc2 cuboctahedra that share corners with twelve Mg(2,2,2)Mg10Sc2 cuboctahedra; edges with four equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Sc(1)Mg12 cuboctahedra; edges with sixteen Mg(2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Sc(1)Mg12 cuboctahedra; and faces with fourteen Mg(2,2,2,2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra. In the sixteenth Mg site, Mg(2) is bonded to two equivalent Mg(1); eight Mg(2,2,2,2,2,2,2,2); and two equivalent Sc(1) atoms to form MgMg10Sc2 cuboctahedra that share corners with twelve Mg(2,2,2)Mg10Sc2 cuboctahedra; edges with four equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Sc(1)Mg12 cuboctahedra; edges with sixteen Mg(2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Sc(1)Mg12 cuboctahedra; and faces with fourteen Mg(2,2,2,2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra. In the seventeenth Mg site, Mg(2) is bonded to two equivalent Mg(1); eight Mg(2,2,2,2,2,2,2,2); and two equivalent Sc(1) atoms to form MgMg10Sc2 cuboctahedra that share corners with twelve Mg(2,2,2)Mg10Sc2 cuboctahedra; edges with four equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Sc(1)Mg12 cuboctahedra; edges with sixteen Mg(2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Sc(1)Mg12 cuboctahedra; and faces with fourteen Mg(2,2,2,2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra. In the eighteenth Mg site, Mg(2) is bonded to two equivalent Mg(1); eight Mg(2,2,2,2,2,2,2,2); and two equivalent Sc(1) atoms to form MgMg10Sc2 cuboctahedra that share corners with twelve Mg(2,2,2)Mg10Sc2 cuboctahedra; edges with four equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Sc(1)Mg12 cuboctahedra; edges with sixteen Mg(2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Sc(1)Mg12 cuboctahedra; and faces with fourteen Mg(2,2,2,2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra. In the nineteenth Mg site, Mg(2) is bonded to two equivalent Mg(1); eight Mg(2,2,2,2,2,2,2,2); and two equivalent Sc(1) atoms to form MgMg10Sc2 cuboctahedra that share corners with twelve Mg(2,2,2)Mg10Sc2 cuboctahedra; edges with four equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Sc(1)Mg12 cuboctahedra; edges with sixteen Mg(2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Sc(1)Mg12 cuboctahedra; and faces with fourteen Mg(2,2,2,2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra. In the twentieth Mg site, Mg(2) is bonded to two equivalent Mg(1); eight Mg(2,2,2,2,2,2,2,2); and two equivalent Sc(1) atoms to form MgMg10Sc2 cuboctahedra that share corners with twelve Mg(2,2,2)Mg10Sc2 cuboctahedra; edges with four equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Sc(1)Mg12 cuboctahedra; edges with sixteen Mg(2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Sc(1)Mg12 cuboctahedra; and faces with fourteen Mg(2,2,2,2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra. In the twenty-first Mg site, Mg(2) is bonded to two equivalent Mg(1); eight Mg(2,2,2,2,2,2,2,2); and two equivalent Sc(1) atoms to form MgMg10Sc2 cuboctahedra that share corners with twelve Mg(2,2,2)Mg10Sc2 cuboctahedra; edges with four equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Sc(1)Mg12 cuboctahedra; edges with sixteen Mg(2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Sc(1)Mg12 cuboctahedra; and faces with fourteen Mg(2,2,2,2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra. In the twenty-second Mg site, Mg(2) is bonded to two equivalent Mg(1); eight Mg(2,2,2,2,2,2,2,2); and two equivalent Sc(1) atoms to form MgMg10Sc2 cuboctahedra that share corners with twelve Mg(2,2,2)Mg10Sc2 cuboctahedra; edges with four equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Sc(1)Mg12 cuboctahedra; edges with sixteen Mg(2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Sc(1)Mg12 cuboctahedra; and faces with fourteen Mg(2,2,2,2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra. In the twenty-third Mg site, Mg(2) is bonded to two equivalent Mg(1); eight Mg(2,2,2,2,2,2,2,2); and two equivalent Sc(1) atoms to form MgMg10Sc2 cuboctahedra that share corners with twelve Mg(2,2,2)Mg10Sc2 cuboctahedra; edges with four equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Sc(1)Mg12 cuboctahedra; edges with sixteen Mg(2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Sc(1)Mg12 cuboctahedra; and faces with fourteen Mg(2,2,2,2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra. In the twenty-fourth Mg site, Mg(2) is bonded to two equivalent Mg(1); eight Mg(2,2,2,2,2,2,2,2); and two equivalent Sc(1) atoms to form MgMg10Sc2 cuboctahedra that share corners with twelve Mg(2,2,2)Mg10Sc2 cuboctahedra; edges with four equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Sc(1)Mg12 cuboctahedra; edges with sixteen Mg(2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Sc(1)Mg12 cuboctahedra; and faces with fourteen Mg(2,2,2,2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra. In the twenty-fifth Mg site, Mg(2) is bonded to two equivalent Mg(1); eight Mg(2,2,2,2,2,2,2,2); and two equivalent Sc(1) atoms to form MgMg10Sc2 cuboctahedra that share corners with twelve Mg(2,2,2)Mg10Sc2 cuboctahedra; edges with four equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Sc(1)Mg12 cuboctahedra; edges with sixteen Mg(2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Sc(1)Mg12 cuboctahedra; and faces with fourteen Mg(2,2,2,2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra. Sc(1) is bonded to twelve Mg(2,2,2,2,2,2,2,2,2,2,2,2) atoms to form ScMg12 cuboctahedra that share corners with twelve equivalent Sc(1)Mg12 cuboctahedra; edges with twenty-four Mg(2,2,2,2,2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra; faces with six equivalent Mg(1)Mg12 cuboctahedra; and faces with twelve Mg(2,2,2,2,2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra.
Mg7Sc is alpha La-derived structured and crystallizes in the cubic Fm-3m space group. There are twenty-five inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to twelve Mg(2,2,2,2,2,2,2,2,2,2,2,2) atoms to form MgMg12 cuboctahedra that share corners with twelve equivalent Mg(1)Mg12 cuboctahedra; edges with twenty-four Mg(2,2,2,2,2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra; faces with six equivalent Sc(1)Mg12 cuboctahedra; and faces with twelve Mg(2,2,2,2,2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra. All Mg(1)-Mg(2,2,2,2,2,2,2,2,2,2,2,2) bond lengths are 3.19 Å. In the second Mg site, Mg(2) is bonded to two equivalent Mg(1); eight Mg(2,2,2,2,2,2,2,2); and two equivalent Sc(1) atoms to form MgMg10Sc2 cuboctahedra that share corners with twelve Mg(2,2,2)Mg10Sc2 cuboctahedra; edges with four equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Sc(1)Mg12 cuboctahedra; edges with sixteen Mg(2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Sc(1)Mg12 cuboctahedra; and faces with fourteen Mg(2,2,2,2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra. Both Mg(2)-Mg(1) bond lengths are 3.19 Å. All Mg(2)-Mg(2,2,2,2,2,2,2,2) bond lengths are 3.19 Å. Both Mg(2)-Sc(1) bond lengths are 3.19 Å. In the third Mg site, Mg(2) is bonded to two equivalent Mg(1); eight Mg(2,2,2,2,2,2,2,2); and two equivalent Sc(1) atoms to form MgMg10Sc2 cuboctahedra that share corners with twelve Mg(2,2,2)Mg10Sc2 cuboctahedra; edges with four equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Sc(1)Mg12 cuboctahedra; edges with sixteen Mg(2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Sc(1)Mg12 cuboctahedra; and faces with fourteen Mg(2,2,2,2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra. All Mg(2)-Mg(2,2,2,2,2,2,2) bond lengths are 3.19 Å. Both Mg(2)-Sc(1) bond lengths are 3.19 Å. In the fourth Mg site, Mg(2) is bonded to two equivalent Mg(1); eight Mg(2,2,2,2,2,2,2,2); and two equivalent Sc(1) atoms to form MgMg10Sc2 cuboctahedra that share corners with twelve Mg(2,2,2)Mg10Sc2 cuboctahedra; edges with four equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Sc(1)Mg12 cuboctahedra; edges with sixteen Mg(2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Sc(1)Mg12 cuboctahedra; and faces with fourteen Mg(2,2,2,2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra. Both Mg(2)-Mg(1) bond lengths are 3.19 Å. All Mg(2)-Mg(2,2,2,2,2,2,2) bond lengths are 3.19 Å. Both Mg(2)-Sc(1) bond lengths are 3.19 Å. In the fifth Mg site, Mg(2) is bonded to two equivalent Mg(1); eight Mg(2,2,2,2,2,2,2,2); and two equivalent Sc(1) atoms to form MgMg10Sc2 cuboctahedra that share corners with twelve Mg(2,2,2)Mg10Sc2 cuboctahedra; edges with four equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Sc(1)Mg12 cuboctahedra; edges with sixteen Mg(2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Sc(1)Mg12 cuboctahedra; and faces with fourteen Mg(2,2,2,2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra. All Mg(2)-Mg(2,2,2,2,2,2) bond lengths are 3.19 Å. Both Mg(2)-Sc(1) bond lengths are 3.19 Å. In the sixth Mg site, Mg(2) is bonded to two equivalent Mg(1); eight Mg(2,2,2,2,2,2,2,2); and two equivalent Sc(1) atoms to form MgMg10Sc2 cuboctahedra that share corners with twelve Mg(2,2,2)Mg10Sc2 cuboctahedra; edges with four equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Sc(1)Mg12 cuboctahedra; edges with sixteen Mg(2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Sc(1)Mg12 cuboctahedra; and faces with fourteen Mg(2,2,2,2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra. All Mg(2)-Mg(2,2,2,2,2) bond lengths are 3.19 Å. Both Mg(2)-Sc(1) bond lengths are 3.19 Å. In the seventh Mg site, Mg(2) is bonded to two equivalent Mg(1); eight Mg(2,2,2,2,2,2,2,2); and two equivalent Sc(1) atoms to form MgMg10Sc2 cuboctahedra that share corners with twelve Mg(2,2,2)Mg10Sc2 cuboctahedra; edges with four equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Sc(1)Mg12 cuboctahedra; edges with sixteen Mg(2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Sc(1)Mg12 cuboctahedra; and faces with fourteen Mg(2,2,2,2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra. All Mg(2)-Mg(2,2,2,2,2) bond lengths are 3.19 Å. Both Mg(2)-Sc(1) bond lengths are 3.19 Å. In the eighth Mg site, Mg(2) is bonded to two equivalent Mg(1); eight Mg(2,2,2,2,2,2,2,2); and two equivalent Sc(1) atoms to form MgMg10Sc2 cuboctahedra that share corners with twelve Mg(2,2,2)Mg10Sc2 cuboctahedra; edges with four equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Sc(1)Mg12 cuboctahedra; edges with sixteen Mg(2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Sc(1)Mg12 cuboctahedra; and faces with fourteen Mg(2,2,2,2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra. Both Mg(2)-Mg(1) bond lengths are 3.19 Å. All Mg(2)-Mg(2,2,2,2,2,2,2,2) bond lengths are 3.19 Å. Both Mg(2)-Sc(1) bond lengths are 3.19 Å. In the ninth Mg site, Mg(2) is bonded to two equivalent Mg(1); eight Mg(2,2,2,2,2,2,2,2); and two equivalent Sc(1) atoms to form MgMg10Sc2 cuboctahedra that share corners with twelve Mg(2,2,2)Mg10Sc2 cuboctahedra; edges with four equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Sc(1)Mg12 cuboctahedra; edges with sixteen Mg(2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Sc(1)Mg12 cuboctahedra; and faces with fourteen Mg(2,2,2,2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra. Both Mg(2)-Mg(1) bond lengths are 3.19 Å. All Mg(2)-Mg(2,2,2,2,2,2,2) bond lengths are 3.19 Å. Both Mg(2)-Sc(1) bond lengths are 3.19 Å. In the tenth Mg site, Mg(2) is bonded to two equivalent Mg(1); eight Mg(2,2,2,2,2,2,2,2); and two equivalent Sc(1) atoms to form MgMg10Sc2 cuboctahedra that share corners with twelve Mg(2,2,2)Mg10Sc2 cuboctahedra; edges with four equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Sc(1)Mg12 cuboctahedra; edges with sixteen Mg(2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Sc(1)Mg12 cuboctahedra; and faces with fourteen Mg(2,2,2,2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra. All Mg(2)-Mg(2,2,2,2,2,2) bond lengths are 3.19 Å. Both Mg(2)-Sc(1) bond lengths are 3.19 Å. In the eleventh Mg site, Mg(2) is bonded to two equivalent Mg(1); eight Mg(2,2,2,2,2,2,2,2); and two equivalent Sc(1) atoms to form MgMg10Sc2 cuboctahedra that share corners with twelve Mg(2,2,2)Mg10Sc2 cuboctahedra; edges with four equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Sc(1)Mg12 cuboctahedra; edges with sixteen Mg(2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Sc(1)Mg12 cuboctahedra; and faces with fourteen Mg(2,2,2,2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra. All Mg(2)-Mg(2,2,2,2,2,2) bond lengths are 3.19 Å. Both Mg(2)-Sc(1) bond lengths are 3.19 Å. In the twelfth Mg site, Mg(2) is bonded to two equivalent Mg(1); eight Mg(2,2,2,2,2,2,2,2); and two equivalent Sc(1) atoms to form MgMg10Sc2 cuboctahedra that share corners with twelve Mg(2,2,2)Mg10Sc2 cuboctahedra; edges with four equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Sc(1)Mg12 cuboctahedra; edges with sixteen Mg(2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Sc(1)Mg12 cuboctahedra; and faces with fourteen Mg(2,2,2,2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra. Both Mg(2)-Mg(1) bond lengths are 3.19 Å. All Mg(2)-Mg(2,2,2) bond lengths are 3.19 Å. Both Mg(2)-Sc(1) bond lengths are 3.19 Å. In the thirteenth Mg site, Mg(2) is bonded to two equivalent Mg(1); eight Mg(2,2,2,2,2,2,2,2); and two equivalent Sc(1) atoms to form MgMg10Sc2 cuboctahedra that share corners with twelve Mg(2,2,2)Mg10Sc2 cuboctahedra; edges with four equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Sc(1)Mg12 cuboctahedra; edges with sixteen Mg(2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Sc(1)Mg12 cuboctahedra; and faces with fourteen Mg(2,2,2,2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra. Both Mg(2)-Mg(1) bond lengths are 3.19 Å. All Mg(2)-Mg(2,2,2,2) bond lengths are 3.19 Å. Both Mg(2)-Sc(1) bond lengths are 3.19 Å. In the fourteenth Mg site, Mg(2) is bonded to two equivalent Mg(1); eight Mg(2,2,2,2,2,2,2,2); and two equivalent Sc(1) atoms to form MgMg10Sc2 cuboctahedra that share corners with twelve Mg(2,2,2)Mg10Sc2 cuboctahedra; edges with four equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Sc(1)Mg12 cuboctahedra; edges with sixteen Mg(2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Sc(1)Mg12 cuboctahedra; and faces with fourteen Mg(2,2,2,2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra. All Mg(2)-Mg(2,2,2,2) bond lengths are 3.19 Å. Both Mg(2)-Sc(1) bond lengths are 3.19 Å. In the fifteenth Mg site, Mg(2) is bonded to two equivalent Mg(1); eight Mg(2,2,2,2,2,2,2,2); and two equivalent Sc(1) atoms to form MgMg10Sc2 cuboctahedra that share corners with twelve Mg(2,2,2)Mg10Sc2 cuboctahedra; edges with four equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Sc(1)Mg12 cuboctahedra; edges with sixteen Mg(2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Sc(1)Mg12 cuboctahedra; and faces with fourteen Mg(2,2,2,2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra. The Mg(2)-Mg(2) bond length is 3.19 Å. Both Mg(2)-Sc(1) bond lengths are 3.19 Å. In the sixteenth Mg site, Mg(2) is bonded to two equivalent Mg(1); eight Mg(2,2,2,2,2,2,2,2); and two equivalent Sc(1) atoms to form MgMg10Sc2 cuboctahedra that share corners with twelve Mg(2,2,2)Mg10Sc2 cuboctahedra; edges with four equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Sc(1)Mg12 cuboctahedra; edges with sixteen Mg(2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Sc(1)Mg12 cuboctahedra; and faces with fourteen Mg(2,2,2,2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra. All Mg(2)-Mg(2,2,2) bond lengths are 3.19 Å. Both Mg(2)-Sc(1) bond lengths are 3.19 Å. In the seventeenth Mg site, Mg(2) is bonded to two equivalent Mg(1); eight Mg(2,2,2,2,2,2,2,2); and two equivalent Sc(1) atoms to form MgMg10Sc2 cuboctahedra that share corners with twelve Mg(2,2,2)Mg10Sc2 cuboctahedra; edges with four equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Sc(1)Mg12 cuboctahedra; edges with sixteen Mg(2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Sc(1)Mg12 cuboctahedra; and faces with fourteen Mg(2,2,2,2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra. Both Mg(2)-Mg(1) bond lengths are 3.19 Å. Both Mg(2)-Mg(2,2) bond lengths are 3.19 Å. Both Mg(2)-Sc(1) bond lengths are 3.19 Å. In the eighteenth Mg site, Mg(2) is bonded to two equivalent Mg(1); eight Mg(2,2,2,2,2,2,2,2); and two equivalent Sc(1) atoms to form MgMg10Sc2 cuboctahedra that share corners with twelve Mg(2,2,2)Mg10Sc2 cuboctahedra; edges with four equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Sc(1)Mg12 cuboctahedra; edges with sixteen Mg(2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Sc(1)Mg12 cuboctahedra; and faces with fourteen Mg(2,2,2,2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra. All Mg(2)-Mg(2,2,2) bond lengths are 3.19 Å. Both Mg(2)-Sc(1) bond lengths are 3.19 Å. In the nineteenth Mg site, Mg(2) is bonded to two equivalent Mg(1); eight Mg(2,2,2,2,2,2,2,2); and two equivalent Sc(1) atoms to form MgMg10Sc2 cuboctahedra that share corners with twelve Mg(2,2,2)Mg10Sc2 cuboctahedra; edges with four equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Sc(1)Mg12 cuboctahedra; edges with sixteen Mg(2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Sc(1)Mg12 cuboctahedra; and faces with fourteen Mg(2,2,2,2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra. Both Mg(2)-Mg(1) bond lengths are 3.19 Å. The Mg(2)-Mg(2) bond length is 3.19 Å. Both Mg(2)-Sc(1) bond lengths are 3.19 Å. In the twentieth Mg site, Mg(2) is bonded to two equivalent Mg(1); eight Mg(2,2,2,2,2,2,2,2); and two equivalent Sc(1) atoms to form MgMg10Sc2 cuboctahedra that share corners with twelve Mg(2,2,2)Mg10Sc2 cuboctahedra; edges with four equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Sc(1)Mg12 cuboctahedra; edges with sixteen Mg(2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Sc(1)Mg12 cuboctahedra; and faces with fourteen Mg(2,2,2,2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra. All Mg(2)-Mg(2,2,2,2) bond lengths are 3.19 Å. Both Mg(2)-Sc(1) bond lengths are 3.19 Å. In the twenty-first Mg site, Mg(2) is bonded to two equivalent Mg(1); eight Mg(2,2,2,2,2,2,2,2); and two equivalent Sc(1) atoms to form MgMg10Sc2 cuboctahedra that share corners with twelve Mg(2,2,2)Mg10Sc2 cuboctahedra; edges with four equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Sc(1)Mg12 cuboctahedra; edges with sixteen Mg(2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Sc(1)Mg12 cuboctahedra; and faces with fourteen Mg(2,2,2,2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra. Both Mg(2)-Mg(1) bond lengths are 3.19 Å. The Mg(2)-Mg(2) bond length is 3.19 Å. Both Mg(2)-Sc(1) bond lengths are 3.19 Å. In the twenty-second Mg site, Mg(2) is bonded to two equivalent Mg(1); eight Mg(2,2,2,2,2,2,2,2); and two equivalent Sc(1) atoms to form MgMg10Sc2 cuboctahedra that share corners with twelve Mg(2,2,2)Mg10Sc2 cuboctahedra; edges with four equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Sc(1)Mg12 cuboctahedra; edges with sixteen Mg(2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Sc(1)Mg12 cuboctahedra; and faces with fourteen Mg(2,2,2,2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra. Both Mg(2)-Mg(1) bond lengths are 3.19 Å. Both Mg(2)-Mg(2,2) bond lengths are 3.19 Å. Both Mg(2)-Sc(1) bond lengths are 3.19 Å. In the twenty-third Mg site, Mg(2) is bonded to two equivalent Mg(1); eight Mg(2,2,2,2,2,2,2,2); and two equivalent Sc(1) atoms to form MgMg10Sc2 cuboctahedra that share corners with twelve Mg(2,2,2)Mg10Sc2 cuboctahedra; edges with four equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Sc(1)Mg12 cuboctahedra; edges with sixteen Mg(2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Sc(1)Mg12 cuboctahedra; and faces with fourteen Mg(2,2,2,2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra. Both Mg(2)-Mg(1) bond lengths are 3.19 Å. Both Mg(2)-Mg(2,2) bond lengths are 3.19 Å. Both Mg(2)-Sc(1) bond lengths are 3.19 Å. In the twenty-fourth Mg site, Mg(2) is bonded to two equivalent Mg(1); eight Mg(2,2,2,2,2,2,2,2); and two equivalent Sc(1) atoms to form MgMg10Sc2 cuboctahedra that share corners with twelve Mg(2,2,2)Mg10Sc2 cuboctahedra; edges with four equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Sc(1)Mg12 cuboctahedra; edges with sixteen Mg(2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Sc(1)Mg12 cuboctahedra; and faces with fourteen Mg(2,2,2,2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra. Both Mg(2)-Mg(1) bond lengths are 3.19 Å. The Mg(2)-Mg(2) bond length is 3.19 Å. Both Mg(2)-Sc(1) bond lengths are 3.19 Å. In the twenty-fifth Mg site, Mg(2) is bonded to two equivalent Mg(1); eight Mg(2,2,2,2,2,2,2,2); and two equivalent Sc(1) atoms to form MgMg10Sc2 cuboctahedra that share corners with twelve Mg(2,2,2)Mg10Sc2 cuboctahedra; edges with four equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Sc(1)Mg12 cuboctahedra; edges with sixteen Mg(2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Sc(1)Mg12 cuboctahedra; and faces with fourteen Mg(2,2,2,2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra. Both Mg(2)-Sc(1) bond lengths are 3.19 Å. Sc(1) is bonded to twelve Mg(2,2,2,2,2,2,2,2,2,2,2,2) atoms to form ScMg12 cuboctahedra that share corners with twelve equivalent Sc(1)Mg12 cuboctahedra; edges with twenty-four Mg(2,2,2,2,2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra; faces with six equivalent Mg(1)Mg12 cuboctahedra; and faces with twelve Mg(2,2,2,2,2,2,2,2,2,2,2,2)Mg10Sc2 cuboctahedra.