Mg14CrBi crystallizes in the orthorhombic Amm2 space group. There are thirteen inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(2); two equivalent Mg(6); four Mg(4,4,4); and four Mg(5,5,5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Bi(1)Mg10Cr2 cuboctahedra; corners with six equivalent Mg(1)Mg12 cuboctahedra; corners with eight Mg(3,3)Mg8Cr2Bi2 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with four equivalent Mg(6)Mg11Cr cuboctahedra; edges with four Mg(4,4,4)Mg12 cuboctahedra; edges with eight Mg(5,5,5,5)Mg10CrBi cuboctahedra; faces with two equivalent Mg(6)Mg11Cr cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Cr(1)Mg10Bi2 cuboctahedra; faces with four Mg(5,5,5)Mg10CrBi cuboctahedra; faces with four Mg(4,4,4)Mg12 cuboctahedra; and faces with six equivalent Mg(7)Mg11Bi cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(1); two equivalent Mg(7); four Mg(4,4,4); and four Mg(5,5,5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Cr(1)Mg10Bi2 cuboctahedra; corners with six equivalent Mg(2)Mg12 cuboctahedra; corners with eight Mg(3,3)Mg8Cr2Bi2 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Mg(7)Mg11Bi cuboctahedra; edges with four Mg(4,4,4)Mg12 cuboctahedra; edges with eight Mg(5,5,5,5)Mg10CrBi cuboctahedra; faces with two equivalent Mg(7)Mg11Bi cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Bi(1)Mg10Cr2 cuboctahedra; faces with four Mg(5,5,5)Mg10CrBi cuboctahedra; faces with four Mg(4,4,4)Mg12 cuboctahedra; and faces with six equivalent Mg(6)Mg11Cr cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(3); two Mg(5,5); two equivalent Mg(6); two equivalent Mg(7); two equivalent Cr(1); and two equivalent Bi(1) atoms to form distorted MgMg8Cr2Bi2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with six Mg(3,3)Mg8Cr2Bi2 cuboctahedra; edges with two equivalent Mg(3)Mg8Cr2Bi2 cuboctahedra; edges with two equivalent Cr(1)Mg10Bi2 cuboctahedra; edges with two equivalent Bi(1)Mg10Cr2 cuboctahedra; edges with four equivalent Mg(5)Mg10CrBi cuboctahedra; edges with four equivalent Mg(7)Mg11Bi cuboctahedra; edges with four equivalent Mg(6)Mg11Cr cuboctahedra; faces with two equivalent Mg(7)Mg11Bi cuboctahedra; faces with two equivalent Mg(6)Mg11Cr cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg8Cr2Bi2 cuboctahedra; faces with two equivalent Cr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Mg10Cr2 cuboctahedra; and faces with eight Mg(5,5,5,5)Mg10CrBi cuboctahedra. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(1); two equivalent Mg(2); two equivalent Mg(4); two Mg(5,5); two equivalent Mg(6); and two equivalent Mg(7) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Mg(3)Mg8Cr2Bi2 cuboctahedra; corners with four equivalent Cr(1)Mg10Bi2 cuboctahedra; corners with four equivalent Bi(1)Mg10Cr2 cuboctahedra; corners with six Mg(4,4)Mg12 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with four equivalent Mg(5)Mg10CrBi cuboctahedra; edges with four equivalent Mg(7)Mg11Bi cuboctahedra; edges with four equivalent Mg(6)Mg11Cr cuboctahedra; faces with two equivalent Mg(7)Mg11Bi cuboctahedra; faces with two equivalent Mg(6)Mg11Cr cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg8Cr2Bi2 cuboctahedra; and faces with eight Mg(5,5,5,5)Mg10CrBi cuboctahedra. In the fifth Mg site, Mg(4) is bonded to two equivalent Mg(1); two equivalent Mg(2); two equivalent Mg(4); two Mg(5,5); two equivalent Mg(6); and two equivalent Mg(7) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Mg(3)Mg8Cr2Bi2 cuboctahedra; corners with four equivalent Cr(1)Mg10Bi2 cuboctahedra; corners with four equivalent Bi(1)Mg10Cr2 cuboctahedra; corners with six equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with four equivalent Mg(5)Mg10CrBi cuboctahedra; edges with four equivalent Mg(7)Mg11Bi cuboctahedra; edges with four equivalent Mg(6)Mg11Cr cuboctahedra; faces with two equivalent Mg(7)Mg11Bi cuboctahedra; faces with two equivalent Mg(6)Mg11Cr cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg8Cr2Bi2 cuboctahedra; and faces with eight Mg(5,5,5)Mg10CrBi cuboctahedra. In the sixth Mg site, Mg(5) is bonded to one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), one Cr(1), and one Bi(1) atom to form distorted MgMg10CrBi cuboctahedra that share corners with four equivalent Mg(7)Mg11Bi cuboctahedra; corners with four equivalent Mg(6)Mg11Cr cuboctahedra; corners with ten equivalent Mg(5)Mg10CrBi cuboctahedra; edges with two equivalent Mg(5)Mg10CrBi cuboctahedra; edges with two equivalent Mg(7)Mg11Bi cuboctahedra; edges with two equivalent Mg(6)Mg11Cr cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Mg(3)Mg8Cr2Bi2 cuboctahedra; edges with two equivalent Cr(1)Mg10Bi2 cuboctahedra; edges with two equivalent Bi(1)Mg10Cr2 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Cr(1)Mg10Bi2 cuboctahedra;  a faceface with one Bi(1)Mg10Cr2 cuboctahedra; faces with two equivalent Mg(7)Mg11Bi cuboctahedra; faces with two equivalent Mg(6)Mg11Cr cuboctahedra; faces with four Mg(5,5)Mg10CrBi cuboctahedra; faces with four Mg(4,4)Mg12 cuboctahedra; and faces with four Mg(3,3)Mg8Cr2Bi2 cuboctahedra. In the seventh Mg site, Mg(5) is bonded to one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), one Cr(1), and one Bi(1) atom to form distorted MgMg10CrBi cuboctahedra that share corners with four equivalent Mg(7)Mg11Bi cuboctahedra; corners with four equivalent Mg(6)Mg11Cr cuboctahedra; corners with ten Mg(5,5,5)Mg10CrBi cuboctahedra; edges with two equivalent Mg(5)Mg10CrBi cuboctahedra; edges with two equivalent Mg(7)Mg11Bi cuboctahedra; edges with two equivalent Mg(6)Mg11Cr cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Mg(3)Mg8Cr2Bi2 cuboctahedra; edges with two equivalent Cr(1)Mg10Bi2 cuboctahedra; edges with two equivalent Bi(1)Mg10Cr2 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Cr(1)Mg10Bi2 cuboctahedra;  a faceface with one Bi(1)Mg10Cr2 cuboctahedra; faces with two equivalent Mg(7)Mg11Bi cuboctahedra; faces with two equivalent Mg(6)Mg11Cr cuboctahedra; faces with four equivalent Mg(5)Mg10CrBi cuboctahedra; faces with four Mg(4,4)Mg12 cuboctahedra; and faces with four Mg(3,3)Mg8Cr2Bi2 cuboctahedra. In the eighth Mg site, Mg(5) is bonded to one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), one Cr(1), and one Bi(1) atom to form distorted MgMg10CrBi cuboctahedra that share corners with four equivalent Mg(7)Mg11Bi cuboctahedra; corners with four equivalent Mg(6)Mg11Cr cuboctahedra; corners with ten Mg(5,5,5)Mg10CrBi cuboctahedra; edges with two equivalent Mg(5)Mg10CrBi cuboctahedra; edges with two equivalent Mg(7)Mg11Bi cuboctahedra; edges with two equivalent Mg(6)Mg11Cr cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Mg(3)Mg8Cr2Bi2 cuboctahedra; edges with two equivalent Cr(1)Mg10Bi2 cuboctahedra; edges with two equivalent Bi(1)Mg10Cr2 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Cr(1)Mg10Bi2 cuboctahedra;  a faceface with one Bi(1)Mg10Cr2 cuboctahedra; faces with two equivalent Mg(7)Mg11Bi cuboctahedra; faces with two equivalent Mg(6)Mg11Cr cuboctahedra; faces with four equivalent Mg(5)Mg10CrBi cuboctahedra; faces with four Mg(4,4,4)Mg12 cuboctahedra; and faces with four Mg(3,3)Mg8Cr2Bi2 cuboctahedra. In the ninth Mg site, Mg(6) is bonded to one Mg(1); two equivalent Mg(3); two Mg(4,4); two equivalent Mg(7); four Mg(5,5,5); and one Cr(1) atom to form distorted MgMg11Cr cuboctahedra that share corners with four equivalent Mg(7)Mg11Bi cuboctahedra; corners with six equivalent Mg(6)Mg11Cr cuboctahedra; corners with eight Mg(5,5,5)Mg10CrBi cuboctahedra; edges with two equivalent Mg(7)Mg11Bi cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Cr(1)Mg10Bi2 cuboctahedra; edges with four Mg(5,5,5)Mg10CrBi cuboctahedra; edges with four Mg(4,4,4)Mg12 cuboctahedra; edges with four Mg(3,3)Mg8Cr2Bi2 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Cr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(7)Mg11Bi cuboctahedra; faces with two equivalent Mg(6)Mg11Cr cuboctahedra; faces with two Mg(4,4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg8Cr2Bi2 cuboctahedra; faces with three equivalent Mg(2)Mg12 cuboctahedra; faces with three equivalent Bi(1)Mg10Cr2 cuboctahedra; and faces with four Mg(5,5,5)Mg10CrBi cuboctahedra. In the tenth Mg site, Mg(7) is bonded to one Mg(2); two equivalent Mg(3); two Mg(4,4); two equivalent Mg(6); four Mg(5,5,5); and one Bi(1) atom to form distorted MgMg11Bi cuboctahedra that share corners with four equivalent Mg(6)Mg11Cr cuboctahedra; corners with six equivalent Mg(7)Mg11Bi cuboctahedra; corners with eight Mg(5,5,5)Mg10CrBi cuboctahedra; edges with two equivalent Mg(6)Mg11Cr cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Bi(1)Mg10Cr2 cuboctahedra; edges with four Mg(5,5,5)Mg10CrBi cuboctahedra; edges with four Mg(4,4,4)Mg12 cuboctahedra; edges with four Mg(3,3)Mg8Cr2Bi2 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Bi(1)Mg10Cr2 cuboctahedra; faces with two equivalent Mg(7)Mg11Bi cuboctahedra; faces with two equivalent Mg(6)Mg11Cr cuboctahedra; faces with two Mg(4,4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg8Cr2Bi2 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; faces with three equivalent Cr(1)Mg10Bi2 cuboctahedra; and faces with four Mg(5,5,5)Mg10CrBi cuboctahedra. In the eleventh Mg site, Mg(3) is bonded to two equivalent Mg(3), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), two equivalent Cr(1), and two equivalent Bi(1) atoms to form distorted MgMg8Cr2Bi2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with six Mg(3,3)Mg8Cr2Bi2 cuboctahedra; edges with two equivalent Mg(3)Mg8Cr2Bi2 cuboctahedra; edges with two equivalent Cr(1)Mg10Bi2 cuboctahedra; edges with two equivalent Bi(1)Mg10Cr2 cuboctahedra; edges with four Mg(5,5)Mg10CrBi cuboctahedra; edges with four equivalent Mg(7)Mg11Bi cuboctahedra; edges with four equivalent Mg(6)Mg11Cr cuboctahedra; faces with two equivalent Mg(7)Mg11Bi cuboctahedra; faces with two equivalent Mg(6)Mg11Cr cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg8Cr2Bi2 cuboctahedra; faces with two equivalent Cr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Mg10Cr2 cuboctahedra; and faces with eight Mg(5,5,5)Mg10CrBi cuboctahedra. In the twelfth Mg site, Mg(4) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), two equivalent Mg(5), two equivalent Mg(6), and two equivalent Mg(7) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Mg(3)Mg8Cr2Bi2 cuboctahedra; corners with four equivalent Cr(1)Mg10Bi2 cuboctahedra; corners with four equivalent Bi(1)Mg10Cr2 cuboctahedra; corners with six Mg(4,4)Mg12 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with four Mg(5,5)Mg10CrBi cuboctahedra; edges with four equivalent Mg(7)Mg11Bi cuboctahedra; edges with four equivalent Mg(6)Mg11Cr cuboctahedra; faces with two equivalent Mg(7)Mg11Bi cuboctahedra; faces with two equivalent Mg(6)Mg11Cr cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg8Cr2Bi2 cuboctahedra; and faces with eight Mg(5,5,5)Mg10CrBi cuboctahedra. In the thirteenth Mg site, Mg(5) is bonded to one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), one Cr(1), and one Bi(1) atom to form distorted MgMg10CrBi cuboctahedra that share corners with four equivalent Mg(7)Mg11Bi cuboctahedra; corners with four equivalent Mg(6)Mg11Cr cuboctahedra; corners with ten Mg(5,5,5)Mg10CrBi cuboctahedra; edges with two equivalent Mg(5)Mg10CrBi cuboctahedra; edges with two equivalent Mg(7)Mg11Bi cuboctahedra; edges with two equivalent Mg(6)Mg11Cr cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Mg(3)Mg8Cr2Bi2 cuboctahedra; edges with two equivalent Cr(1)Mg10Bi2 cuboctahedra; edges with two equivalent Bi(1)Mg10Cr2 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Cr(1)Mg10Bi2 cuboctahedra;  a faceface with one Bi(1)Mg10Cr2 cuboctahedra; faces with two equivalent Mg(7)Mg11Bi cuboctahedra; faces with two equivalent Mg(6)Mg11Cr cuboctahedra; faces with four Mg(5,5)Mg10CrBi cuboctahedra; faces with four Mg(4,4,4)Mg12 cuboctahedra; and faces with four Mg(3,3)Mg8Cr2Bi2 cuboctahedra. Cr(1) is bonded to two equivalent Mg(6); four Mg(3,3); four Mg(5,5,5); and two equivalent Bi(1) atoms to form CrMg10Bi2 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with six equivalent Cr(1)Mg10Bi2 cuboctahedra; corners with eight Mg(4,4,4)Mg12 cuboctahedra; edges with two equivalent Bi(1)Mg10Cr2 cuboctahedra; edges with four equivalent Mg(6)Mg11Cr cuboctahedra; edges with four Mg(3,3)Mg8Cr2Bi2 cuboctahedra; edges with eight Mg(5,5,5,5)Mg10CrBi cuboctahedra; faces with two equivalent Mg(6)Mg11Cr cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Bi(1)Mg10Cr2 cuboctahedra; faces with four Mg(5,5,5)Mg10CrBi cuboctahedra; faces with four Mg(3,3)Mg8Cr2Bi2 cuboctahedra; and faces with six equivalent Mg(7)Mg11Bi cuboctahedra. Bi(1) is bonded to two equivalent Mg(7); four Mg(3,3); four Mg(5,5,5); and two equivalent Cr(1) atoms to form BiMg10Cr2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Bi(1)Mg10Cr2 cuboctahedra; corners with eight Mg(4,4,4)Mg12 cuboctahedra; edges with two equivalent Cr(1)Mg10Bi2 cuboctahedra; edges with four equivalent Mg(7)Mg11Bi cuboctahedra; edges with four Mg(3,3)Mg8Cr2Bi2 cuboctahedra; edges with eight Mg(5,5,5,5)Mg10CrBi cuboctahedra; faces with two equivalent Mg(7)Mg11Bi cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Cr(1)Mg10Bi2 cuboctahedra; faces with four Mg(5,5,5)Mg10CrBi cuboctahedra; faces with four Mg(3,3)Mg8Cr2Bi2 cuboctahedra; and faces with six equivalent Mg(6)Mg11Cr cuboctahedra.
Mg14CrBi crystallizes in the orthorhombic Amm2 space group. There are thirteen inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(2); two equivalent Mg(6); four Mg(4,4,4); and four Mg(5,5,5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Bi(1)Mg10Cr2 cuboctahedra; corners with six equivalent Mg(1)Mg12 cuboctahedra; corners with eight Mg(3,3)Mg8Cr2Bi2 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with four equivalent Mg(6)Mg11Cr cuboctahedra; edges with four Mg(4,4,4)Mg12 cuboctahedra; edges with eight Mg(5,5,5,5)Mg10CrBi cuboctahedra; faces with two equivalent Mg(6)Mg11Cr cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Cr(1)Mg10Bi2 cuboctahedra; faces with four Mg(5,5,5)Mg10CrBi cuboctahedra; faces with four Mg(4,4,4)Mg12 cuboctahedra; and faces with six equivalent Mg(7)Mg11Bi cuboctahedra. Both Mg(1)-Mg(2) bond lengths are 3.18 Å. Both Mg(1)-Mg(6) bond lengths are 3.19 Å. All Mg(1)-Mg(4,4,4) bond lengths are 3.19 Å. All Mg(1)-Mg(5,5,5) bond lengths are 3.16 Å. In the second Mg site, Mg(2) is bonded to two equivalent Mg(1); two equivalent Mg(7); four Mg(4,4,4); and four Mg(5,5,5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Cr(1)Mg10Bi2 cuboctahedra; corners with six equivalent Mg(2)Mg12 cuboctahedra; corners with eight Mg(3,3)Mg8Cr2Bi2 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Mg(7)Mg11Bi cuboctahedra; edges with four Mg(4,4,4)Mg12 cuboctahedra; edges with eight Mg(5,5,5,5)Mg10CrBi cuboctahedra; faces with two equivalent Mg(7)Mg11Bi cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Bi(1)Mg10Cr2 cuboctahedra; faces with four Mg(5,5,5)Mg10CrBi cuboctahedra; faces with four Mg(4,4,4)Mg12 cuboctahedra; and faces with six equivalent Mg(6)Mg11Cr cuboctahedra. Both Mg(2)-Mg(7) bond lengths are 3.16 Å. All Mg(2)-Mg(4,4,4) bond lengths are 3.19 Å. All Mg(2)-Mg(5,5,5) bond lengths are 3.20 Å. In the third Mg site, Mg(3) is bonded to two equivalent Mg(3); two Mg(5,5); two equivalent Mg(6); two equivalent Mg(7); two equivalent Cr(1); and two equivalent Bi(1) atoms to form distorted MgMg8Cr2Bi2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with six Mg(3,3)Mg8Cr2Bi2 cuboctahedra; edges with two equivalent Mg(3)Mg8Cr2Bi2 cuboctahedra; edges with two equivalent Cr(1)Mg10Bi2 cuboctahedra; edges with two equivalent Bi(1)Mg10Cr2 cuboctahedra; edges with four equivalent Mg(5)Mg10CrBi cuboctahedra; edges with four equivalent Mg(7)Mg11Bi cuboctahedra; edges with four equivalent Mg(6)Mg11Cr cuboctahedra; faces with two equivalent Mg(7)Mg11Bi cuboctahedra; faces with two equivalent Mg(6)Mg11Cr cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg8Cr2Bi2 cuboctahedra; faces with two equivalent Cr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Mg10Cr2 cuboctahedra; and faces with eight Mg(5,5,5,5)Mg10CrBi cuboctahedra. There is one shorter (3.17 Å) and one longer (3.19 Å) Mg(3)-Mg(3) bond length. Both Mg(3)-Mg(5,5) bond lengths are 3.19 Å. Both Mg(3)-Mg(6) bond lengths are 3.17 Å. Both Mg(3)-Mg(7) bond lengths are 3.21 Å. There is one shorter (3.18 Å) and one longer (3.20 Å) Mg(3)-Cr(1) bond length. There is one shorter (3.17 Å) and one longer (3.20 Å) Mg(3)-Bi(1) bond length. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(1); two equivalent Mg(2); two equivalent Mg(4); two Mg(5,5); two equivalent Mg(6); and two equivalent Mg(7) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Mg(3)Mg8Cr2Bi2 cuboctahedra; corners with four equivalent Cr(1)Mg10Bi2 cuboctahedra; corners with four equivalent Bi(1)Mg10Cr2 cuboctahedra; corners with six Mg(4,4)Mg12 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with four equivalent Mg(5)Mg10CrBi cuboctahedra; edges with four equivalent Mg(7)Mg11Bi cuboctahedra; edges with four equivalent Mg(6)Mg11Cr cuboctahedra; faces with two equivalent Mg(7)Mg11Bi cuboctahedra; faces with two equivalent Mg(6)Mg11Cr cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg8Cr2Bi2 cuboctahedra; and faces with eight Mg(5,5,5,5)Mg10CrBi cuboctahedra. Both Mg(4)-Mg(4) bond lengths are 3.18 Å. Both Mg(4)-Mg(5,5) bond lengths are 3.18 Å. Both Mg(4)-Mg(6) bond lengths are 3.21 Å. Both Mg(4)-Mg(7) bond lengths are 3.14 Å. In the fifth Mg site, Mg(4) is bonded to two equivalent Mg(1); two equivalent Mg(2); two equivalent Mg(4); two Mg(5,5); two equivalent Mg(6); and two equivalent Mg(7) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Mg(3)Mg8Cr2Bi2 cuboctahedra; corners with four equivalent Cr(1)Mg10Bi2 cuboctahedra; corners with four equivalent Bi(1)Mg10Cr2 cuboctahedra; corners with six equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with four equivalent Mg(5)Mg10CrBi cuboctahedra; edges with four equivalent Mg(7)Mg11Bi cuboctahedra; edges with four equivalent Mg(6)Mg11Cr cuboctahedra; faces with two equivalent Mg(7)Mg11Bi cuboctahedra; faces with two equivalent Mg(6)Mg11Cr cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg8Cr2Bi2 cuboctahedra; and faces with eight Mg(5,5,5)Mg10CrBi cuboctahedra. Both Mg(4)-Mg(5,5) bond lengths are 3.18 Å. Both Mg(4)-Mg(6) bond lengths are 3.21 Å. Both Mg(4)-Mg(7) bond lengths are 3.14 Å. In the sixth Mg site, Mg(5) is bonded to one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), one Cr(1), and one Bi(1) atom to form distorted MgMg10CrBi cuboctahedra that share corners with four equivalent Mg(7)Mg11Bi cuboctahedra; corners with four equivalent Mg(6)Mg11Cr cuboctahedra; corners with ten equivalent Mg(5)Mg10CrBi cuboctahedra; edges with two equivalent Mg(5)Mg10CrBi cuboctahedra; edges with two equivalent Mg(7)Mg11Bi cuboctahedra; edges with two equivalent Mg(6)Mg11Cr cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Mg(3)Mg8Cr2Bi2 cuboctahedra; edges with two equivalent Cr(1)Mg10Bi2 cuboctahedra; edges with two equivalent Bi(1)Mg10Cr2 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Cr(1)Mg10Bi2 cuboctahedra;  a faceface with one Bi(1)Mg10Cr2 cuboctahedra; faces with two equivalent Mg(7)Mg11Bi cuboctahedra; faces with two equivalent Mg(6)Mg11Cr cuboctahedra; faces with four Mg(5,5)Mg10CrBi cuboctahedra; faces with four Mg(4,4)Mg12 cuboctahedra; and faces with four Mg(3,3)Mg8Cr2Bi2 cuboctahedra. There is one shorter (3.11 Å) and one longer (3.26 Å) Mg(5)-Mg(5) bond length. There is one shorter (3.15 Å) and one longer (3.22 Å) Mg(5)-Mg(6) bond length. There is one shorter (3.15 Å) and one longer (3.23 Å) Mg(5)-Mg(7) bond length. The Mg(5)-Cr(1) bond length is 3.17 Å. The Mg(5)-Bi(1) bond length is 3.21 Å. In the seventh Mg site, Mg(5) is bonded to one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), one Cr(1), and one Bi(1) atom to form distorted MgMg10CrBi cuboctahedra that share corners with four equivalent Mg(7)Mg11Bi cuboctahedra; corners with four equivalent Mg(6)Mg11Cr cuboctahedra; corners with ten Mg(5,5,5)Mg10CrBi cuboctahedra; edges with two equivalent Mg(5)Mg10CrBi cuboctahedra; edges with two equivalent Mg(7)Mg11Bi cuboctahedra; edges with two equivalent Mg(6)Mg11Cr cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Mg(3)Mg8Cr2Bi2 cuboctahedra; edges with two equivalent Cr(1)Mg10Bi2 cuboctahedra; edges with two equivalent Bi(1)Mg10Cr2 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Cr(1)Mg10Bi2 cuboctahedra;  a faceface with one Bi(1)Mg10Cr2 cuboctahedra; faces with two equivalent Mg(7)Mg11Bi cuboctahedra; faces with two equivalent Mg(6)Mg11Cr cuboctahedra; faces with four equivalent Mg(5)Mg10CrBi cuboctahedra; faces with four Mg(4,4)Mg12 cuboctahedra; and faces with four Mg(3,3)Mg8Cr2Bi2 cuboctahedra. There is one shorter (3.11 Å) and one longer (3.26 Å) Mg(5)-Mg(5) bond length. There is one shorter (3.15 Å) and one longer (3.22 Å) Mg(5)-Mg(6) bond length. There is one shorter (3.15 Å) and one longer (3.23 Å) Mg(5)-Mg(7) bond length. The Mg(5)-Cr(1) bond length is 3.17 Å. The Mg(5)-Bi(1) bond length is 3.21 Å. In the eighth Mg site, Mg(5) is bonded to one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), one Cr(1), and one Bi(1) atom to form distorted MgMg10CrBi cuboctahedra that share corners with four equivalent Mg(7)Mg11Bi cuboctahedra; corners with four equivalent Mg(6)Mg11Cr cuboctahedra; corners with ten Mg(5,5,5)Mg10CrBi cuboctahedra; edges with two equivalent Mg(5)Mg10CrBi cuboctahedra; edges with two equivalent Mg(7)Mg11Bi cuboctahedra; edges with two equivalent Mg(6)Mg11Cr cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Mg(3)Mg8Cr2Bi2 cuboctahedra; edges with two equivalent Cr(1)Mg10Bi2 cuboctahedra; edges with two equivalent Bi(1)Mg10Cr2 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Cr(1)Mg10Bi2 cuboctahedra;  a faceface with one Bi(1)Mg10Cr2 cuboctahedra; faces with two equivalent Mg(7)Mg11Bi cuboctahedra; faces with two equivalent Mg(6)Mg11Cr cuboctahedra; faces with four equivalent Mg(5)Mg10CrBi cuboctahedra; faces with four Mg(4,4,4)Mg12 cuboctahedra; and faces with four Mg(3,3)Mg8Cr2Bi2 cuboctahedra. The Mg(5)-Mg(3) bond length is 3.19 Å. There is one shorter (3.15 Å) and one longer (3.22 Å) Mg(5)-Mg(6) bond length. There is one shorter (3.15 Å) and one longer (3.23 Å) Mg(5)-Mg(7) bond length. The Mg(5)-Cr(1) bond length is 3.17 Å. The Mg(5)-Bi(1) bond length is 3.21 Å. In the ninth Mg site, Mg(6) is bonded to one Mg(1); two equivalent Mg(3); two Mg(4,4); two equivalent Mg(7); four Mg(5,5,5); and one Cr(1) atom to form distorted MgMg11Cr cuboctahedra that share corners with four equivalent Mg(7)Mg11Bi cuboctahedra; corners with six equivalent Mg(6)Mg11Cr cuboctahedra; corners with eight Mg(5,5,5)Mg10CrBi cuboctahedra; edges with two equivalent Mg(7)Mg11Bi cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Cr(1)Mg10Bi2 cuboctahedra; edges with four Mg(5,5,5)Mg10CrBi cuboctahedra; edges with four Mg(4,4,4)Mg12 cuboctahedra; edges with four Mg(3,3)Mg8Cr2Bi2 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Cr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(7)Mg11Bi cuboctahedra; faces with two equivalent Mg(6)Mg11Cr cuboctahedra; faces with two Mg(4,4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg8Cr2Bi2 cuboctahedra; faces with three equivalent Mg(2)Mg12 cuboctahedra; faces with three equivalent Bi(1)Mg10Cr2 cuboctahedra; and faces with four Mg(5,5,5)Mg10CrBi cuboctahedra. Both Mg(6)-Mg(7) bond lengths are 3.18 Å. The Mg(6)-Mg(5) bond length is 3.15 Å. The Mg(6)-Cr(1) bond length is 3.15 Å. In the tenth Mg site, Mg(7) is bonded to one Mg(2); two equivalent Mg(3); two Mg(4,4); two equivalent Mg(6); four Mg(5,5,5); and one Bi(1) atom to form distorted MgMg11Bi cuboctahedra that share corners with four equivalent Mg(6)Mg11Cr cuboctahedra; corners with six equivalent Mg(7)Mg11Bi cuboctahedra; corners with eight Mg(5,5,5)Mg10CrBi cuboctahedra; edges with two equivalent Mg(6)Mg11Cr cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Bi(1)Mg10Cr2 cuboctahedra; edges with four Mg(5,5,5)Mg10CrBi cuboctahedra; edges with four Mg(4,4,4)Mg12 cuboctahedra; edges with four Mg(3,3)Mg8Cr2Bi2 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Bi(1)Mg10Cr2 cuboctahedra; faces with two equivalent Mg(7)Mg11Bi cuboctahedra; faces with two equivalent Mg(6)Mg11Cr cuboctahedra; faces with two Mg(4,4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg8Cr2Bi2 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; faces with three equivalent Cr(1)Mg10Bi2 cuboctahedra; and faces with four Mg(5,5,5)Mg10CrBi cuboctahedra. The Mg(7)-Mg(5) bond length is 3.23 Å. The Mg(7)-Bi(1) bond length is 3.23 Å. In the eleventh Mg site, Mg(3) is bonded to two equivalent Mg(3), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), two equivalent Cr(1), and two equivalent Bi(1) atoms to form distorted MgMg8Cr2Bi2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with six Mg(3,3)Mg8Cr2Bi2 cuboctahedra; edges with two equivalent Mg(3)Mg8Cr2Bi2 cuboctahedra; edges with two equivalent Cr(1)Mg10Bi2 cuboctahedra; edges with two equivalent Bi(1)Mg10Cr2 cuboctahedra; edges with four Mg(5,5)Mg10CrBi cuboctahedra; edges with four equivalent Mg(7)Mg11Bi cuboctahedra; edges with four equivalent Mg(6)Mg11Cr cuboctahedra; faces with two equivalent Mg(7)Mg11Bi cuboctahedra; faces with two equivalent Mg(6)Mg11Cr cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg8Cr2Bi2 cuboctahedra; faces with two equivalent Cr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Mg10Cr2 cuboctahedra; and faces with eight Mg(5,5,5)Mg10CrBi cuboctahedra. There is one shorter (3.17 Å) and one longer (3.19 Å) Mg(3)-Mg(3) bond length. Both Mg(3)-Mg(5) bond lengths are 3.19 Å. Both Mg(3)-Mg(6) bond lengths are 3.17 Å. Both Mg(3)-Mg(7) bond lengths are 3.21 Å. There is one shorter (3.18 Å) and one longer (3.20 Å) Mg(3)-Cr(1) bond length. There is one shorter (3.17 Å) and one longer (3.20 Å) Mg(3)-Bi(1) bond length. In the twelfth Mg site, Mg(4) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), two equivalent Mg(5), two equivalent Mg(6), and two equivalent Mg(7) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Mg(3)Mg8Cr2Bi2 cuboctahedra; corners with four equivalent Cr(1)Mg10Bi2 cuboctahedra; corners with four equivalent Bi(1)Mg10Cr2 cuboctahedra; corners with six Mg(4,4)Mg12 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with four Mg(5,5)Mg10CrBi cuboctahedra; edges with four equivalent Mg(7)Mg11Bi cuboctahedra; edges with four equivalent Mg(6)Mg11Cr cuboctahedra; faces with two equivalent Mg(7)Mg11Bi cuboctahedra; faces with two equivalent Mg(6)Mg11Cr cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg8Cr2Bi2 cuboctahedra; and faces with eight Mg(5,5,5)Mg10CrBi cuboctahedra. Both Mg(4)-Mg(4) bond lengths are 3.18 Å. Both Mg(4)-Mg(5) bond lengths are 3.18 Å. Both Mg(4)-Mg(6) bond lengths are 3.21 Å. Both Mg(4)-Mg(7) bond lengths are 3.14 Å. In the thirteenth Mg site, Mg(5) is bonded to one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), one Cr(1), and one Bi(1) atom to form distorted MgMg10CrBi cuboctahedra that share corners with four equivalent Mg(7)Mg11Bi cuboctahedra; corners with four equivalent Mg(6)Mg11Cr cuboctahedra; corners with ten Mg(5,5,5)Mg10CrBi cuboctahedra; edges with two equivalent Mg(5)Mg10CrBi cuboctahedra; edges with two equivalent Mg(7)Mg11Bi cuboctahedra; edges with two equivalent Mg(6)Mg11Cr cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Mg(3)Mg8Cr2Bi2 cuboctahedra; edges with two equivalent Cr(1)Mg10Bi2 cuboctahedra; edges with two equivalent Bi(1)Mg10Cr2 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Cr(1)Mg10Bi2 cuboctahedra;  a faceface with one Bi(1)Mg10Cr2 cuboctahedra; faces with two equivalent Mg(7)Mg11Bi cuboctahedra; faces with two equivalent Mg(6)Mg11Cr cuboctahedra; faces with four Mg(5,5)Mg10CrBi cuboctahedra; faces with four Mg(4,4,4)Mg12 cuboctahedra; and faces with four Mg(3,3)Mg8Cr2Bi2 cuboctahedra. The Mg(5)-Mg(1) bond length is 3.16 Å. The Mg(5)-Mg(2) bond length is 3.20 Å. The Mg(5)-Mg(3) bond length is 3.19 Å. The Mg(5)-Mg(4) bond length is 3.18 Å. There is one shorter (3.11 Å) and one longer (3.26 Å) Mg(5)-Mg(5) bond length. The Mg(5)-Cr(1) bond length is 3.17 Å. The Mg(5)-Bi(1) bond length is 3.21 Å. Cr(1) is bonded to two equivalent Mg(6); four Mg(3,3); four Mg(5,5,5); and two equivalent Bi(1) atoms to form CrMg10Bi2 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with six equivalent Cr(1)Mg10Bi2 cuboctahedra; corners with eight Mg(4,4,4)Mg12 cuboctahedra; edges with two equivalent Bi(1)Mg10Cr2 cuboctahedra; edges with four equivalent Mg(6)Mg11Cr cuboctahedra; edges with four Mg(3,3)Mg8Cr2Bi2 cuboctahedra; edges with eight Mg(5,5,5,5)Mg10CrBi cuboctahedra; faces with two equivalent Mg(6)Mg11Cr cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Bi(1)Mg10Cr2 cuboctahedra; faces with four Mg(5,5,5)Mg10CrBi cuboctahedra; faces with four Mg(3,3)Mg8Cr2Bi2 cuboctahedra; and faces with six equivalent Mg(7)Mg11Bi cuboctahedra. Both Cr(1)-Bi(1) bond lengths are 3.18 Å. Bi(1) is bonded to two equivalent Mg(7); four Mg(3,3); four Mg(5,5,5); and two equivalent Cr(1) atoms to form BiMg10Cr2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Bi(1)Mg10Cr2 cuboctahedra; corners with eight Mg(4,4,4)Mg12 cuboctahedra; edges with two equivalent Cr(1)Mg10Bi2 cuboctahedra; edges with four equivalent Mg(7)Mg11Bi cuboctahedra; edges with four Mg(3,3)Mg8Cr2Bi2 cuboctahedra; edges with eight Mg(5,5,5,5)Mg10CrBi cuboctahedra; faces with two equivalent Mg(7)Mg11Bi cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Cr(1)Mg10Bi2 cuboctahedra; faces with four Mg(5,5,5)Mg10CrBi cuboctahedra; faces with four Mg(3,3)Mg8Cr2Bi2 cuboctahedra; and faces with six equivalent Mg(6)Mg11Cr cuboctahedra.