Mg15Bi crystallizes in the hexagonal P-6m2 space group. There are seven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to six equivalent Mg(3) and six Mg(4,4) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(1)Mg12 cuboctahedra; corners with twelve Mg(2,2)Mg10Bi2 cuboctahedra; edges with six equivalent Mg(3)Mg12 cuboctahedra; edges with twelve Mg(4,4)Mg11Bi cuboctahedra; faces with two equivalent Bi(1)Mg12 cuboctahedra; faces with six Mg(4,4)Mg11Bi cuboctahedra; faces with six equivalent Mg(3)Mg12 cuboctahedra; and faces with six equivalent Mg(5)Mg12 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(5), four equivalent Mg(2), four equivalent Mg(4), and two equivalent Bi(1) atoms to form distorted MgMg10Bi2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Bi2 cuboctahedra; corners with eight equivalent Mg(3)Mg12 cuboctahedra; edges with two equivalent Bi(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Bi2 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight equivalent Mg(4)Mg11Bi cuboctahedra; faces with two equivalent Mg(3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with two equivalent Bi(1)Mg12 cuboctahedra; faces with four equivalent Mg(2)Mg10Bi2 cuboctahedra; and faces with ten Mg(4,4)Mg11Bi cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(1), two equivalent Mg(5), four equivalent Mg(3), and four equivalent Mg(4) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Bi(1)Mg12 cuboctahedra; corners with six equivalent Mg(3)Mg12 cuboctahedra; corners with eight equivalent Mg(2)Mg10Bi2 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Mg(3)Mg12 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight equivalent Mg(4)Mg11Bi cuboctahedra; faces with two equivalent Mg(2)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with four equivalent Mg(3)Mg12 cuboctahedra; and faces with ten Mg(4,4)Mg11Bi cuboctahedra. In the fourth Mg site, Mg(2) is bonded to two equivalent Mg(5); four Mg(2,2); four Mg(4,4); and two equivalent Bi(1) atoms to form distorted MgMg10Bi2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Bi2 cuboctahedra; corners with eight equivalent Mg(3)Mg12 cuboctahedra; edges with two equivalent Bi(1)Mg12 cuboctahedra; edges with four Mg(2,2)Mg10Bi2 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight Mg(4,4)Mg11Bi cuboctahedra; faces with two equivalent Mg(3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with two equivalent Bi(1)Mg12 cuboctahedra; faces with four Mg(2,2)Mg10Bi2 cuboctahedra; and faces with ten Mg(4,4)Mg11Bi cuboctahedra. In the fifth Mg site, Mg(4) is bonded to one Mg(1); two Mg(2,2); two equivalent Mg(3); two equivalent Mg(5); four Mg(4,4); and one Bi(1) atom to form distorted MgMg11Bi cuboctahedra that share corners with four equivalent Mg(5)Mg12 cuboctahedra; corners with fourteen Mg(4,4)Mg11Bi cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(5)Mg12 cuboctahedra; edges with two equivalent Bi(1)Mg12 cuboctahedra; edges with four Mg(2,2)Mg10Bi2 cuboctahedra; edges with four Mg(4,4)Mg11Bi cuboctahedra; edges with four equivalent Mg(3)Mg12 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Bi(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with five Mg(2,2)Mg10Bi2 cuboctahedra; faces with five equivalent Mg(3)Mg12 cuboctahedra; and faces with six Mg(4,4)Mg11Bi cuboctahedra. In the sixth Mg site, Mg(4) is bonded to one Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(5), four equivalent Mg(4), and one Bi(1) atom to form distorted MgMg11Bi cuboctahedra that share corners with four equivalent Mg(5)Mg12 cuboctahedra; corners with fourteen Mg(4,4)Mg11Bi cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(5)Mg12 cuboctahedra; edges with two equivalent Bi(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Bi2 cuboctahedra; edges with four equivalent Mg(4)Mg11Bi cuboctahedra; edges with four equivalent Mg(3)Mg12 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Bi(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with five Mg(2,2)Mg10Bi2 cuboctahedra; faces with five equivalent Mg(3)Mg12 cuboctahedra; and faces with six Mg(4,4)Mg11Bi cuboctahedra. In the seventh Mg site, Mg(5) is bonded to three Mg(2,2); three equivalent Mg(3); and six Mg(4,4) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(5)Mg12 cuboctahedra; corners with twelve Mg(4,4)Mg11Bi cuboctahedra; edges with six Mg(2,2)Mg10Bi2 cuboctahedra; edges with six Mg(4,4)Mg11Bi cuboctahedra; edges with six equivalent Mg(3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with three Mg(2,2)Mg10Bi2 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; faces with three equivalent Mg(3)Mg12 cuboctahedra; faces with three equivalent Bi(1)Mg12 cuboctahedra; and faces with six Mg(4,4)Mg11Bi cuboctahedra. Bi(1) is bonded to six Mg(2,2) and six Mg(4,4) atoms to form BiMg12 cuboctahedra that share corners with six equivalent Bi(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(3)Mg12 cuboctahedra; edges with six Mg(2,2)Mg10Bi2 cuboctahedra; edges with twelve Mg(4,4)Mg11Bi cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with six Mg(2,2)Mg10Bi2 cuboctahedra; faces with six Mg(4,4)Mg11Bi cuboctahedra; and faces with six equivalent Mg(5)Mg12 cuboctahedra.
Mg15Bi crystallizes in the hexagonal P-6m2 space group. There are seven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to six equivalent Mg(3) and six Mg(4,4) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(1)Mg12 cuboctahedra; corners with twelve Mg(2,2)Mg10Bi2 cuboctahedra; edges with six equivalent Mg(3)Mg12 cuboctahedra; edges with twelve Mg(4,4)Mg11Bi cuboctahedra; faces with two equivalent Bi(1)Mg12 cuboctahedra; faces with six Mg(4,4)Mg11Bi cuboctahedra; faces with six equivalent Mg(3)Mg12 cuboctahedra; and faces with six equivalent Mg(5)Mg12 cuboctahedra. All Mg(1)-Mg(3) bond lengths are 3.20 Å. All Mg(1)-Mg(4,4) bond lengths are 3.16 Å. In the second Mg site, Mg(2) is bonded to two equivalent Mg(5), four equivalent Mg(2), four equivalent Mg(4), and two equivalent Bi(1) atoms to form distorted MgMg10Bi2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Bi2 cuboctahedra; corners with eight equivalent Mg(3)Mg12 cuboctahedra; edges with two equivalent Bi(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Bi2 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight equivalent Mg(4)Mg11Bi cuboctahedra; faces with two equivalent Mg(3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with two equivalent Bi(1)Mg12 cuboctahedra; faces with four equivalent Mg(2)Mg10Bi2 cuboctahedra; and faces with ten Mg(4,4)Mg11Bi cuboctahedra. Both Mg(2)-Mg(5) bond lengths are 3.17 Å. There are two shorter (3.19 Å) and two longer (3.20 Å) Mg(2)-Mg(2) bond lengths. All Mg(2)-Mg(4) bond lengths are 3.20 Å. Both Mg(2)-Bi(1) bond lengths are 3.20 Å. In the third Mg site, Mg(3) is bonded to two equivalent Mg(1), two equivalent Mg(5), four equivalent Mg(3), and four equivalent Mg(4) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Bi(1)Mg12 cuboctahedra; corners with six equivalent Mg(3)Mg12 cuboctahedra; corners with eight equivalent Mg(2)Mg10Bi2 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Mg(3)Mg12 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight equivalent Mg(4)Mg11Bi cuboctahedra; faces with two equivalent Mg(2)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with four equivalent Mg(3)Mg12 cuboctahedra; and faces with ten Mg(4,4)Mg11Bi cuboctahedra. Both Mg(3)-Mg(5) bond lengths are 3.17 Å. There are two shorter (3.19 Å) and two longer (3.20 Å) Mg(3)-Mg(3) bond lengths. All Mg(3)-Mg(4) bond lengths are 3.13 Å. In the fourth Mg site, Mg(2) is bonded to two equivalent Mg(5); four Mg(2,2); four Mg(4,4); and two equivalent Bi(1) atoms to form distorted MgMg10Bi2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Bi2 cuboctahedra; corners with eight equivalent Mg(3)Mg12 cuboctahedra; edges with two equivalent Bi(1)Mg12 cuboctahedra; edges with four Mg(2,2)Mg10Bi2 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight Mg(4,4)Mg11Bi cuboctahedra; faces with two equivalent Mg(3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with two equivalent Bi(1)Mg12 cuboctahedra; faces with four Mg(2,2)Mg10Bi2 cuboctahedra; and faces with ten Mg(4,4)Mg11Bi cuboctahedra. Both Mg(2)-Mg(5) bond lengths are 3.17 Å. There is one shorter (3.19 Å) and one longer (3.20 Å) Mg(2)-Mg(2) bond length. All Mg(2)-Mg(4,4) bond lengths are 3.20 Å. Both Mg(2)-Bi(1) bond lengths are 3.20 Å. In the fifth Mg site, Mg(4) is bonded to one Mg(1); two Mg(2,2); two equivalent Mg(3); two equivalent Mg(5); four Mg(4,4); and one Bi(1) atom to form distorted MgMg11Bi cuboctahedra that share corners with four equivalent Mg(5)Mg12 cuboctahedra; corners with fourteen Mg(4,4)Mg11Bi cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(5)Mg12 cuboctahedra; edges with two equivalent Bi(1)Mg12 cuboctahedra; edges with four Mg(2,2)Mg10Bi2 cuboctahedra; edges with four Mg(4,4)Mg11Bi cuboctahedra; edges with four equivalent Mg(3)Mg12 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Bi(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with five Mg(2,2)Mg10Bi2 cuboctahedra; faces with five equivalent Mg(3)Mg12 cuboctahedra; and faces with six Mg(4,4)Mg11Bi cuboctahedra. Both Mg(4)-Mg(5) bond lengths are 3.20 Å. There are two shorter (3.14 Å) and two longer (3.25 Å) Mg(4)-Mg(4,4) bond lengths. The Mg(4)-Bi(1) bond length is 3.22 Å. In the sixth Mg site, Mg(4) is bonded to one Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(5), four equivalent Mg(4), and one Bi(1) atom to form distorted MgMg11Bi cuboctahedra that share corners with four equivalent Mg(5)Mg12 cuboctahedra; corners with fourteen Mg(4,4)Mg11Bi cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(5)Mg12 cuboctahedra; edges with two equivalent Bi(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Bi2 cuboctahedra; edges with four equivalent Mg(4)Mg11Bi cuboctahedra; edges with four equivalent Mg(3)Mg12 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Bi(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with five Mg(2,2)Mg10Bi2 cuboctahedra; faces with five equivalent Mg(3)Mg12 cuboctahedra; and faces with six Mg(4,4)Mg11Bi cuboctahedra. Both Mg(4)-Mg(3) bond lengths are 3.13 Å. Both Mg(4)-Mg(5) bond lengths are 3.20 Å. The Mg(4)-Bi(1) bond length is 3.22 Å. In the seventh Mg site, Mg(5) is bonded to three Mg(2,2); three equivalent Mg(3); and six Mg(4,4) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(5)Mg12 cuboctahedra; corners with twelve Mg(4,4)Mg11Bi cuboctahedra; edges with six Mg(2,2)Mg10Bi2 cuboctahedra; edges with six Mg(4,4)Mg11Bi cuboctahedra; edges with six equivalent Mg(3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with three Mg(2,2)Mg10Bi2 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; faces with three equivalent Mg(3)Mg12 cuboctahedra; faces with three equivalent Bi(1)Mg12 cuboctahedra; and faces with six Mg(4,4)Mg11Bi cuboctahedra. Bi(1) is bonded to six Mg(2,2) and six Mg(4,4) atoms to form BiMg12 cuboctahedra that share corners with six equivalent Bi(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(3)Mg12 cuboctahedra; edges with six Mg(2,2)Mg10Bi2 cuboctahedra; edges with twelve Mg(4,4)Mg11Bi cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with six Mg(2,2)Mg10Bi2 cuboctahedra; faces with six Mg(4,4)Mg11Bi cuboctahedra; and faces with six equivalent Mg(5)Mg12 cuboctahedra.