Mg15Nb crystallizes in the hexagonal P-6m2 space group. There are eight inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to six Mg(3,3,3) and six Mg(4,4) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(2)Mg10Nb2 cuboctahedra; edges with six Mg(3,3,3)Mg12 cuboctahedra; edges with twelve Mg(4,4)Mg11Nb cuboctahedra; faces with two equivalent Nb(1)Mg12 cuboctahedra; faces with six Mg(4,4)Mg11Nb cuboctahedra; faces with six Mg(3,3,3)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 Mg(4,4); and two equivalent Nb(1) atoms to form MgMg10Nb2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Nb2 cuboctahedra; corners with eight Mg(3,3)Mg12 cuboctahedra; edges with two equivalent Nb(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Nb2 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight Mg(4,4)Mg11Nb cuboctahedra; faces with two equivalent Mg(3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with two equivalent Nb(1)Mg12 cuboctahedra; faces with four equivalent Mg(2)Mg10Nb2 cuboctahedra; and faces with ten Mg(4,4)Mg11Nb cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(1); two equivalent Mg(5); four Mg(3,3); and four Mg(4,4) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Nb(1)Mg12 cuboctahedra; corners with six equivalent Mg(3)Mg12 cuboctahedra; corners with eight equivalent Mg(2)Mg10Nb2 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four Mg(3,3)Mg12 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight Mg(4,4)Mg11Nb cuboctahedra; faces with two equivalent Mg(2)Mg10Nb2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with four Mg(3,3)Mg12 cuboctahedra; and faces with ten Mg(4,4)Mg11Nb cuboctahedra. In the fourth Mg site, Mg(3) is bonded to two equivalent Mg(1); two equivalent Mg(5); four Mg(3,3); and four equivalent Mg(4) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Nb(1)Mg12 cuboctahedra; corners with six equivalent Mg(3)Mg12 cuboctahedra; corners with eight equivalent Mg(2)Mg10Nb2 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four Mg(3,3)Mg12 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight equivalent Mg(4)Mg11Nb cuboctahedra; faces with two equivalent Mg(2)Mg10Nb2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with four Mg(3,3)Mg12 cuboctahedra; and faces with ten Mg(4,4)Mg11Nb cuboctahedra. In the fifth Mg site, Mg(3) is bonded to two equivalent Mg(1); two equivalent Mg(5); four Mg(3,3); and four Mg(4,4) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Nb(1)Mg12 cuboctahedra; corners with six equivalent Mg(3)Mg12 cuboctahedra; corners with eight equivalent Mg(2)Mg10Nb2 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four Mg(3,3)Mg12 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight Mg(4,4)Mg11Nb cuboctahedra; faces with two equivalent Mg(2)Mg10Nb2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with four Mg(3,3)Mg12 cuboctahedra; and faces with ten Mg(4,4)Mg11Nb cuboctahedra. In the sixth Mg site, Mg(4) is bonded to one Mg(1); two equivalent Mg(2); two Mg(3,3); two equivalent Mg(5); four Mg(4,4); and one Nb(1) atom to form distorted MgMg11Nb cuboctahedra that share corners with four equivalent Mg(5)Mg12 cuboctahedra; corners with fourteen Mg(4,4)Mg11Nb cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(5)Mg12 cuboctahedra; edges with two equivalent Nb(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Nb2 cuboctahedra; edges with four Mg(4,4)Mg11Nb cuboctahedra; edges with four Mg(3,3)Mg12 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Nb(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with five equivalent Mg(2)Mg10Nb2 cuboctahedra; faces with five Mg(3,3,3)Mg12 cuboctahedra; and faces with six Mg(4,4)Mg11Nb cuboctahedra. In the seventh Mg site, Mg(4) is bonded to one Mg(1); two equivalent Mg(2); two Mg(3,3); two equivalent Mg(5); four equivalent Mg(4); and one Nb(1) atom to form distorted MgMg11Nb cuboctahedra that share corners with four equivalent Mg(5)Mg12 cuboctahedra; corners with fourteen Mg(4,4)Mg11Nb cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(5)Mg12 cuboctahedra; edges with two equivalent Nb(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Nb2 cuboctahedra; edges with four equivalent Mg(4)Mg11Nb cuboctahedra; edges with four Mg(3,3)Mg12 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Nb(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with five equivalent Mg(2)Mg10Nb2 cuboctahedra; faces with five Mg(3,3,3)Mg12 cuboctahedra; and faces with six Mg(4,4)Mg11Nb cuboctahedra. In the eighth Mg site, Mg(5) is bonded to three equivalent Mg(2); three Mg(3,3,3); 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)Mg11Nb cuboctahedra; edges with six equivalent Mg(2)Mg10Nb2 cuboctahedra; edges with six Mg(4,4)Mg11Nb cuboctahedra; edges with six Mg(3,3,3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with three equivalent Mg(2)Mg10Nb2 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; faces with three Mg(3,3,3)Mg12 cuboctahedra; faces with three equivalent Nb(1)Mg12 cuboctahedra; and faces with six Mg(4,4)Mg11Nb cuboctahedra. Nb(1) is bonded to six equivalent Mg(2) and six Mg(4,4) atoms to form NbMg12 cuboctahedra that share corners with six equivalent Nb(1)Mg12 cuboctahedra; corners with twelve Mg(3,3,3)Mg12 cuboctahedra; edges with six equivalent Mg(2)Mg10Nb2 cuboctahedra; edges with twelve Mg(4,4)Mg11Nb cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with six equivalent Mg(2)Mg10Nb2 cuboctahedra; faces with six Mg(4,4)Mg11Nb cuboctahedra; and faces with six equivalent Mg(5)Mg12 cuboctahedra.
Mg15Nb crystallizes in the hexagonal P-6m2 space group. There are eight inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to six Mg(3,3,3) and six Mg(4,4) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(2)Mg10Nb2 cuboctahedra; edges with six Mg(3,3,3)Mg12 cuboctahedra; edges with twelve Mg(4,4)Mg11Nb cuboctahedra; faces with two equivalent Nb(1)Mg12 cuboctahedra; faces with six Mg(4,4)Mg11Nb cuboctahedra; faces with six Mg(3,3,3)Mg12 cuboctahedra; and faces with six equivalent Mg(5)Mg12 cuboctahedra. All Mg(1)-Mg(3,3,3) bond lengths are 3.18 Å. All Mg(1)-Mg(4,4) bond lengths are 3.13 Å. In the second Mg site, Mg(2) is bonded to two equivalent Mg(5); four equivalent Mg(2); four Mg(4,4); and two equivalent Nb(1) atoms to form MgMg10Nb2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Nb2 cuboctahedra; corners with eight Mg(3,3)Mg12 cuboctahedra; edges with two equivalent Nb(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Nb2 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight Mg(4,4)Mg11Nb cuboctahedra; faces with two equivalent Mg(3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with two equivalent Nb(1)Mg12 cuboctahedra; faces with four equivalent Mg(2)Mg10Nb2 cuboctahedra; and faces with ten Mg(4,4)Mg11Nb cuboctahedra. Both Mg(2)-Mg(5) bond lengths are 3.13 Å. There are two shorter (3.16 Å) and two longer (3.20 Å) Mg(2)-Mg(2) bond lengths. All Mg(2)-Mg(4,4) bond lengths are 3.10 Å. Both Mg(2)-Nb(1) bond lengths are 3.18 Å. In the third Mg site, Mg(3) is bonded to two equivalent Mg(1); two equivalent Mg(5); four Mg(3,3); and four Mg(4,4) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Nb(1)Mg12 cuboctahedra; corners with six equivalent Mg(3)Mg12 cuboctahedra; corners with eight equivalent Mg(2)Mg10Nb2 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four Mg(3,3)Mg12 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight Mg(4,4)Mg11Nb cuboctahedra; faces with two equivalent Mg(2)Mg10Nb2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with four Mg(3,3)Mg12 cuboctahedra; and faces with ten Mg(4,4)Mg11Nb cuboctahedra. Both Mg(3)-Mg(5) bond lengths are 3.12 Å. There are two shorter (3.17 Å) and two longer (3.18 Å) Mg(3)-Mg(3,3) bond lengths. All Mg(3)-Mg(4,4) bond lengths are 3.17 Å. In the fourth Mg site, Mg(3) is bonded to two equivalent Mg(1); two equivalent Mg(5); four Mg(3,3); and four equivalent Mg(4) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Nb(1)Mg12 cuboctahedra; corners with six equivalent Mg(3)Mg12 cuboctahedra; corners with eight equivalent Mg(2)Mg10Nb2 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four Mg(3,3)Mg12 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight equivalent Mg(4)Mg11Nb cuboctahedra; faces with two equivalent Mg(2)Mg10Nb2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with four Mg(3,3)Mg12 cuboctahedra; and faces with ten Mg(4,4)Mg11Nb cuboctahedra. Both Mg(3)-Mg(5) bond lengths are 3.12 Å. There is one shorter (3.17 Å) and one longer (3.18 Å) Mg(3)-Mg(3) bond length. All Mg(3)-Mg(4) bond lengths are 3.17 Å. In the fifth Mg site, Mg(3) is bonded to two equivalent Mg(1); two equivalent Mg(5); four Mg(3,3); and four Mg(4,4) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Nb(1)Mg12 cuboctahedra; corners with six equivalent Mg(3)Mg12 cuboctahedra; corners with eight equivalent Mg(2)Mg10Nb2 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four Mg(3,3)Mg12 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight Mg(4,4)Mg11Nb cuboctahedra; faces with two equivalent Mg(2)Mg10Nb2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with four Mg(3,3)Mg12 cuboctahedra; and faces with ten Mg(4,4)Mg11Nb cuboctahedra. Both Mg(3)-Mg(5) bond lengths are 3.12 Å. All Mg(3)-Mg(4,4) bond lengths are 3.17 Å. In the sixth Mg site, Mg(4) is bonded to one Mg(1); two equivalent Mg(2); two Mg(3,3); two equivalent Mg(5); four Mg(4,4); and one Nb(1) atom to form distorted MgMg11Nb cuboctahedra that share corners with four equivalent Mg(5)Mg12 cuboctahedra; corners with fourteen Mg(4,4)Mg11Nb cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(5)Mg12 cuboctahedra; edges with two equivalent Nb(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Nb2 cuboctahedra; edges with four Mg(4,4)Mg11Nb cuboctahedra; edges with four Mg(3,3)Mg12 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Nb(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with five equivalent Mg(2)Mg10Nb2 cuboctahedra; faces with five Mg(3,3,3)Mg12 cuboctahedra; and faces with six Mg(4,4)Mg11Nb cuboctahedra. Both Mg(4)-Mg(5) bond lengths are 3.18 Å. There are two shorter (3.10 Å) and two longer (3.26 Å) Mg(4)-Mg(4,4) bond lengths. The Mg(4)-Nb(1) bond length is 3.06 Å. In the seventh Mg site, Mg(4) is bonded to one Mg(1); two equivalent Mg(2); two Mg(3,3); two equivalent Mg(5); four equivalent Mg(4); and one Nb(1) atom to form distorted MgMg11Nb cuboctahedra that share corners with four equivalent Mg(5)Mg12 cuboctahedra; corners with fourteen Mg(4,4)Mg11Nb cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(5)Mg12 cuboctahedra; edges with two equivalent Nb(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Nb2 cuboctahedra; edges with four equivalent Mg(4)Mg11Nb cuboctahedra; edges with four Mg(3,3)Mg12 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Nb(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with five equivalent Mg(2)Mg10Nb2 cuboctahedra; faces with five Mg(3,3,3)Mg12 cuboctahedra; and faces with six Mg(4,4)Mg11Nb cuboctahedra. Both Mg(4)-Mg(5) bond lengths are 3.18 Å. The Mg(4)-Nb(1) bond length is 3.06 Å. In the eighth Mg site, Mg(5) is bonded to three equivalent Mg(2); three Mg(3,3,3); 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)Mg11Nb cuboctahedra; edges with six equivalent Mg(2)Mg10Nb2 cuboctahedra; edges with six Mg(4,4)Mg11Nb cuboctahedra; edges with six Mg(3,3,3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with three equivalent Mg(2)Mg10Nb2 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; faces with three Mg(3,3,3)Mg12 cuboctahedra; faces with three equivalent Nb(1)Mg12 cuboctahedra; and faces with six Mg(4,4)Mg11Nb cuboctahedra. Nb(1) is bonded to six equivalent Mg(2) and six Mg(4,4) atoms to form NbMg12 cuboctahedra that share corners with six equivalent Nb(1)Mg12 cuboctahedra; corners with twelve Mg(3,3,3)Mg12 cuboctahedra; edges with six equivalent Mg(2)Mg10Nb2 cuboctahedra; edges with twelve Mg(4,4)Mg11Nb cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with six equivalent Mg(2)Mg10Nb2 cuboctahedra; faces with six Mg(4,4)Mg11Nb cuboctahedra; and faces with six equivalent Mg(5)Mg12 cuboctahedra.