Mg15La crystallizes in the hexagonal P-6m2 space group. There are six 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 equivalent Mg(2)La2Mg10 cuboctahedra; edges with six equivalent Mg(3)Mg12 cuboctahedra; edges with twelve Mg(4,4)LaMg11 cuboctahedra; faces with two equivalent La(1)Mg12 cuboctahedra; faces with six Mg(4,4)LaMg11 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 Mg(4,4); and two equivalent La(1) atoms to form distorted MgLa2Mg10 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)La2Mg10 cuboctahedra; corners with eight equivalent Mg(3)Mg12 cuboctahedra; edges with two equivalent La(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)La2Mg10 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight Mg(4,4)LaMg11 cuboctahedra; faces with two equivalent Mg(3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with two equivalent La(1)Mg12 cuboctahedra; faces with four equivalent Mg(2)La2Mg10 cuboctahedra; and faces with ten Mg(4,4)LaMg11 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 Mg(4,4) atoms to form MgMg12 cuboctahedra that share corners with four equivalent La(1)Mg12 cuboctahedra; corners with six equivalent Mg(3)Mg12 cuboctahedra; corners with eight equivalent Mg(2)La2Mg10 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 Mg(4,4)LaMg11 cuboctahedra; faces with two equivalent Mg(2)La2Mg10 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)LaMg11 cuboctahedra. In the fourth 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 La(1) atom to form MgLaMg11 cuboctahedra that share corners with four equivalent Mg(5)Mg12 cuboctahedra; corners with fourteen Mg(4,4)LaMg11 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(5)Mg12 cuboctahedra; edges with two equivalent La(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)La2Mg10 cuboctahedra; edges with four equivalent Mg(4)LaMg11 cuboctahedra; edges with four equivalent Mg(3)Mg12 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one La(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with five equivalent Mg(2)La2Mg10 cuboctahedra; faces with five equivalent Mg(3)Mg12 cuboctahedra; and faces with six Mg(4,4)LaMg11 cuboctahedra. In the fifth Mg site, Mg(4) is bonded to one Mg(1); two equivalent Mg(2); two equivalent Mg(3); two equivalent Mg(5); four Mg(4,4); and one La(1) atom to form MgLaMg11 cuboctahedra that share corners with four equivalent Mg(5)Mg12 cuboctahedra; corners with fourteen Mg(4,4)LaMg11 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(5)Mg12 cuboctahedra; edges with two equivalent La(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)La2Mg10 cuboctahedra; edges with four Mg(4,4)LaMg11 cuboctahedra; edges with four equivalent Mg(3)Mg12 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one La(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with five equivalent Mg(2)La2Mg10 cuboctahedra; faces with five equivalent Mg(3)Mg12 cuboctahedra; and faces with six Mg(4,4)LaMg11 cuboctahedra. In the sixth Mg site, Mg(5) is bonded to three equivalent Mg(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)LaMg11 cuboctahedra; edges with six equivalent Mg(2)La2Mg10 cuboctahedra; edges with six Mg(4,4)LaMg11 cuboctahedra; edges with six equivalent Mg(3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with three equivalent Mg(2)La2Mg10 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; faces with three equivalent Mg(3)Mg12 cuboctahedra; faces with three equivalent La(1)Mg12 cuboctahedra; and faces with six Mg(4,4)LaMg11 cuboctahedra. La(1) is bonded to six equivalent Mg(2) and six Mg(4,4) atoms to form LaMg12 cuboctahedra that share corners with six equivalent La(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(3)Mg12 cuboctahedra; edges with six equivalent Mg(2)La2Mg10 cuboctahedra; edges with twelve Mg(4,4)LaMg11 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with six equivalent Mg(2)La2Mg10 cuboctahedra; faces with six Mg(4,4)LaMg11 cuboctahedra; and faces with six equivalent Mg(5)Mg12 cuboctahedra.
Mg15La crystallizes in the hexagonal P-6m2 space group. There are six 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 equivalent Mg(2)La2Mg10 cuboctahedra; edges with six equivalent Mg(3)Mg12 cuboctahedra; edges with twelve Mg(4,4)LaMg11 cuboctahedra; faces with two equivalent La(1)Mg12 cuboctahedra; faces with six Mg(4,4)LaMg11 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 3.30 Å. All Mg(1)-Mg(4,4) bond lengths are 3.18 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 La(1) atoms to form distorted MgLa2Mg10 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)La2Mg10 cuboctahedra; corners with eight equivalent Mg(3)Mg12 cuboctahedra; edges with two equivalent La(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)La2Mg10 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight Mg(4,4)LaMg11 cuboctahedra; faces with two equivalent Mg(3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with two equivalent La(1)Mg12 cuboctahedra; faces with four equivalent Mg(2)La2Mg10 cuboctahedra; and faces with ten Mg(4,4)LaMg11 cuboctahedra. Both Mg(2)-Mg(5) bond lengths are 3.21 Å. There are two shorter (3.19 Å) and two longer (3.41 Å) Mg(2)-Mg(2) bond lengths. All Mg(2)-Mg(4,4) bond lengths are 3.24 Å. Both Mg(2)-La(1) bond lengths are 3.30 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 Mg(4,4) atoms to form MgMg12 cuboctahedra that share corners with four equivalent La(1)Mg12 cuboctahedra; corners with six equivalent Mg(3)Mg12 cuboctahedra; corners with eight equivalent Mg(2)La2Mg10 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 Mg(4,4)LaMg11 cuboctahedra; faces with two equivalent Mg(2)La2Mg10 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)LaMg11 cuboctahedra. Both Mg(3)-Mg(5) bond lengths are 3.25 Å. There are two shorter (3.28 Å) and two longer (3.32 Å) Mg(3)-Mg(3) bond lengths. All Mg(3)-Mg(4,4) bond lengths are 3.16 Å. In the fourth 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 La(1) atom to form MgLaMg11 cuboctahedra that share corners with four equivalent Mg(5)Mg12 cuboctahedra; corners with fourteen Mg(4,4)LaMg11 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(5)Mg12 cuboctahedra; edges with two equivalent La(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)La2Mg10 cuboctahedra; edges with four equivalent Mg(4)LaMg11 cuboctahedra; edges with four equivalent Mg(3)Mg12 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one La(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with five equivalent Mg(2)La2Mg10 cuboctahedra; faces with five equivalent Mg(3)Mg12 cuboctahedra; and faces with six Mg(4,4)LaMg11 cuboctahedra. Both Mg(4)-Mg(5) bond lengths are 3.30 Å. There are two shorter (3.27 Å) and two longer (3.33 Å) Mg(4)-Mg(4) bond lengths. The Mg(4)-La(1) bond length is 3.27 Å. In the fifth Mg site, Mg(4) is bonded to one Mg(1); two equivalent Mg(2); two equivalent Mg(3); two equivalent Mg(5); four Mg(4,4); and one La(1) atom to form MgLaMg11 cuboctahedra that share corners with four equivalent Mg(5)Mg12 cuboctahedra; corners with fourteen Mg(4,4)LaMg11 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(5)Mg12 cuboctahedra; edges with two equivalent La(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)La2Mg10 cuboctahedra; edges with four Mg(4,4)LaMg11 cuboctahedra; edges with four equivalent Mg(3)Mg12 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one La(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with five equivalent Mg(2)La2Mg10 cuboctahedra; faces with five equivalent Mg(3)Mg12 cuboctahedra; and faces with six Mg(4,4)LaMg11 cuboctahedra. Both Mg(4)-Mg(5) bond lengths are 3.30 Å. There is one shorter (3.27 Å) and one longer (3.33 Å) Mg(4)-Mg(4) bond length. The Mg(4)-La(1) bond length is 3.27 Å. In the sixth Mg site, Mg(5) is bonded to three equivalent Mg(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)LaMg11 cuboctahedra; edges with six equivalent Mg(2)La2Mg10 cuboctahedra; edges with six Mg(4,4)LaMg11 cuboctahedra; edges with six equivalent Mg(3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with three equivalent Mg(2)La2Mg10 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; faces with three equivalent Mg(3)Mg12 cuboctahedra; faces with three equivalent La(1)Mg12 cuboctahedra; and faces with six Mg(4,4)LaMg11 cuboctahedra. La(1) is bonded to six equivalent Mg(2) and six Mg(4,4) atoms to form LaMg12 cuboctahedra that share corners with six equivalent La(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(3)Mg12 cuboctahedra; edges with six equivalent Mg(2)La2Mg10 cuboctahedra; edges with twelve Mg(4,4)LaMg11 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with six equivalent Mg(2)La2Mg10 cuboctahedra; faces with six Mg(4,4)LaMg11 cuboctahedra; and faces with six equivalent Mg(5)Mg12 cuboctahedra.