BaMg14Sn crystallizes in the hexagonal P-6m2 space group. Ba(1) is bonded to six equivalent Mg(2) and six Mg(3,3) atoms to form BaMg12 cuboctahedra that share corners with six equivalent Ba(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(1)Mg10Sn2 cuboctahedra; edges with six equivalent Mg(2)Ba2Mg10 cuboctahedra; edges with twelve Mg(3,3)BaMg10Sn cuboctahedra; faces with two equivalent Sn(1)Mg12 cuboctahedra; faces with six equivalent Mg(2)Ba2Mg10 cuboctahedra; faces with six Mg(3,3)BaMg10Sn cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. There are five inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Sn(1) atoms to form distorted MgMg10Sn2 cuboctahedra that share corners with four equivalent Ba(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Sn2 cuboctahedra; corners with eight equivalent Mg(2)Ba2Mg10 cuboctahedra; edges with two equivalent Sn(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Mg10Sn2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)BaMg10Sn cuboctahedra; faces with two equivalent Mg(2)Ba2Mg10 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Sn(1)Mg12 cuboctahedra; faces with four equivalent Mg(1)Mg10Sn2 cuboctahedra; and faces with ten Mg(3,3)BaMg10Sn cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Ba(1), two equivalent Mg(4), four equivalent Mg(2), and four equivalent Mg(3) atoms to form distorted MgBa2Mg10 cuboctahedra that share corners with four equivalent Sn(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Ba2Mg10 cuboctahedra; corners with eight equivalent Mg(1)Mg10Sn2 cuboctahedra; edges with two equivalent Ba(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Ba2Mg10 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)BaMg10Sn cuboctahedra; faces with two equivalent Ba(1)Mg12 cuboctahedra; faces with two equivalent Mg(1)Mg10Sn2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with four equivalent Mg(2)Ba2Mg10 cuboctahedra; and faces with ten Mg(3,3)BaMg10Sn cuboctahedra. In the third Mg site, Mg(3) is bonded to one Ba(1); two equivalent Mg(1); two equivalent Mg(2); two equivalent Mg(4); four Mg(3,3); and one Sn(1) atom to form distorted MgBaMg10Sn cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)BaMg10Sn cuboctahedra; edges with two equivalent Ba(1)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Sn(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Ba2Mg10 cuboctahedra; edges with four Mg(3,3)BaMg10Sn cuboctahedra; edges with four equivalent Mg(1)Mg10Sn2 cuboctahedra;  a faceface with one Ba(1)Mg12 cuboctahedra;  a faceface with one Sn(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five equivalent Mg(2)Ba2Mg10 cuboctahedra; faces with five equivalent Mg(1)Mg10Sn2 cuboctahedra; and faces with six Mg(3,3)BaMg10Sn cuboctahedra. In the fourth Mg site, Mg(3) is bonded to one Ba(1), two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), four equivalent Mg(3), and one Sn(1) atom to form distorted MgBaMg10Sn cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)BaMg10Sn cuboctahedra; edges with two equivalent Ba(1)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Sn(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Ba2Mg10 cuboctahedra; edges with four equivalent Mg(3)BaMg10Sn cuboctahedra; edges with four equivalent Mg(1)Mg10Sn2 cuboctahedra;  a faceface with one Ba(1)Mg12 cuboctahedra;  a faceface with one Sn(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five equivalent Mg(2)Ba2Mg10 cuboctahedra; faces with five equivalent Mg(1)Mg10Sn2 cuboctahedra; and faces with six Mg(3,3)BaMg10Sn cuboctahedra. In the fifth Mg site, Mg(4) is bonded to three equivalent Mg(1); three equivalent Mg(2); and six Mg(3,3) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(4)Mg12 cuboctahedra; corners with twelve Mg(3,3)BaMg10Sn cuboctahedra; edges with six equivalent Mg(2)Ba2Mg10 cuboctahedra; edges with six Mg(3,3)BaMg10Sn cuboctahedra; edges with six equivalent Mg(1)Mg10Sn2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Ba(1)Mg12 cuboctahedra; faces with three equivalent Mg(2)Ba2Mg10 cuboctahedra; faces with three equivalent Mg(1)Mg10Sn2 cuboctahedra; faces with three equivalent Sn(1)Mg12 cuboctahedra; and faces with six Mg(3,3)BaMg10Sn cuboctahedra. Sn(1) is bonded to six equivalent Mg(1) and six Mg(3,3) atoms to form SnMg12 cuboctahedra that share corners with six equivalent Sn(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(2)Ba2Mg10 cuboctahedra; edges with six equivalent Mg(1)Mg10Sn2 cuboctahedra; edges with twelve Mg(3,3)BaMg10Sn cuboctahedra; faces with two equivalent Ba(1)Mg12 cuboctahedra; faces with six Mg(3,3)BaMg10Sn cuboctahedra; faces with six equivalent Mg(1)Mg10Sn2 cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra.
BaMg14Sn crystallizes in the hexagonal P-6m2 space group. Ba(1) is bonded to six equivalent Mg(2) and six Mg(3,3) atoms to form BaMg12 cuboctahedra that share corners with six equivalent Ba(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(1)Mg10Sn2 cuboctahedra; edges with six equivalent Mg(2)Ba2Mg10 cuboctahedra; edges with twelve Mg(3,3)BaMg10Sn cuboctahedra; faces with two equivalent Sn(1)Mg12 cuboctahedra; faces with six equivalent Mg(2)Ba2Mg10 cuboctahedra; faces with six Mg(3,3)BaMg10Sn cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. All Ba(1)-Mg(2) bond lengths are 3.29 Å. All Ba(1)-Mg(3,3) bond lengths are 3.43 Å. There are five inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Sn(1) atoms to form distorted MgMg10Sn2 cuboctahedra that share corners with four equivalent Ba(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Sn2 cuboctahedra; corners with eight equivalent Mg(2)Ba2Mg10 cuboctahedra; edges with two equivalent Sn(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Mg10Sn2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)BaMg10Sn cuboctahedra; faces with two equivalent Mg(2)Ba2Mg10 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Sn(1)Mg12 cuboctahedra; faces with four equivalent Mg(1)Mg10Sn2 cuboctahedra; and faces with ten Mg(3,3)BaMg10Sn cuboctahedra. Both Mg(1)-Mg(4) bond lengths are 3.34 Å. There are two shorter (3.24 Å) and two longer (3.34 Å) Mg(1)-Mg(1) bond lengths. All Mg(1)-Mg(3) bond lengths are 3.18 Å. Both Mg(1)-Sn(1) bond lengths are 3.29 Å. In the second Mg site, Mg(2) is bonded to two equivalent Ba(1), two equivalent Mg(4), four equivalent Mg(2), and four equivalent Mg(3) atoms to form distorted MgBa2Mg10 cuboctahedra that share corners with four equivalent Sn(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Ba2Mg10 cuboctahedra; corners with eight equivalent Mg(1)Mg10Sn2 cuboctahedra; edges with two equivalent Ba(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Ba2Mg10 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)BaMg10Sn cuboctahedra; faces with two equivalent Ba(1)Mg12 cuboctahedra; faces with two equivalent Mg(1)Mg10Sn2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with four equivalent Mg(2)Ba2Mg10 cuboctahedra; and faces with ten Mg(3,3)BaMg10Sn cuboctahedra. Both Mg(2)-Mg(4) bond lengths are 3.27 Å. There are two shorter (3.17 Å) and two longer (3.41 Å) Mg(2)-Mg(2) bond lengths. All Mg(2)-Mg(3) bond lengths are 3.36 Å. In the third Mg site, Mg(3) is bonded to one Ba(1); two equivalent Mg(1); two equivalent Mg(2); two equivalent Mg(4); four Mg(3,3); and one Sn(1) atom to form distorted MgBaMg10Sn cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)BaMg10Sn cuboctahedra; edges with two equivalent Ba(1)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Sn(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Ba2Mg10 cuboctahedra; edges with four Mg(3,3)BaMg10Sn cuboctahedra; edges with four equivalent Mg(1)Mg10Sn2 cuboctahedra;  a faceface with one Ba(1)Mg12 cuboctahedra;  a faceface with one Sn(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five equivalent Mg(2)Ba2Mg10 cuboctahedra; faces with five equivalent Mg(1)Mg10Sn2 cuboctahedra; and faces with six Mg(3,3)BaMg10Sn cuboctahedra. Both Mg(3)-Mg(4) bond lengths are 3.30 Å. There are two shorter (3.18 Å) and two longer (3.40 Å) Mg(3)-Mg(3,3) bond lengths. The Mg(3)-Sn(1) bond length is 3.23 Å. In the fourth Mg site, Mg(3) is bonded to one Ba(1), two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), four equivalent Mg(3), and one Sn(1) atom to form distorted MgBaMg10Sn cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)BaMg10Sn cuboctahedra; edges with two equivalent Ba(1)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Sn(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Ba2Mg10 cuboctahedra; edges with four equivalent Mg(3)BaMg10Sn cuboctahedra; edges with four equivalent Mg(1)Mg10Sn2 cuboctahedra;  a faceface with one Ba(1)Mg12 cuboctahedra;  a faceface with one Sn(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five equivalent Mg(2)Ba2Mg10 cuboctahedra; faces with five equivalent Mg(1)Mg10Sn2 cuboctahedra; and faces with six Mg(3,3)BaMg10Sn cuboctahedra. Both Mg(3)-Mg(1) bond lengths are 3.18 Å. Both Mg(3)-Mg(2) bond lengths are 3.36 Å. Both Mg(3)-Mg(4) bond lengths are 3.30 Å. The Mg(3)-Sn(1) bond length is 3.23 Å. In the fifth Mg site, Mg(4) is bonded to three equivalent Mg(1); three equivalent Mg(2); and six Mg(3,3) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(4)Mg12 cuboctahedra; corners with twelve Mg(3,3)BaMg10Sn cuboctahedra; edges with six equivalent Mg(2)Ba2Mg10 cuboctahedra; edges with six Mg(3,3)BaMg10Sn cuboctahedra; edges with six equivalent Mg(1)Mg10Sn2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Ba(1)Mg12 cuboctahedra; faces with three equivalent Mg(2)Ba2Mg10 cuboctahedra; faces with three equivalent Mg(1)Mg10Sn2 cuboctahedra; faces with three equivalent Sn(1)Mg12 cuboctahedra; and faces with six Mg(3,3)BaMg10Sn cuboctahedra. Sn(1) is bonded to six equivalent Mg(1) and six Mg(3,3) atoms to form SnMg12 cuboctahedra that share corners with six equivalent Sn(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(2)Ba2Mg10 cuboctahedra; edges with six equivalent Mg(1)Mg10Sn2 cuboctahedra; edges with twelve Mg(3,3)BaMg10Sn cuboctahedra; faces with two equivalent Ba(1)Mg12 cuboctahedra; faces with six Mg(3,3)BaMg10Sn cuboctahedra; faces with six equivalent Mg(1)Mg10Sn2 cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra.