KBaMg14 crystallizes in the hexagonal P-6m2 space group. K(1) is bonded to six equivalent Mg(1) and six equivalent Mg(3) atoms to form KMg12 cuboctahedra that share corners with six equivalent K(1)Mg12 cuboctahedra, edges with six equivalent Mg(1)K2Mg10 cuboctahedra, faces with two equivalent Ba(1)Mg12 cuboctahedra, faces with six equivalent Mg(1)K2Mg10 cuboctahedra, and faces with six equivalent Mg(4)Mg12 cuboctahedra. Ba(1) is bonded to six equivalent Mg(2) and six equivalent Mg(3) atoms to form BaMg12 cuboctahedra that share corners with six equivalent Ba(1)Mg12 cuboctahedra, corners with twelve equivalent Mg(1)K2Mg10 cuboctahedra, faces with two equivalent K(1)Mg12 cuboctahedra, and faces with six equivalent Mg(4)Mg12 cuboctahedra. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent K(1), two equivalent Mg(4), four equivalent Mg(1), and four equivalent Mg(3) atoms to form distorted MgK2Mg10 cuboctahedra that share corners with four equivalent Ba(1)Mg12 cuboctahedra, corners with six equivalent Mg(1)K2Mg10 cuboctahedra, edges with two equivalent K(1)Mg12 cuboctahedra, edges with four equivalent Mg(1)K2Mg10 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent K(1)Mg12 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, and faces with four equivalent Mg(1)K2Mg10 cuboctahedra. In the second Mg site, Mg(2) is bonded in a 10-coordinate geometry to two equivalent Ba(1), two equivalent Mg(2), two equivalent Mg(4), and four equivalent Mg(3) atoms. In the third Mg site, Mg(3) is bonded in a 10-coordinate geometry to one K(1), one Ba(1), two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), and two equivalent Mg(4) atoms. In the fourth Mg site, Mg(4) is bonded to three equivalent Mg(1), three equivalent Mg(2), and six equivalent Mg(3) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(4)Mg12 cuboctahedra, edges with six equivalent Mg(1)K2Mg10 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with three equivalent K(1)Mg12 cuboctahedra, faces with three equivalent Ba(1)Mg12 cuboctahedra, and faces with three equivalent Mg(1)K2Mg10 cuboctahedra.
KBaMg14 crystallizes in the hexagonal P-6m2 space group. K(1) is bonded to six equivalent Mg(1) and six equivalent Mg(3) atoms to form KMg12 cuboctahedra that share corners with six equivalent K(1)Mg12 cuboctahedra, edges with six equivalent Mg(1)K2Mg10 cuboctahedra, faces with two equivalent Ba(1)Mg12 cuboctahedra, faces with six equivalent Mg(1)K2Mg10 cuboctahedra, and faces with six equivalent Mg(4)Mg12 cuboctahedra. All K(1)-Mg(1) bond lengths are 3.45 Å. All K(1)-Mg(3) bond lengths are 3.38 Å. Ba(1) is bonded to six equivalent Mg(2) and six equivalent Mg(3) atoms to form BaMg12 cuboctahedra that share corners with six equivalent Ba(1)Mg12 cuboctahedra, corners with twelve equivalent Mg(1)K2Mg10 cuboctahedra, faces with two equivalent K(1)Mg12 cuboctahedra, and faces with six equivalent Mg(4)Mg12 cuboctahedra. All Ba(1)-Mg(2) bond lengths are 3.45 Å. All Ba(1)-Mg(3) bond lengths are 3.42 Å. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent K(1), two equivalent Mg(4), four equivalent Mg(1), and four equivalent Mg(3) atoms to form distorted MgK2Mg10 cuboctahedra that share corners with four equivalent Ba(1)Mg12 cuboctahedra, corners with six equivalent Mg(1)K2Mg10 cuboctahedra, edges with two equivalent K(1)Mg12 cuboctahedra, edges with four equivalent Mg(1)K2Mg10 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent K(1)Mg12 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, and faces with four equivalent Mg(1)K2Mg10 cuboctahedra. Both Mg(1)-Mg(4) bond lengths are 3.33 Å. There are two shorter (3.41 Å) and two longer (3.48 Å) Mg(1)-Mg(1) bond lengths. All Mg(1)-Mg(3) bond lengths are 3.25 Å. In the second Mg site, Mg(2) is bonded in a 10-coordinate geometry to two equivalent Ba(1), two equivalent Mg(2), two equivalent Mg(4), and four equivalent Mg(3) atoms. Both Mg(2)-Mg(2) bond lengths are 3.33 Å. Both Mg(2)-Mg(4) bond lengths are 3.34 Å. All Mg(2)-Mg(3) bond lengths are 3.27 Å. In the third Mg site, Mg(3) is bonded in a 10-coordinate geometry to one K(1), one Ba(1), two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), and two equivalent Mg(4) atoms. Both Mg(3)-Mg(3) bond lengths are 3.19 Å. Both Mg(3)-Mg(4) bond lengths are 3.45 Å. In the fourth Mg site, Mg(4) is bonded to three equivalent Mg(1), three equivalent Mg(2), and six equivalent Mg(3) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(4)Mg12 cuboctahedra, edges with six equivalent Mg(1)K2Mg10 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with three equivalent K(1)Mg12 cuboctahedra, faces with three equivalent Ba(1)Mg12 cuboctahedra, and faces with three equivalent Mg(1)K2Mg10 cuboctahedra.