KMg14Co crystallizes in the orthorhombic Amm2 space group. K(1) is bonded to two equivalent Mg(7), four equivalent Mg(3), four equivalent Mg(5), and two equivalent Co(1) atoms to form KMg10Co2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra, corners with six equivalent K(1)Mg10Co2 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Co(1)K2Mg10 cuboctahedra, edges with four equivalent Mg(7)KMg11 cuboctahedra, faces with two equivalent Mg(7)KMg11 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, and faces with two equivalent Co(1)K2Mg10 cuboctahedra. There are seven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(2), two equivalent Mg(6), four equivalent Mg(4), and four equivalent Mg(5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent K(1)Mg10Co2 cuboctahedra, corners with six equivalent Mg(1)Mg12 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with two equivalent Co(1)K2Mg10 cuboctahedra, faces with four equivalent Mg(4)Mg12 cuboctahedra, and faces with six equivalent Mg(7)KMg11 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(1), two equivalent Mg(7), four equivalent Mg(4), and four equivalent Mg(5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Co(1)K2Mg10 cuboctahedra, corners with six equivalent Mg(2)Mg12 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with four equivalent Mg(7)KMg11 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent K(1)Mg10Co2 cuboctahedra, faces with two equivalent Mg(7)KMg11 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, and faces with four equivalent Mg(4)Mg12 cuboctahedra. In the third Mg site, Mg(3) is bonded in a 12-coordinate geometry to two equivalent K(1), two equivalent Mg(3), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and two equivalent Co(1) atoms. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), two equivalent Mg(5), two equivalent Mg(6), and two equivalent Mg(7) atoms to form MgMg12 cuboctahedra that share corners with four equivalent K(1)Mg10Co2 cuboctahedra, corners with four equivalent Co(1)K2Mg10 cuboctahedra, corners with six equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with two equivalent Mg(4)Mg12 cuboctahedra, edges with four equivalent Mg(7)KMg11 cuboctahedra, faces with two equivalent Mg(7)KMg11 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, and faces with two equivalent Mg(4)Mg12 cuboctahedra. In the fifth Mg site, Mg(5) is bonded in a 12-coordinate geometry to one K(1), one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and one Co(1) atom. In the sixth Mg site, Mg(6) is bonded in a distorted single-bond geometry to one Mg(1), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(7), four equivalent Mg(5), and one Co(1) atom. In the seventh Mg site, Mg(7) is bonded to one K(1), one Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(6), and four equivalent Mg(5) atoms to form distorted MgKMg11 cuboctahedra that share corners with six equivalent Mg(7)KMg11 cuboctahedra, edges with two equivalent K(1)Mg10Co2 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra,  a faceface with one K(1)Mg10Co2 cuboctahedra,  a faceface with one Mg(2)Mg12 cuboctahedra, faces with two equivalent Mg(7)KMg11 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with three equivalent Mg(1)Mg12 cuboctahedra, and faces with three equivalent Co(1)K2Mg10 cuboctahedra. Co(1) is bonded to two equivalent K(1), two equivalent Mg(6), four equivalent Mg(3), and four equivalent Mg(5) atoms to form CoK2Mg10 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra, corners with six equivalent Co(1)K2Mg10 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent K(1)Mg10Co2 cuboctahedra, faces with two equivalent K(1)Mg10Co2 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, and faces with six equivalent Mg(7)KMg11 cuboctahedra.
KMg14Co crystallizes in the orthorhombic Amm2 space group. K(1) is bonded to two equivalent Mg(7), four equivalent Mg(3), four equivalent Mg(5), and two equivalent Co(1) atoms to form KMg10Co2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra, corners with six equivalent K(1)Mg10Co2 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Co(1)K2Mg10 cuboctahedra, edges with four equivalent Mg(7)KMg11 cuboctahedra, faces with two equivalent Mg(7)KMg11 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, and faces with two equivalent Co(1)K2Mg10 cuboctahedra. Both K(1)-Mg(7) bond lengths are 3.35 Å. There are two shorter (3.17 Å) and two longer (3.19 Å) K(1)-Mg(3) bond lengths. All K(1)-Mg(5) bond lengths are 3.26 Å. Both K(1)-Co(1) bond lengths are 3.25 Å. There are seven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(2), two equivalent Mg(6), four equivalent Mg(4), and four equivalent Mg(5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent K(1)Mg10Co2 cuboctahedra, corners with six equivalent Mg(1)Mg12 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with two equivalent Co(1)K2Mg10 cuboctahedra, faces with four equivalent Mg(4)Mg12 cuboctahedra, and faces with six equivalent Mg(7)KMg11 cuboctahedra. Both Mg(1)-Mg(2) bond lengths are 3.25 Å. Both Mg(1)-Mg(6) bond lengths are 3.36 Å. There are two shorter (3.16 Å) and two longer (3.20 Å) Mg(1)-Mg(4) bond lengths. All Mg(1)-Mg(5) bond lengths are 3.22 Å. In the second Mg site, Mg(2) is bonded to two equivalent Mg(1), two equivalent Mg(7), four equivalent Mg(4), and four equivalent Mg(5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Co(1)K2Mg10 cuboctahedra, corners with six equivalent Mg(2)Mg12 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with four equivalent Mg(7)KMg11 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent K(1)Mg10Co2 cuboctahedra, faces with two equivalent Mg(7)KMg11 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, and faces with four equivalent Mg(4)Mg12 cuboctahedra. Both Mg(2)-Mg(7) bond lengths are 3.14 Å. There are two shorter (3.14 Å) and two longer (3.22 Å) Mg(2)-Mg(4) bond lengths. All Mg(2)-Mg(5) bond lengths are 3.29 Å. In the third Mg site, Mg(3) is bonded in a 12-coordinate geometry to two equivalent K(1), two equivalent Mg(3), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and two equivalent Co(1) atoms. There is one shorter (3.16 Å) and one longer (3.33 Å) Mg(3)-Mg(3) bond length. Both Mg(3)-Mg(5) bond lengths are 3.19 Å. Both Mg(3)-Mg(6) bond lengths are 3.12 Å. Both Mg(3)-Mg(7) bond lengths are 3.34 Å. There is one shorter (3.05 Å) and one longer (3.32 Å) Mg(3)-Co(1) bond length. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), two equivalent Mg(5), two equivalent Mg(6), and two equivalent Mg(7) atoms to form MgMg12 cuboctahedra that share corners with four equivalent K(1)Mg10Co2 cuboctahedra, corners with four equivalent Co(1)K2Mg10 cuboctahedra, corners with six equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with two equivalent Mg(4)Mg12 cuboctahedra, edges with four equivalent Mg(7)KMg11 cuboctahedra, faces with two equivalent Mg(7)KMg11 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, and faces with two equivalent Mg(4)Mg12 cuboctahedra. There is one shorter (3.19 Å) and one longer (3.30 Å) Mg(4)-Mg(4) bond length. Both Mg(4)-Mg(5) bond lengths are 3.25 Å. Both Mg(4)-Mg(6) bond lengths are 3.42 Å. Both Mg(4)-Mg(7) bond lengths are 3.12 Å. In the fifth Mg site, Mg(5) is bonded in a 12-coordinate geometry to one K(1), one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and one Co(1) atom. There is one shorter (3.07 Å) and one longer (3.42 Å) Mg(5)-Mg(5) bond length. There is one shorter (3.08 Å) and one longer (3.30 Å) Mg(5)-Mg(6) bond length. There is one shorter (3.12 Å) and one longer (3.25 Å) Mg(5)-Mg(7) bond length. The Mg(5)-Co(1) bond length is 3.15 Å. In the sixth Mg site, Mg(6) is bonded in a distorted single-bond geometry to one Mg(1), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(7), four equivalent Mg(5), and one Co(1) atom. Both Mg(6)-Mg(7) bond lengths are 3.27 Å. The Mg(6)-Co(1) bond length is 3.06 Å. In the seventh Mg site, Mg(7) is bonded to one K(1), one Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(6), and four equivalent Mg(5) atoms to form distorted MgKMg11 cuboctahedra that share corners with six equivalent Mg(7)KMg11 cuboctahedra, edges with two equivalent K(1)Mg10Co2 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra,  a faceface with one K(1)Mg10Co2 cuboctahedra,  a faceface with one Mg(2)Mg12 cuboctahedra, faces with two equivalent Mg(7)KMg11 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with three equivalent Mg(1)Mg12 cuboctahedra, and faces with three equivalent Co(1)K2Mg10 cuboctahedra. Co(1) is bonded to two equivalent K(1), two equivalent Mg(6), four equivalent Mg(3), and four equivalent Mg(5) atoms to form CoK2Mg10 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra, corners with six equivalent Co(1)K2Mg10 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent K(1)Mg10Co2 cuboctahedra, faces with two equivalent K(1)Mg10Co2 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, and faces with six equivalent Mg(7)KMg11 cuboctahedra.