BaMg14Bi crystallizes in the orthorhombic Amm2 space group. Ba(1) is bonded to two equivalent Mg(6), four equivalent Mg(3), four equivalent Mg(5), and two equivalent Bi(1) atoms to form BaMg10Bi2 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra, corners with six equivalent Ba(1)Mg10Bi2 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Bi(1)Ba2Mg10 cuboctahedra, edges with four equivalent Mg(6)BaMg11 cuboctahedra, faces with two equivalent Mg(6)BaMg11 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, and faces with two equivalent Bi(1)Ba2Mg10 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 Bi(1)Ba2Mg10 cuboctahedra, corners with six equivalent Mg(1)Mg12 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with four equivalent Mg(6)BaMg11 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Ba(1)Mg10Bi2 cuboctahedra, faces with two equivalent Mg(6)BaMg11 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, and faces with four equivalent Mg(4)Mg12 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 Ba(1)Mg10Bi2 cuboctahedra, corners with six equivalent Mg(2)Mg12 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Bi(1)Ba2Mg10 cuboctahedra, faces with four equivalent Mg(4)Mg12 cuboctahedra, and faces with six equivalent Mg(6)BaMg11 cuboctahedra. In the third Mg site, Mg(3) is bonded in a 12-coordinate geometry to two equivalent Ba(1), two equivalent Mg(3), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and two equivalent Bi(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 Ba(1)Mg10Bi2 cuboctahedra, corners with four equivalent Bi(1)Ba2Mg10 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(6)BaMg11 cuboctahedra, faces with two equivalent Mg(6)BaMg11 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 Ba(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 Bi(1) atom. In the sixth Mg site, Mg(6) is bonded to one Ba(1), one Mg(1), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(7), and four equivalent Mg(5) atoms to form distorted MgBaMg11 cuboctahedra that share corners with six equivalent Mg(6)BaMg11 cuboctahedra, edges with two equivalent Ba(1)Mg10Bi2 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra,  a faceface with one Ba(1)Mg10Bi2 cuboctahedra,  a faceface with one Mg(1)Mg12 cuboctahedra, faces with two equivalent Mg(6)BaMg11 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with three equivalent Mg(2)Mg12 cuboctahedra, and faces with three equivalent Bi(1)Ba2Mg10 cuboctahedra. In the seventh Mg site, Mg(7) is bonded in a distorted single-bond geometry to one Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(6), four equivalent Mg(5), and one Bi(1) atom. Bi(1) is bonded to two equivalent Ba(1), two equivalent Mg(7), four equivalent Mg(3), and four equivalent Mg(5) atoms to form BiBa2Mg10 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra, corners with six equivalent Bi(1)Ba2Mg10 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Ba(1)Mg10Bi2 cuboctahedra, faces with two equivalent Ba(1)Mg10Bi2 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, and faces with six equivalent Mg(6)BaMg11 cuboctahedra.
BaMg14Bi crystallizes in the orthorhombic Amm2 space group. Ba(1) is bonded to two equivalent Mg(6), four equivalent Mg(3), four equivalent Mg(5), and two equivalent Bi(1) atoms to form BaMg10Bi2 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra, corners with six equivalent Ba(1)Mg10Bi2 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Bi(1)Ba2Mg10 cuboctahedra, edges with four equivalent Mg(6)BaMg11 cuboctahedra, faces with two equivalent Mg(6)BaMg11 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, and faces with two equivalent Bi(1)Ba2Mg10 cuboctahedra. Both Ba(1)-Mg(6) bond lengths are 3.47 Å. There are two shorter (3.34 Å) and two longer (3.35 Å) Ba(1)-Mg(3) bond lengths. All Ba(1)-Mg(5) bond lengths are 3.46 Å. Both Ba(1)-Bi(1) bond lengths are 3.34 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 Bi(1)Ba2Mg10 cuboctahedra, corners with six equivalent Mg(1)Mg12 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with four equivalent Mg(6)BaMg11 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Ba(1)Mg10Bi2 cuboctahedra, faces with two equivalent Mg(6)BaMg11 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, and faces with four equivalent Mg(4)Mg12 cuboctahedra. Both Mg(1)-Mg(2) bond lengths are 3.33 Å. Both Mg(1)-Mg(6) bond lengths are 3.19 Å. There are two shorter (3.33 Å) and two longer (3.36 Å) Mg(1)-Mg(4) bond lengths. All Mg(1)-Mg(5) bond lengths are 3.16 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 Ba(1)Mg10Bi2 cuboctahedra, corners with six equivalent Mg(2)Mg12 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Bi(1)Ba2Mg10 cuboctahedra, faces with four equivalent Mg(4)Mg12 cuboctahedra, and faces with six equivalent Mg(6)BaMg11 cuboctahedra. Both Mg(2)-Mg(7) bond lengths are 3.29 Å. There are two shorter (3.30 Å) and two longer (3.39 Å) Mg(2)-Mg(4) bond lengths. All Mg(2)-Mg(5) bond lengths are 3.12 Å. In the third Mg site, Mg(3) is bonded in a 12-coordinate geometry to two equivalent Ba(1), two equivalent Mg(3), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and two equivalent Bi(1) atoms. There is one shorter (3.24 Å) and one longer (3.43 Å) Mg(3)-Mg(3) bond length. Both Mg(3)-Mg(5) bond lengths are 3.41 Å. Both Mg(3)-Mg(6) bond lengths are 3.36 Å. Both Mg(3)-Mg(7) bond lengths are 3.29 Å. There is one shorter (3.27 Å) and one longer (3.42 Å) Mg(3)-Bi(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 Ba(1)Mg10Bi2 cuboctahedra, corners with four equivalent Bi(1)Ba2Mg10 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(6)BaMg11 cuboctahedra, faces with two equivalent Mg(6)BaMg11 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 (3.30 Å) and one longer (3.37 Å) Mg(4)-Mg(4) bond length. Both Mg(4)-Mg(5) bond lengths are 3.11 Å. Both Mg(4)-Mg(6) bond lengths are 3.13 Å. Both Mg(4)-Mg(7) bond lengths are 3.25 Å. In the fifth Mg site, Mg(5) is bonded in a 12-coordinate geometry to one Ba(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 Bi(1) atom. There is one shorter (3.24 Å) and one longer (3.43 Å) Mg(5)-Mg(5) bond length. There is one shorter (3.21 Å) and one longer (3.48 Å) Mg(5)-Mg(6) bond length. There is one shorter (3.30 Å) and one longer (3.40 Å) Mg(5)-Mg(7) bond length. The Mg(5)-Bi(1) bond length is 3.41 Å. In the sixth Mg site, Mg(6) is bonded to one Ba(1), one Mg(1), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(7), and four equivalent Mg(5) atoms to form distorted MgBaMg11 cuboctahedra that share corners with six equivalent Mg(6)BaMg11 cuboctahedra, edges with two equivalent Ba(1)Mg10Bi2 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra,  a faceface with one Ba(1)Mg10Bi2 cuboctahedra,  a faceface with one Mg(1)Mg12 cuboctahedra, faces with two equivalent Mg(6)BaMg11 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with three equivalent Mg(2)Mg12 cuboctahedra, and faces with three equivalent Bi(1)Ba2Mg10 cuboctahedra. Both Mg(6)-Mg(7) bond lengths are 3.34 Å. In the seventh Mg site, Mg(7) is bonded in a distorted single-bond geometry to one Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(6), four equivalent Mg(5), and one Bi(1) atom. The Mg(7)-Bi(1) bond length is 3.33 Å. Bi(1) is bonded to two equivalent Ba(1), two equivalent Mg(7), four equivalent Mg(3), and four equivalent Mg(5) atoms to form BiBa2Mg10 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra, corners with six equivalent Bi(1)Ba2Mg10 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Ba(1)Mg10Bi2 cuboctahedra, faces with two equivalent Ba(1)Mg10Bi2 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, and faces with six equivalent Mg(6)BaMg11 cuboctahedra.