BaSrMg14 crystallizes in the orthorhombic Amm2 space group. Ba(1) is bonded to two equivalent Sr(1), two equivalent Mg(7), four equivalent Mg(3), and four equivalent Mg(5) atoms to form BaSr2Mg10 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra, corners with six equivalent Ba(1)Sr2Mg10 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Sr(1)Ba2Mg10 cuboctahedra, edges with eight equivalent Mg(5)BaSrMg10 cuboctahedra, faces with two equivalent Sr(1)Ba2Mg10 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with four equivalent Mg(5)BaSrMg10 cuboctahedra, and faces with six equivalent Mg(6)SrMg11 cuboctahedra. Sr(1) is bonded to two equivalent Ba(1), two equivalent Mg(6), four equivalent Mg(3), and four equivalent Mg(5) atoms to form SrBa2Mg10 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra, corners with six equivalent Sr(1)Ba2Mg10 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Ba(1)Sr2Mg10 cuboctahedra, edges with four equivalent Mg(6)SrMg11 cuboctahedra, edges with eight equivalent Mg(5)BaSrMg10 cuboctahedra, faces with two equivalent Ba(1)Sr2Mg10 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Mg(6)SrMg11 cuboctahedra, and faces with four equivalent Mg(5)BaSrMg10 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 Ba(1)Sr2Mg10 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, edges with four equivalent Mg(6)SrMg11 cuboctahedra, edges with eight equivalent Mg(5)BaSrMg10 cuboctahedra, faces with two equivalent Sr(1)Ba2Mg10 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with two equivalent Mg(6)SrMg11 cuboctahedra, faces with four equivalent Mg(5)BaSrMg10 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 Sr(1)Ba2Mg10 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, edges with eight equivalent Mg(5)BaSrMg10 cuboctahedra, faces with two equivalent Ba(1)Sr2Mg10 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with four equivalent Mg(5)BaSrMg10 cuboctahedra, faces with four equivalent Mg(4)Mg12 cuboctahedra, and faces with six equivalent Mg(6)SrMg11 cuboctahedra. In the third Mg site, Mg(3) is bonded in a 4-coordinate geometry to two equivalent Ba(1), two equivalent Sr(1), two equivalent Mg(5), two equivalent Mg(6), and two equivalent Mg(7) 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)Sr2Mg10 cuboctahedra, corners with four equivalent Sr(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(5)BaSrMg10 cuboctahedra, edges with four equivalent Mg(6)SrMg11 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(6)SrMg11 cuboctahedra, and faces with eight equivalent Mg(5)BaSrMg10 cuboctahedra. In the fifth Mg site, Mg(5) is bonded to one Ba(1), one Sr(1), one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Mg(6), and two equivalent Mg(7) atoms to form distorted MgBaSrMg10 cuboctahedra that share corners with four equivalent Mg(6)SrMg11 cuboctahedra, corners with ten equivalent Mg(5)BaSrMg10 cuboctahedra, edges with two equivalent Ba(1)Sr2Mg10 cuboctahedra, edges with two equivalent Sr(1)Ba2Mg10 cuboctahedra, edges with two equivalent Mg(5)BaSrMg10 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 two equivalent Mg(6)SrMg11 cuboctahedra,  a faceface with one Ba(1)Sr2Mg10 cuboctahedra,  a faceface with one Sr(1)Ba2Mg10 cuboctahedra,  a faceface with one Mg(1)Mg12 cuboctahedra,  a faceface with one Mg(2)Mg12 cuboctahedra, faces with two equivalent Mg(6)SrMg11 cuboctahedra, faces with four equivalent Mg(5)BaSrMg10 cuboctahedra, and faces with four equivalent Mg(4)Mg12 cuboctahedra. In the sixth Mg site, Mg(6) is bonded to one Sr(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 MgSrMg11 cuboctahedra that share corners with six equivalent Mg(6)SrMg11 cuboctahedra, corners with eight equivalent Mg(5)BaSrMg10 cuboctahedra, edges with two equivalent Sr(1)Ba2Mg10 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with four equivalent Mg(5)BaSrMg10 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra,  a faceface with one Sr(1)Ba2Mg10 cuboctahedra,  a faceface with one Mg(1)Mg12 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(6)SrMg11 cuboctahedra, faces with three equivalent Ba(1)Sr2Mg10 cuboctahedra, faces with three equivalent Mg(2)Mg12 cuboctahedra, and faces with four equivalent Mg(5)BaSrMg10 cuboctahedra. In the seventh Mg site, Mg(7) is bonded in a 12-coordinate geometry to one Ba(1), one Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(6), and four equivalent Mg(5) atoms.
BaSrMg14 crystallizes in the orthorhombic Amm2 space group. Ba(1) is bonded to two equivalent Sr(1), two equivalent Mg(7), four equivalent Mg(3), and four equivalent Mg(5) atoms to form BaSr2Mg10 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra, corners with six equivalent Ba(1)Sr2Mg10 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Sr(1)Ba2Mg10 cuboctahedra, edges with eight equivalent Mg(5)BaSrMg10 cuboctahedra, faces with two equivalent Sr(1)Ba2Mg10 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with four equivalent Mg(5)BaSrMg10 cuboctahedra, and faces with six equivalent Mg(6)SrMg11 cuboctahedra. Both Ba(1)-Sr(1) bond lengths are 3.35 Å. Both Ba(1)-Mg(7) bond lengths are 3.49 Å. There are two shorter (3.37 Å) and two longer (3.39 Å) Ba(1)-Mg(3) bond lengths. All Ba(1)-Mg(5) bond lengths are 3.55 Å. Sr(1) is bonded to two equivalent Ba(1), two equivalent Mg(6), four equivalent Mg(3), and four equivalent Mg(5) atoms to form SrBa2Mg10 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra, corners with six equivalent Sr(1)Ba2Mg10 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Ba(1)Sr2Mg10 cuboctahedra, edges with four equivalent Mg(6)SrMg11 cuboctahedra, edges with eight equivalent Mg(5)BaSrMg10 cuboctahedra, faces with two equivalent Ba(1)Sr2Mg10 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Mg(6)SrMg11 cuboctahedra, and faces with four equivalent Mg(5)BaSrMg10 cuboctahedra. Both Sr(1)-Mg(6) bond lengths are 3.46 Å. There are two shorter (3.33 Å) and two longer (3.43 Å) Sr(1)-Mg(3) bond lengths. All Sr(1)-Mg(5) bond lengths are 3.52 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 Ba(1)Sr2Mg10 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, edges with four equivalent Mg(6)SrMg11 cuboctahedra, edges with eight equivalent Mg(5)BaSrMg10 cuboctahedra, faces with two equivalent Sr(1)Ba2Mg10 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with two equivalent Mg(6)SrMg11 cuboctahedra, faces with four equivalent Mg(5)BaSrMg10 cuboctahedra, and faces with four equivalent Mg(4)Mg12 cuboctahedra. Both Mg(1)-Mg(2) bond lengths are 3.35 Å. Both Mg(1)-Mg(6) bond lengths are 3.30 Å. There are two shorter (3.34 Å) and two longer (3.42 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 Sr(1)Ba2Mg10 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, edges with eight equivalent Mg(5)BaSrMg10 cuboctahedra, faces with two equivalent Ba(1)Sr2Mg10 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with four equivalent Mg(5)BaSrMg10 cuboctahedra, faces with four equivalent Mg(4)Mg12 cuboctahedra, and faces with six equivalent Mg(6)SrMg11 cuboctahedra. Both Mg(2)-Mg(7) bond lengths are 3.28 Å. There are two shorter (3.35 Å) and two longer (3.42 Å) Mg(2)-Mg(4) bond lengths. All Mg(2)-Mg(5) bond lengths are 3.17 Å. In the third Mg site, Mg(3) is bonded in a 4-coordinate geometry to two equivalent Ba(1), two equivalent Sr(1), two equivalent Mg(5), two equivalent Mg(6), and two equivalent Mg(7) atoms. Both Mg(3)-Mg(5) bond lengths are 3.50 Å. Both Mg(3)-Mg(6) bond lengths are 3.37 Å. Both Mg(3)-Mg(7) bond lengths are 3.41 Å. 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)Sr2Mg10 cuboctahedra, corners with four equivalent Sr(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(5)BaSrMg10 cuboctahedra, edges with four equivalent Mg(6)SrMg11 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(6)SrMg11 cuboctahedra, and faces with eight equivalent Mg(5)BaSrMg10 cuboctahedra. There is one shorter (3.35 Å) and one longer (3.36 Å) Mg(4)-Mg(4) bond length. Both Mg(4)-Mg(5) bond lengths are 3.12 Å. Both Mg(4)-Mg(6) bond lengths are 3.25 Å. Both Mg(4)-Mg(7) bond lengths are 3.21 Å. In the fifth Mg site, Mg(5) is bonded to one Ba(1), one Sr(1), one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Mg(6), and two equivalent Mg(7) atoms to form distorted MgBaSrMg10 cuboctahedra that share corners with four equivalent Mg(6)SrMg11 cuboctahedra, corners with ten equivalent Mg(5)BaSrMg10 cuboctahedra, edges with two equivalent Ba(1)Sr2Mg10 cuboctahedra, edges with two equivalent Sr(1)Ba2Mg10 cuboctahedra, edges with two equivalent Mg(5)BaSrMg10 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 two equivalent Mg(6)SrMg11 cuboctahedra,  a faceface with one Ba(1)Sr2Mg10 cuboctahedra,  a faceface with one Sr(1)Ba2Mg10 cuboctahedra,  a faceface with one Mg(1)Mg12 cuboctahedra,  a faceface with one Mg(2)Mg12 cuboctahedra, faces with two equivalent Mg(6)SrMg11 cuboctahedra, faces with four equivalent Mg(5)BaSrMg10 cuboctahedra, and faces with four equivalent Mg(4)Mg12 cuboctahedra. There is one shorter (3.33 Å) and one longer (3.38 Å) Mg(5)-Mg(5) bond length. There is one shorter (3.29 Å) and one longer (3.48 Å) Mg(5)-Mg(6) bond length. There is one shorter (3.26 Å) and one longer (3.51 Å) Mg(5)-Mg(7) bond length. In the sixth Mg site, Mg(6) is bonded to one Sr(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 MgSrMg11 cuboctahedra that share corners with six equivalent Mg(6)SrMg11 cuboctahedra, corners with eight equivalent Mg(5)BaSrMg10 cuboctahedra, edges with two equivalent Sr(1)Ba2Mg10 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with four equivalent Mg(5)BaSrMg10 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra,  a faceface with one Sr(1)Ba2Mg10 cuboctahedra,  a faceface with one Mg(1)Mg12 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(6)SrMg11 cuboctahedra, faces with three equivalent Ba(1)Sr2Mg10 cuboctahedra, faces with three equivalent Mg(2)Mg12 cuboctahedra, and faces with four equivalent Mg(5)BaSrMg10 cuboctahedra. Both Mg(6)-Mg(7) bond lengths are 3.35 Å. In the seventh Mg site, Mg(7) is bonded in a 12-coordinate geometry to one Ba(1), one Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(6), and four equivalent Mg(5) atoms.