BaMg14Cr crystallizes in the hexagonal P-6m2 space group. Ba(1) is bonded to six Mg(1,1) 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(2)Mg10Cr2 cuboctahedra; edges with six Mg(1,1)Ba2Mg10 cuboctahedra; edges with twelve Mg(3,3)BaMg10Cr cuboctahedra; faces with two equivalent Cr(1)Mg12 cuboctahedra; faces with six Mg(1,1)Ba2Mg10 cuboctahedra; faces with six Mg(3,3)BaMg10Cr cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. There are six inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Ba(1), two equivalent Mg(4), four equivalent Mg(1), and four equivalent Mg(3) atoms to form distorted MgBa2Mg10 cuboctahedra that share corners with four equivalent Cr(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Ba2Mg10 cuboctahedra; corners with eight equivalent Mg(2)Mg10Cr2 cuboctahedra; edges with two equivalent Ba(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Ba2Mg10 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)BaMg10Cr cuboctahedra; faces with two equivalent Ba(1)Mg12 cuboctahedra; faces with two equivalent Mg(2)Mg10Cr2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with four equivalent Mg(1)Ba2Mg10 cuboctahedra; and faces with ten Mg(3,3)BaMg10Cr cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(4), four equivalent Mg(2), four equivalent Mg(3), and two equivalent Cr(1) atoms to form distorted MgMg10Cr2 cuboctahedra that share corners with four equivalent Ba(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Cr2 cuboctahedra; corners with eight equivalent Mg(1)Ba2Mg10 cuboctahedra; edges with two equivalent Cr(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Cr2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)BaMg10Cr cuboctahedra; faces with two equivalent Mg(1)Ba2Mg10 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Cr(1)Mg12 cuboctahedra; faces with four equivalent Mg(2)Mg10Cr2 cuboctahedra; and faces with ten Mg(3,3)BaMg10Cr cuboctahedra. In the third Mg site, Mg(1) is bonded to two equivalent Ba(1); two equivalent Mg(4); four Mg(1,1); and four Mg(3,3) atoms to form distorted MgBa2Mg10 cuboctahedra that share corners with four equivalent Cr(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Ba2Mg10 cuboctahedra; corners with eight equivalent Mg(2)Mg10Cr2 cuboctahedra; edges with two equivalent Ba(1)Mg12 cuboctahedra; edges with four Mg(1,1)Ba2Mg10 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)BaMg10Cr cuboctahedra; faces with two equivalent Ba(1)Mg12 cuboctahedra; faces with two equivalent Mg(2)Mg10Cr2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with four Mg(1,1)Ba2Mg10 cuboctahedra; and faces with ten Mg(3,3)BaMg10Cr cuboctahedra. In the fourth Mg site, Mg(3) is bonded to one Ba(1); two Mg(1,1); two equivalent Mg(2); two equivalent Mg(4); four Mg(3,3); and one Cr(1) atom to form distorted MgBaMg10Cr cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)BaMg10Cr cuboctahedra; edges with two equivalent Ba(1)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Cr(1)Mg12 cuboctahedra; edges with four Mg(1,1)Ba2Mg10 cuboctahedra; edges with four Mg(3,3)BaMg10Cr cuboctahedra; edges with four equivalent Mg(2)Mg10Cr2 cuboctahedra;  a faceface with one Ba(1)Mg12 cuboctahedra;  a faceface with one Cr(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(1,1)Ba2Mg10 cuboctahedra; faces with five equivalent Mg(2)Mg10Cr2 cuboctahedra; and faces with six Mg(3,3)BaMg10Cr cuboctahedra. In the fifth 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 Cr(1) atom to form distorted MgBaMg10Cr cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)BaMg10Cr cuboctahedra; edges with two equivalent Ba(1)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Cr(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Ba2Mg10 cuboctahedra; edges with four equivalent Mg(3)BaMg10Cr cuboctahedra; edges with four equivalent Mg(2)Mg10Cr2 cuboctahedra;  a faceface with one Ba(1)Mg12 cuboctahedra;  a faceface with one Cr(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(1,1)Ba2Mg10 cuboctahedra; faces with five equivalent Mg(2)Mg10Cr2 cuboctahedra; and faces with six Mg(3,3)BaMg10Cr cuboctahedra. In the sixth Mg site, Mg(4) is bonded to three Mg(1,1); 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)BaMg10Cr cuboctahedra; edges with six Mg(1,1)Ba2Mg10 cuboctahedra; edges with six Mg(3,3)BaMg10Cr cuboctahedra; edges with six equivalent Mg(2)Mg10Cr2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Ba(1)Mg12 cuboctahedra; faces with three Mg(1,1)Ba2Mg10 cuboctahedra; faces with three equivalent Mg(2)Mg10Cr2 cuboctahedra; faces with three equivalent Cr(1)Mg12 cuboctahedra; and faces with six Mg(3,3)BaMg10Cr cuboctahedra. Cr(1) is bonded to six equivalent Mg(2) and six Mg(3,3) atoms to form CrMg12 cuboctahedra that share corners with six equivalent Cr(1)Mg12 cuboctahedra; corners with twelve Mg(1,1)Ba2Mg10 cuboctahedra; edges with six equivalent Mg(2)Mg10Cr2 cuboctahedra; edges with twelve Mg(3,3)BaMg10Cr cuboctahedra; faces with two equivalent Ba(1)Mg12 cuboctahedra; faces with six Mg(3,3)BaMg10Cr cuboctahedra; faces with six equivalent Mg(2)Mg10Cr2 cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra.
BaMg14Cr crystallizes in the hexagonal P-6m2 space group. Ba(1) is bonded to six Mg(1,1) 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(2)Mg10Cr2 cuboctahedra; edges with six Mg(1,1)Ba2Mg10 cuboctahedra; edges with twelve Mg(3,3)BaMg10Cr cuboctahedra; faces with two equivalent Cr(1)Mg12 cuboctahedra; faces with six Mg(1,1)Ba2Mg10 cuboctahedra; faces with six Mg(3,3)BaMg10Cr cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. All Ba(1)-Mg(1,1) bond lengths are 3.29 Å. All Ba(1)-Mg(3,3) bond lengths are 3.42 Å. There are six inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Ba(1), two equivalent Mg(4), four equivalent Mg(1), and four equivalent Mg(3) atoms to form distorted MgBa2Mg10 cuboctahedra that share corners with four equivalent Cr(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Ba2Mg10 cuboctahedra; corners with eight equivalent Mg(2)Mg10Cr2 cuboctahedra; edges with two equivalent Ba(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Ba2Mg10 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)BaMg10Cr cuboctahedra; faces with two equivalent Ba(1)Mg12 cuboctahedra; faces with two equivalent Mg(2)Mg10Cr2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with four equivalent Mg(1)Ba2Mg10 cuboctahedra; and faces with ten Mg(3,3)BaMg10Cr cuboctahedra. Both Mg(1)-Mg(4) bond lengths are 3.23 Å. There are two shorter (3.17 Å) and two longer (3.42 Å) Mg(1)-Mg(1) bond lengths. All Mg(1)-Mg(3) bond lengths are 3.38 Å. In the second Mg site, Mg(2) is bonded to two equivalent Mg(4), four equivalent Mg(2), four equivalent Mg(3), and two equivalent Cr(1) atoms to form distorted MgMg10Cr2 cuboctahedra that share corners with four equivalent Ba(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Cr2 cuboctahedra; corners with eight equivalent Mg(1)Ba2Mg10 cuboctahedra; edges with two equivalent Cr(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Cr2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)BaMg10Cr cuboctahedra; faces with two equivalent Mg(1)Ba2Mg10 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Cr(1)Mg12 cuboctahedra; faces with four equivalent Mg(2)Mg10Cr2 cuboctahedra; and faces with ten Mg(3,3)BaMg10Cr cuboctahedra. Both Mg(2)-Mg(4) bond lengths are 3.29 Å. There are two shorter (3.25 Å) and two longer (3.34 Å) Mg(2)-Mg(2) bond lengths. All Mg(2)-Mg(3) bond lengths are 3.09 Å. Both Mg(2)-Cr(1) bond lengths are 3.29 Å. In the third Mg site, Mg(1) is bonded to two equivalent Ba(1); two equivalent Mg(4); four Mg(1,1); and four Mg(3,3) atoms to form distorted MgBa2Mg10 cuboctahedra that share corners with four equivalent Cr(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Ba2Mg10 cuboctahedra; corners with eight equivalent Mg(2)Mg10Cr2 cuboctahedra; edges with two equivalent Ba(1)Mg12 cuboctahedra; edges with four Mg(1,1)Ba2Mg10 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)BaMg10Cr cuboctahedra; faces with two equivalent Ba(1)Mg12 cuboctahedra; faces with two equivalent Mg(2)Mg10Cr2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with four Mg(1,1)Ba2Mg10 cuboctahedra; and faces with ten Mg(3,3)BaMg10Cr cuboctahedra. Both Mg(1)-Mg(4) bond lengths are 3.23 Å. There is one shorter (3.17 Å) and one longer (3.42 Å) Mg(1)-Mg(1) bond length. All Mg(1)-Mg(3,3) bond lengths are 3.38 Å. In the fourth Mg site, Mg(3) is bonded to one Ba(1); two Mg(1,1); two equivalent Mg(2); two equivalent Mg(4); four Mg(3,3); and one Cr(1) atom to form distorted MgBaMg10Cr cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)BaMg10Cr cuboctahedra; edges with two equivalent Ba(1)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Cr(1)Mg12 cuboctahedra; edges with four Mg(1,1)Ba2Mg10 cuboctahedra; edges with four Mg(3,3)BaMg10Cr cuboctahedra; edges with four equivalent Mg(2)Mg10Cr2 cuboctahedra;  a faceface with one Ba(1)Mg12 cuboctahedra;  a faceface with one Cr(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(1,1)Ba2Mg10 cuboctahedra; faces with five equivalent Mg(2)Mg10Cr2 cuboctahedra; and faces with six Mg(3,3)BaMg10Cr cuboctahedra. Both Mg(3)-Mg(4) bond lengths are 3.30 Å. There are two shorter (3.24 Å) and two longer (3.35 Å) Mg(3)-Mg(3,3) bond lengths. The Mg(3)-Cr(1) bond length is 3.11 Å. In the fifth 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 Cr(1) atom to form distorted MgBaMg10Cr cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)BaMg10Cr cuboctahedra; edges with two equivalent Ba(1)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Cr(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Ba2Mg10 cuboctahedra; edges with four equivalent Mg(3)BaMg10Cr cuboctahedra; edges with four equivalent Mg(2)Mg10Cr2 cuboctahedra;  a faceface with one Ba(1)Mg12 cuboctahedra;  a faceface with one Cr(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(1,1)Ba2Mg10 cuboctahedra; faces with five equivalent Mg(2)Mg10Cr2 cuboctahedra; and faces with six Mg(3,3)BaMg10Cr cuboctahedra. Both Mg(3)-Mg(2) bond lengths are 3.09 Å. Both Mg(3)-Mg(4) bond lengths are 3.30 Å. The Mg(3)-Cr(1) bond length is 3.11 Å. In the sixth Mg site, Mg(4) is bonded to three Mg(1,1); 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)BaMg10Cr cuboctahedra; edges with six Mg(1,1)Ba2Mg10 cuboctahedra; edges with six Mg(3,3)BaMg10Cr cuboctahedra; edges with six equivalent Mg(2)Mg10Cr2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Ba(1)Mg12 cuboctahedra; faces with three Mg(1,1)Ba2Mg10 cuboctahedra; faces with three equivalent Mg(2)Mg10Cr2 cuboctahedra; faces with three equivalent Cr(1)Mg12 cuboctahedra; and faces with six Mg(3,3)BaMg10Cr cuboctahedra. Cr(1) is bonded to six equivalent Mg(2) and six Mg(3,3) atoms to form CrMg12 cuboctahedra that share corners with six equivalent Cr(1)Mg12 cuboctahedra; corners with twelve Mg(1,1)Ba2Mg10 cuboctahedra; edges with six equivalent Mg(2)Mg10Cr2 cuboctahedra; edges with twelve Mg(3,3)BaMg10Cr cuboctahedra; faces with two equivalent Ba(1)Mg12 cuboctahedra; faces with six Mg(3,3)BaMg10Cr cuboctahedra; faces with six equivalent Mg(2)Mg10Cr2 cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra.