MgTi2 is beta-derived structured and crystallizes in the monoclinic P2_1/m space group. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one Mg(2), one Mg(3), two equivalent Mg(4), one Ti(2), one Ti(4), three equivalent Ti(6), and three equivalent Ti(7) atoms to form distorted MgMg4Ti8 cuboctahedra that share  a cornercorner with one Mg(4)Mg6Ti6 cuboctahedra,  a cornercorner with one Ti(3)Mg2Ti10 cuboctahedra, corners with two equivalent Mg(2)Mg4Ti8 cuboctahedra, corners with two equivalent Ti(4)Mg3Ti9 cuboctahedra, corners with two equivalent Ti(1)Mg4Ti8 cuboctahedra, corners with two equivalent Ti(2)Mg4Ti8 cuboctahedra, corners with two equivalent Ti(7)Mg5Ti7 cuboctahedra, corners with three equivalent Mg(3)Mg4Ti8 cuboctahedra, corners with three equivalent Ti(6)Mg4Ti8 cuboctahedra,  an edgeedge with one Mg(4)Mg6Ti6 cuboctahedra,  an edgeedge with one Ti(3)Mg2Ti10 cuboctahedra,  an edgeedge with one Ti(4)Mg3Ti9 cuboctahedra,  an edgeedge with one Ti(5)Mg3Ti9 cuboctahedra,  an edgeedge with one Ti(7)Mg5Ti7 cuboctahedra, edges with two equivalent Mg(3)Mg4Ti8 cuboctahedra, edges with two equivalent Ti(1)Mg4Ti8 cuboctahedra, edges with two equivalent Ti(2)Mg4Ti8 cuboctahedra, edges with three equivalent Ti(8)Mg5Ti7 cuboctahedra, edges with four equivalent Mg(1)Mg4Ti8 cuboctahedra,  a faceface with one Mg(2)Mg4Ti8 cuboctahedra,  a faceface with one Mg(3)Mg4Ti8 cuboctahedra, faces with two equivalent Mg(1)Mg4Ti8 cuboctahedra, faces with two equivalent Mg(4)Mg6Ti6 cuboctahedra, faces with two equivalent Ti(5)Mg3Ti9 cuboctahedra, faces with three equivalent Ti(4)Mg3Ti9 cuboctahedra, faces with three equivalent Ti(2)Mg4Ti8 cuboctahedra, faces with three equivalent Ti(6)Mg4Ti8 cuboctahedra, and faces with three equivalent Ti(7)Mg5Ti7 cuboctahedra. In the second Mg site, Mg(2) is bonded to one Mg(1), one Mg(3), two equivalent Mg(4), one Ti(1), one Ti(3), one Ti(4), two equivalent Ti(5), and three equivalent Ti(8) atoms to form distorted MgMg4Ti8 cuboctahedra that share  a cornercorner with one Ti(5)Mg3Ti9 cuboctahedra,  a cornercorner with one Ti(7)Mg5Ti7 cuboctahedra, corners with two equivalent Mg(1)Mg4Ti8 cuboctahedra, corners with two equivalent Mg(3)Mg4Ti8 cuboctahedra, corners with two equivalent Ti(3)Mg2Ti10 cuboctahedra, corners with two equivalent Ti(1)Mg4Ti8 cuboctahedra, corners with two equivalent Ti(2)Mg4Ti8 cuboctahedra, corners with three equivalent Ti(4)Mg3Ti9 cuboctahedra, corners with three equivalent Ti(8)Mg5Ti7 cuboctahedra,  an edgeedge with one Mg(4)Mg6Ti6 cuboctahedra,  an edgeedge with one Ti(3)Mg2Ti10 cuboctahedra,  an edgeedge with one Ti(5)Mg3Ti9 cuboctahedra,  an edgeedge with one Ti(6)Mg4Ti8 cuboctahedra, edges with two equivalent Mg(2)Mg4Ti8 cuboctahedra, edges with two equivalent Ti(1)Mg4Ti8 cuboctahedra, edges with three equivalent Mg(3)Mg4Ti8 cuboctahedra, edges with three equivalent Ti(7)Mg5Ti7 cuboctahedra, edges with four equivalent Ti(2)Mg4Ti8 cuboctahedra,  a faceface with one Mg(1)Mg4Ti8 cuboctahedra,  a faceface with one Mg(3)Mg4Ti8 cuboctahedra,  a faceface with one Ti(4)Mg3Ti9 cuboctahedra, faces with two equivalent Mg(2)Mg4Ti8 cuboctahedra, faces with two equivalent Mg(4)Mg6Ti6 cuboctahedra, faces with two equivalent Ti(5)Mg3Ti9 cuboctahedra, faces with two equivalent Ti(6)Mg4Ti8 cuboctahedra, faces with three equivalent Ti(3)Mg2Ti10 cuboctahedra, faces with three equivalent Ti(1)Mg4Ti8 cuboctahedra, and faces with three equivalent Ti(8)Mg5Ti7 cuboctahedra. In the third Mg site, Mg(3) is bonded to one Mg(1), one Mg(2), two equivalent Mg(4), one Ti(3), one Ti(4), one Ti(7), one Ti(8), two equivalent Ti(1), and two equivalent Ti(2) atoms to form distorted MgMg4Ti8 cuboctahedra that share  a cornercorner with one Ti(1)Mg4Ti8 cuboctahedra,  a cornercorner with one Ti(6)Mg4Ti8 cuboctahedra, corners with two equivalent Mg(2)Mg4Ti8 cuboctahedra, corners with two equivalent Mg(4)Mg6Ti6 cuboctahedra, corners with two equivalent Ti(4)Mg3Ti9 cuboctahedra, corners with two equivalent Ti(7)Mg5Ti7 cuboctahedra, corners with two equivalent Ti(8)Mg5Ti7 cuboctahedra, corners with three equivalent Mg(1)Mg4Ti8 cuboctahedra, corners with three equivalent Ti(3)Mg2Ti10 cuboctahedra,  an edgeedge with one Ti(4)Mg3Ti9 cuboctahedra,  an edgeedge with one Ti(1)Mg4Ti8 cuboctahedra,  an edgeedge with one Ti(2)Mg4Ti8 cuboctahedra, edges with two equivalent Mg(1)Mg4Ti8 cuboctahedra, edges with two equivalent Ti(3)Mg2Ti10 cuboctahedra, edges with three equivalent Mg(2)Mg4Ti8 cuboctahedra, edges with three equivalent Ti(5)Mg3Ti9 cuboctahedra, edges with five equivalent Ti(6)Mg4Ti8 cuboctahedra,  a faceface with one Mg(1)Mg4Ti8 cuboctahedra,  a faceface with one Mg(2)Mg4Ti8 cuboctahedra,  a faceface with one Ti(3)Mg2Ti10 cuboctahedra,  a faceface with one Ti(4)Mg3Ti9 cuboctahedra, faces with two equivalent Mg(3)Mg4Ti8 cuboctahedra, faces with two equivalent Mg(4)Mg6Ti6 cuboctahedra, faces with two equivalent Ti(5)Mg3Ti9 cuboctahedra, faces with two equivalent Ti(1)Mg4Ti8 cuboctahedra, faces with two equivalent Ti(2)Mg4Ti8 cuboctahedra, faces with three equivalent Ti(7)Mg5Ti7 cuboctahedra, and faces with three equivalent Ti(8)Mg5Ti7 cuboctahedra. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), one Ti(1), one Ti(2), one Ti(5), one Ti(6), one Ti(7), and one Ti(8) atom to form MgMg6Ti6 cuboctahedra that share  a cornercorner with one Mg(1)Mg4Ti8 cuboctahedra,  a cornercorner with one Ti(3)Mg2Ti10 cuboctahedra, corners with two equivalent Mg(3)Mg4Ti8 cuboctahedra, corners with two equivalent Ti(5)Mg3Ti9 cuboctahedra, corners with two equivalent Ti(2)Mg4Ti8 cuboctahedra, corners with two equivalent Ti(7)Mg5Ti7 cuboctahedra, corners with two equivalent Ti(8)Mg5Ti7 cuboctahedra, corners with three equivalent Ti(1)Mg4Ti8 cuboctahedra, corners with three equivalent Ti(6)Mg4Ti8 cuboctahedra,  an edgeedge with one Mg(1)Mg4Ti8 cuboctahedra,  an edgeedge with one Mg(2)Mg4Ti8 cuboctahedra,  an edgeedge with one Ti(5)Mg3Ti9 cuboctahedra, edges with two equivalent Ti(1)Mg4Ti8 cuboctahedra, edges with two equivalent Ti(6)Mg4Ti8 cuboctahedra, edges with three equivalent Ti(4)Mg3Ti9 cuboctahedra, edges with three equivalent Ti(2)Mg4Ti8 cuboctahedra, edges with five equivalent Ti(3)Mg2Ti10 cuboctahedra,  a faceface with one Ti(5)Mg3Ti9 cuboctahedra,  a faceface with one Ti(1)Mg4Ti8 cuboctahedra,  a faceface with one Ti(2)Mg4Ti8 cuboctahedra,  a faceface with one Ti(6)Mg4Ti8 cuboctahedra, faces with two equivalent Mg(1)Mg4Ti8 cuboctahedra, faces with two equivalent Mg(2)Mg4Ti8 cuboctahedra, faces with two equivalent Mg(3)Mg4Ti8 cuboctahedra, faces with two equivalent Mg(4)Mg6Ti6 cuboctahedra, faces with two equivalent Ti(4)Mg3Ti9 cuboctahedra, faces with three equivalent Ti(7)Mg5Ti7 cuboctahedra, and faces with three equivalent Ti(8)Mg5Ti7 cuboctahedra. There are eight inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one Mg(2), one Mg(4), two equivalent Mg(3), one Ti(2), one Ti(5), three equivalent Ti(3), and three equivalent Ti(8) atoms to form distorted TiMg4Ti8 cuboctahedra that share  a cornercorner with one Mg(3)Mg4Ti8 cuboctahedra,  a cornercorner with one Ti(6)Mg4Ti8 cuboctahedra, corners with two equivalent Mg(1)Mg4Ti8 cuboctahedra, corners with two equivalent Mg(2)Mg4Ti8 cuboctahedra, corners with two equivalent Ti(5)Mg3Ti9 cuboctahedra, corners with two equivalent Ti(2)Mg4Ti8 cuboctahedra, corners with two equivalent Ti(8)Mg5Ti7 cuboctahedra, corners with three equivalent Mg(4)Mg6Ti6 cuboctahedra, corners with three equivalent Ti(3)Mg2Ti10 cuboctahedra,  an edgeedge with one Mg(3)Mg4Ti8 cuboctahedra,  an edgeedge with one Ti(4)Mg3Ti9 cuboctahedra,  an edgeedge with one Ti(5)Mg3Ti9 cuboctahedra,  an edgeedge with one Ti(6)Mg4Ti8 cuboctahedra,  an edgeedge with one Ti(8)Mg5Ti7 cuboctahedra, edges with two equivalent Mg(1)Mg4Ti8 cuboctahedra, edges with two equivalent Mg(2)Mg4Ti8 cuboctahedra, edges with two equivalent Mg(4)Mg6Ti6 cuboctahedra, edges with three equivalent Ti(7)Mg5Ti7 cuboctahedra, edges with four equivalent Ti(1)Mg4Ti8 cuboctahedra,  a faceface with one Mg(4)Mg6Ti6 cuboctahedra,  a faceface with one Ti(2)Mg4Ti8 cuboctahedra, faces with two equivalent Mg(3)Mg4Ti8 cuboctahedra, faces with two equivalent Ti(4)Mg3Ti9 cuboctahedra, faces with two equivalent Ti(1)Mg4Ti8 cuboctahedra, faces with three equivalent Mg(2)Mg4Ti8 cuboctahedra, faces with three equivalent Ti(3)Mg2Ti10 cuboctahedra, faces with three equivalent Ti(5)Mg3Ti9 cuboctahedra, and faces with three equivalent Ti(8)Mg5Ti7 cuboctahedra. In the second Ti site, Ti(2) is bonded to one Mg(1), one Mg(4), two equivalent Mg(3), one Ti(1), one Ti(5), one Ti(6), two equivalent Ti(4), and three equivalent Ti(7) atoms to form distorted TiMg4Ti8 cuboctahedra that share  a cornercorner with one Ti(4)Mg3Ti9 cuboctahedra,  a cornercorner with one Ti(8)Mg5Ti7 cuboctahedra, corners with two equivalent Mg(1)Mg4Ti8 cuboctahedra, corners with two equivalent Mg(2)Mg4Ti8 cuboctahedra, corners with two equivalent Mg(4)Mg6Ti6 cuboctahedra, corners with two equivalent Ti(1)Mg4Ti8 cuboctahedra, corners with two equivalent Ti(6)Mg4Ti8 cuboctahedra, corners with three equivalent Ti(5)Mg3Ti9 cuboctahedra, corners with three equivalent Ti(7)Mg5Ti7 cuboctahedra,  an edgeedge with one Mg(3)Mg4Ti8 cuboctahedra,  an edgeedge with one Ti(3)Mg2Ti10 cuboctahedra,  an edgeedge with one Ti(4)Mg3Ti9 cuboctahedra,  an edgeedge with one Ti(6)Mg4Ti8 cuboctahedra, edges with two equivalent Mg(1)Mg4Ti8 cuboctahedra, edges with two equivalent Ti(2)Mg4Ti8 cuboctahedra, edges with three equivalent Mg(4)Mg6Ti6 cuboctahedra, edges with three equivalent Ti(8)Mg5Ti7 cuboctahedra, edges with four equivalent Mg(2)Mg4Ti8 cuboctahedra,  a faceface with one Mg(4)Mg6Ti6 cuboctahedra,  a faceface with one Ti(5)Mg3Ti9 cuboctahedra,  a faceface with one Ti(1)Mg4Ti8 cuboctahedra, faces with two equivalent Mg(3)Mg4Ti8 cuboctahedra, faces with two equivalent Ti(3)Mg2Ti10 cuboctahedra, faces with two equivalent Ti(4)Mg3Ti9 cuboctahedra, faces with two equivalent Ti(2)Mg4Ti8 cuboctahedra, faces with three equivalent Mg(1)Mg4Ti8 cuboctahedra, faces with three equivalent Ti(6)Mg4Ti8 cuboctahedra, and faces with three equivalent Ti(7)Mg5Ti7 cuboctahedra. In the third Ti site, Ti(3) is bonded to one Mg(2), one Mg(3), one Ti(4), one Ti(8), two equivalent Ti(3), three equivalent Ti(1), and three equivalent Ti(5) atoms to form distorted TiMg2Ti10 cuboctahedra that share  a cornercorner with one Mg(1)Mg4Ti8 cuboctahedra,  a cornercorner with one Mg(4)Mg6Ti6 cuboctahedra, corners with two equivalent Mg(2)Mg4Ti8 cuboctahedra, corners with two equivalent Ti(4)Mg3Ti9 cuboctahedra, corners with two equivalent Ti(5)Mg3Ti9 cuboctahedra, corners with two equivalent Ti(6)Mg4Ti8 cuboctahedra, corners with two equivalent Ti(8)Mg5Ti7 cuboctahedra, corners with three equivalent Mg(3)Mg4Ti8 cuboctahedra, corners with three equivalent Ti(1)Mg4Ti8 cuboctahedra,  an edgeedge with one Mg(1)Mg4Ti8 cuboctahedra,  an edgeedge with one Mg(2)Mg4Ti8 cuboctahedra,  an edgeedge with one Ti(2)Mg4Ti8 cuboctahedra,  an edgeedge with one Ti(7)Mg5Ti7 cuboctahedra, edges with two equivalent Mg(3)Mg4Ti8 cuboctahedra, edges with two equivalent Ti(4)Mg3Ti9 cuboctahedra, edges with two equivalent Ti(6)Mg4Ti8 cuboctahedra, edges with three equivalent Ti(8)Mg5Ti7 cuboctahedra, edges with five equivalent Mg(4)Mg6Ti6 cuboctahedra,  a faceface with one Mg(3)Mg4Ti8 cuboctahedra,  a faceface with one Ti(4)Mg3Ti9 cuboctahedra, faces with two equivalent Ti(2)Mg4Ti8 cuboctahedra, faces with three equivalent Mg(2)Mg4Ti8 cuboctahedra, faces with three equivalent Ti(5)Mg3Ti9 cuboctahedra, faces with three equivalent Ti(1)Mg4Ti8 cuboctahedra, faces with three equivalent Ti(8)Mg5Ti7 cuboctahedra, and faces with four equivalent Ti(3)Mg2Ti10 cuboctahedra. In the fourth Ti site, Ti(4) is bonded to one Mg(1), one Mg(2), one Mg(3), one Ti(3), one Ti(7), two equivalent Ti(2), two equivalent Ti(5), and three equivalent Ti(6) atoms to form distorted TiMg3Ti9 cuboctahedra that share  a cornercorner with one Ti(2)Mg4Ti8 cuboctahedra,  a cornercorner with one Ti(8)Mg5Ti7 cuboctahedra, corners with two equivalent Mg(1)Mg4Ti8 cuboctahedra, corners with two equivalent Mg(3)Mg4Ti8 cuboctahedra, corners with two equivalent Ti(3)Mg2Ti10 cuboctahedra, corners with two equivalent Ti(5)Mg3Ti9 cuboctahedra, corners with two equivalent Ti(6)Mg4Ti8 cuboctahedra, corners with three equivalent Mg(2)Mg4Ti8 cuboctahedra, corners with three equivalent Ti(7)Mg5Ti7 cuboctahedra,  an edgeedge with one Mg(1)Mg4Ti8 cuboctahedra,  an edgeedge with one Mg(3)Mg4Ti8 cuboctahedra,  an edgeedge with one Ti(1)Mg4Ti8 cuboctahedra,  an edgeedge with one Ti(2)Mg4Ti8 cuboctahedra, edges with two equivalent Ti(3)Mg2Ti10 cuboctahedra, edges with two equivalent Ti(4)Mg3Ti9 cuboctahedra, edges with three equivalent Mg(4)Mg6Ti6 cuboctahedra, edges with three equivalent Ti(8)Mg5Ti7 cuboctahedra, edges with four equivalent Ti(7)Mg5Ti7 cuboctahedra,  a faceface with one Mg(2)Mg4Ti8 cuboctahedra,  a faceface with one Mg(3)Mg4Ti8 cuboctahedra,  a faceface with one Ti(3)Mg2Ti10 cuboctahedra,  a faceface with one Ti(7)Mg5Ti7 cuboctahedra, faces with two equivalent Mg(4)Mg6Ti6 cuboctahedra, faces with two equivalent Ti(4)Mg3Ti9 cuboctahedra, faces with two equivalent Ti(5)Mg3Ti9 cuboctahedra, faces with two equivalent Ti(1)Mg4Ti8 cuboctahedra, faces with two equivalent Ti(2)Mg4Ti8 cuboctahedra, faces with three equivalent Mg(1)Mg4Ti8 cuboctahedra, and faces with three equivalent Ti(6)Mg4Ti8 cuboctahedra. In the fifth Ti site, Ti(5) is bonded to one Mg(4), two equivalent Mg(2), one Ti(1), one Ti(2), one Ti(6), one Ti(8), two equivalent Ti(4), and three equivalent Ti(3) atoms to form distorted TiMg3Ti9 cuboctahedra that share  a cornercorner with one Mg(2)Mg4Ti8 cuboctahedra,  a cornercorner with one Ti(7)Mg5Ti7 cuboctahedra, corners with two equivalent Mg(4)Mg6Ti6 cuboctahedra, corners with two equivalent Ti(3)Mg2Ti10 cuboctahedra, corners with two equivalent Ti(4)Mg3Ti9 cuboctahedra, corners with two equivalent Ti(1)Mg4Ti8 cuboctahedra, corners with two equivalent Ti(6)Mg4Ti8 cuboctahedra, corners with three equivalent Ti(2)Mg4Ti8 cuboctahedra, corners with three equivalent Ti(8)Mg5Ti7 cuboctahedra,  an edgeedge with one Mg(1)Mg4Ti8 cuboctahedra,  an edgeedge with one Mg(2)Mg4Ti8 cuboctahedra,  an edgeedge with one Mg(4)Mg6Ti6 cuboctahedra,  an edgeedge with one Ti(1)Mg4Ti8 cuboctahedra, edges with two equivalent Ti(5)Mg3Ti9 cuboctahedra, edges with two equivalent Ti(6)Mg4Ti8 cuboctahedra, edges with three equivalent Mg(3)Mg4Ti8 cuboctahedra, edges with three equivalent Ti(7)Mg5Ti7 cuboctahedra, edges with four equivalent Ti(8)Mg5Ti7 cuboctahedra,  a faceface with one Mg(4)Mg6Ti6 cuboctahedra,  a faceface with one Ti(2)Mg4Ti8 cuboctahedra,  a faceface with one Ti(6)Mg4Ti8 cuboctahedra,  a faceface with one Ti(8)Mg5Ti7 cuboctahedra, faces with two equivalent Mg(1)Mg4Ti8 cuboctahedra, faces with two equivalent Mg(2)Mg4Ti8 cuboctahedra, faces with two equivalent Mg(3)Mg4Ti8 cuboctahedra, faces with two equivalent Ti(4)Mg3Ti9 cuboctahedra, faces with two equivalent Ti(5)Mg3Ti9 cuboctahedra, faces with three equivalent Ti(3)Mg2Ti10 cuboctahedra, and faces with three equivalent Ti(1)Mg4Ti8 cuboctahedra. In the sixth Ti site, Ti(6) is bonded to one Mg(4), three equivalent Mg(1), one Ti(2), one Ti(5), one Ti(7), two equivalent Ti(6), and three equivalent Ti(4) atoms to form distorted TiMg4Ti8 cuboctahedra that share  a cornercorner with one Mg(3)Mg4Ti8 cuboctahedra,  a cornercorner with one Ti(1)Mg4Ti8 cuboctahedra, corners with two equivalent Ti(3)Mg2Ti10 cuboctahedra, corners with two equivalent Ti(4)Mg3Ti9 cuboctahedra, corners with two equivalent Ti(5)Mg3Ti9 cuboctahedra, corners with two equivalent Ti(2)Mg4Ti8 cuboctahedra, corners with two equivalent Ti(7)Mg5Ti7 cuboctahedra, corners with three equivalent Mg(1)Mg4Ti8 cuboctahedra, corners with three equivalent Mg(4)Mg6Ti6 cuboctahedra,  an edgeedge with one Mg(2)Mg4Ti8 cuboctahedra,  an edgeedge with one Ti(1)Mg4Ti8 cuboctahedra,  an edgeedge with one Ti(2)Mg4Ti8 cuboctahedra,  an edgeedge with one Ti(8)Mg5Ti7 cuboctahedra, edges with two equivalent Mg(4)Mg6Ti6 cuboctahedra, edges with two equivalent Ti(3)Mg2Ti10 cuboctahedra, edges with two equivalent Ti(5)Mg3Ti9 cuboctahedra, edges with three equivalent Ti(7)Mg5Ti7 cuboctahedra, edges with five equivalent Mg(3)Mg4Ti8 cuboctahedra,  a faceface with one Mg(4)Mg6Ti6 cuboctahedra,  a faceface with one Ti(5)Mg3Ti9 cuboctahedra, faces with two equivalent Mg(2)Mg4Ti8 cuboctahedra, faces with three equivalent Mg(1)Mg4Ti8 cuboctahedra, faces with three equivalent Ti(4)Mg3Ti9 cuboctahedra, faces with three equivalent Ti(2)Mg4Ti8 cuboctahedra, faces with three equivalent Ti(7)Mg5Ti7 cuboctahedra, and faces with four equivalent Ti(6)Mg4Ti8 cuboctahedra. In the seventh Ti site, Ti(7) is bonded to one Mg(3), one Mg(4), three equivalent Mg(1), one Ti(4), one Ti(6), two equivalent Ti(7), and three equivalent Ti(2) atoms to form distorted TiMg5Ti7 cuboctahedra that share  a cornercorner with one Mg(2)Mg4Ti8 cuboctahedra,  a cornercorner with one Ti(5)Mg3Ti9 cuboctahedra, corners with two equivalent Mg(1)Mg4Ti8 cuboctahedra, corners with two equivalent Mg(3)Mg4Ti8 cuboctahedra, corners with two equivalent Mg(4)Mg6Ti6 cuboctahedra, corners with two equivalent Ti(6)Mg4Ti8 cuboctahedra, corners with two equivalent Ti(8)Mg5Ti7 cuboctahedra, corners with three equivalent Ti(4)Mg3Ti9 cuboctahedra, corners with three equivalent Ti(2)Mg4Ti8 cuboctahedra,  an edgeedge with one Mg(1)Mg4Ti8 cuboctahedra,  an edgeedge with one Ti(3)Mg2Ti10 cuboctahedra, edges with three equivalent Mg(2)Mg4Ti8 cuboctahedra, edges with three equivalent Ti(5)Mg3Ti9 cuboctahedra, edges with three equivalent Ti(1)Mg4Ti8 cuboctahedra, edges with three equivalent Ti(6)Mg4Ti8 cuboctahedra, edges with four equivalent Ti(4)Mg3Ti9 cuboctahedra,  a faceface with one Ti(4)Mg3Ti9 cuboctahedra, faces with three equivalent Mg(1)Mg4Ti8 cuboctahedra, faces with three equivalent Mg(3)Mg4Ti8 cuboctahedra, faces with three equivalent Mg(4)Mg6Ti6 cuboctahedra, faces with three equivalent Ti(2)Mg4Ti8 cuboctahedra, faces with three equivalent Ti(6)Mg4Ti8 cuboctahedra, and faces with four equivalent Ti(7)Mg5Ti7 cuboctahedra. In the eighth Ti site, Ti(8) is bonded to one Mg(3), one Mg(4), three equivalent Mg(2), one Ti(3), one Ti(5), two equivalent Ti(8), and three equivalent Ti(1) atoms to form distorted TiMg5Ti7 cuboctahedra that share  a cornercorner with one Ti(4)Mg3Ti9 cuboctahedra,  a cornercorner with one Ti(2)Mg4Ti8 cuboctahedra, corners with two equivalent Mg(3)Mg4Ti8 cuboctahedra, corners with two equivalent Mg(4)Mg6Ti6 cuboctahedra, corners with two equivalent Ti(3)Mg2Ti10 cuboctahedra, corners with two equivalent Ti(1)Mg4Ti8 cuboctahedra, corners with two equivalent Ti(7)Mg5Ti7 cuboctahedra, corners with three equivalent Mg(2)Mg4Ti8 cuboctahedra, corners with three equivalent Ti(5)Mg3Ti9 cuboctahedra,  an edgeedge with one Ti(1)Mg4Ti8 cuboctahedra,  an edgeedge with one Ti(6)Mg4Ti8 cuboctahedra, edges with three equivalent Mg(1)Mg4Ti8 cuboctahedra, edges with three equivalent Ti(3)Mg2Ti10 cuboctahedra, edges with three equivalent Ti(4)Mg3Ti9 cuboctahedra, edges with three equivalent Ti(2)Mg4Ti8 cuboctahedra, edges with four equivalent Ti(5)Mg3Ti9 cuboctahedra,  a faceface with one Ti(5)Mg3Ti9 cuboctahedra, faces with three equivalent Mg(2)Mg4Ti8 cuboctahedra, faces with three equivalent Mg(3)Mg4Ti8 cuboctahedra, faces with three equivalent Mg(4)Mg6Ti6 cuboctahedra, faces with three equivalent Ti(3)Mg2Ti10 cuboctahedra, faces with three equivalent Ti(1)Mg4Ti8 cuboctahedra, and faces with four equivalent Ti(8)Mg5Ti7 cuboctahedra.
MgTi2 is beta-derived structured and crystallizes in the monoclinic P2_1/m space group. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one Mg(2), one Mg(3), two equivalent Mg(4), one Ti(2), one Ti(4), three equivalent Ti(6), and three equivalent Ti(7) atoms to form distorted MgMg4Ti8 cuboctahedra that share  a cornercorner with one Mg(4)Mg6Ti6 cuboctahedra,  a cornercorner with one Ti(3)Mg2Ti10 cuboctahedra, corners with two equivalent Mg(2)Mg4Ti8 cuboctahedra, corners with two equivalent Ti(4)Mg3Ti9 cuboctahedra, corners with two equivalent Ti(1)Mg4Ti8 cuboctahedra, corners with two equivalent Ti(2)Mg4Ti8 cuboctahedra, corners with two equivalent Ti(7)Mg5Ti7 cuboctahedra, corners with three equivalent Mg(3)Mg4Ti8 cuboctahedra, corners with three equivalent Ti(6)Mg4Ti8 cuboctahedra,  an edgeedge with one Mg(4)Mg6Ti6 cuboctahedra,  an edgeedge with one Ti(3)Mg2Ti10 cuboctahedra,  an edgeedge with one Ti(4)Mg3Ti9 cuboctahedra,  an edgeedge with one Ti(5)Mg3Ti9 cuboctahedra,  an edgeedge with one Ti(7)Mg5Ti7 cuboctahedra, edges with two equivalent Mg(3)Mg4Ti8 cuboctahedra, edges with two equivalent Ti(1)Mg4Ti8 cuboctahedra, edges with two equivalent Ti(2)Mg4Ti8 cuboctahedra, edges with three equivalent Ti(8)Mg5Ti7 cuboctahedra, edges with four equivalent Mg(1)Mg4Ti8 cuboctahedra,  a faceface with one Mg(2)Mg4Ti8 cuboctahedra,  a faceface with one Mg(3)Mg4Ti8 cuboctahedra, faces with two equivalent Mg(1)Mg4Ti8 cuboctahedra, faces with two equivalent Mg(4)Mg6Ti6 cuboctahedra, faces with two equivalent Ti(5)Mg3Ti9 cuboctahedra, faces with three equivalent Ti(4)Mg3Ti9 cuboctahedra, faces with three equivalent Ti(2)Mg4Ti8 cuboctahedra, faces with three equivalent Ti(6)Mg4Ti8 cuboctahedra, and faces with three equivalent Ti(7)Mg5Ti7 cuboctahedra. The Mg(1)-Mg(2) bond length is 3.11 Å. The Mg(1)-Mg(3) bond length is 3.14 Å. Both Mg(1)-Mg(4) bond lengths are 2.97 Å. The Mg(1)-Ti(2) bond length is 2.94 Å. The Mg(1)-Ti(4) bond length is 3.07 Å. There is one shorter (2.92 Å) and two longer (2.95 Å) Mg(1)-Ti(6) bond lengths. There are two shorter (2.93 Å) and one longer (3.02 Å) Mg(1)-Ti(7) bond length. In the second Mg site, Mg(2) is bonded to one Mg(1), one Mg(3), two equivalent Mg(4), one Ti(1), one Ti(3), one Ti(4), two equivalent Ti(5), and three equivalent Ti(8) atoms to form distorted MgMg4Ti8 cuboctahedra that share  a cornercorner with one Ti(5)Mg3Ti9 cuboctahedra,  a cornercorner with one Ti(7)Mg5Ti7 cuboctahedra, corners with two equivalent Mg(1)Mg4Ti8 cuboctahedra, corners with two equivalent Mg(3)Mg4Ti8 cuboctahedra, corners with two equivalent Ti(3)Mg2Ti10 cuboctahedra, corners with two equivalent Ti(1)Mg4Ti8 cuboctahedra, corners with two equivalent Ti(2)Mg4Ti8 cuboctahedra, corners with three equivalent Ti(4)Mg3Ti9 cuboctahedra, corners with three equivalent Ti(8)Mg5Ti7 cuboctahedra,  an edgeedge with one Mg(4)Mg6Ti6 cuboctahedra,  an edgeedge with one Ti(3)Mg2Ti10 cuboctahedra,  an edgeedge with one Ti(5)Mg3Ti9 cuboctahedra,  an edgeedge with one Ti(6)Mg4Ti8 cuboctahedra, edges with two equivalent Mg(2)Mg4Ti8 cuboctahedra, edges with two equivalent Ti(1)Mg4Ti8 cuboctahedra, edges with three equivalent Mg(3)Mg4Ti8 cuboctahedra, edges with three equivalent Ti(7)Mg5Ti7 cuboctahedra, edges with four equivalent Ti(2)Mg4Ti8 cuboctahedra,  a faceface with one Mg(1)Mg4Ti8 cuboctahedra,  a faceface with one Mg(3)Mg4Ti8 cuboctahedra,  a faceface with one Ti(4)Mg3Ti9 cuboctahedra, faces with two equivalent Mg(2)Mg4Ti8 cuboctahedra, faces with two equivalent Mg(4)Mg6Ti6 cuboctahedra, faces with two equivalent Ti(5)Mg3Ti9 cuboctahedra, faces with two equivalent Ti(6)Mg4Ti8 cuboctahedra, faces with three equivalent Ti(3)Mg2Ti10 cuboctahedra, faces with three equivalent Ti(1)Mg4Ti8 cuboctahedra, and faces with three equivalent Ti(8)Mg5Ti7 cuboctahedra. The Mg(2)-Mg(3) bond length is 3.14 Å. Both Mg(2)-Mg(4) bond lengths are 2.97 Å. The Mg(2)-Ti(1) bond length is 2.93 Å. The Mg(2)-Ti(3) bond length is 2.97 Å. The Mg(2)-Ti(4) bond length is 3.06 Å. Both Mg(2)-Ti(5) bond lengths are 2.96 Å. There are two shorter (2.94 Å) and one longer (3.02 Å) Mg(2)-Ti(8) bond length. In the third Mg site, Mg(3) is bonded to one Mg(1), one Mg(2), two equivalent Mg(4), one Ti(3), one Ti(4), one Ti(7), one Ti(8), two equivalent Ti(1), and two equivalent Ti(2) atoms to form distorted MgMg4Ti8 cuboctahedra that share  a cornercorner with one Ti(1)Mg4Ti8 cuboctahedra,  a cornercorner with one Ti(6)Mg4Ti8 cuboctahedra, corners with two equivalent Mg(2)Mg4Ti8 cuboctahedra, corners with two equivalent Mg(4)Mg6Ti6 cuboctahedra, corners with two equivalent Ti(4)Mg3Ti9 cuboctahedra, corners with two equivalent Ti(7)Mg5Ti7 cuboctahedra, corners with two equivalent Ti(8)Mg5Ti7 cuboctahedra, corners with three equivalent Mg(1)Mg4Ti8 cuboctahedra, corners with three equivalent Ti(3)Mg2Ti10 cuboctahedra,  an edgeedge with one Ti(4)Mg3Ti9 cuboctahedra,  an edgeedge with one Ti(1)Mg4Ti8 cuboctahedra,  an edgeedge with one Ti(2)Mg4Ti8 cuboctahedra, edges with two equivalent Mg(1)Mg4Ti8 cuboctahedra, edges with two equivalent Ti(3)Mg2Ti10 cuboctahedra, edges with three equivalent Mg(2)Mg4Ti8 cuboctahedra, edges with three equivalent Ti(5)Mg3Ti9 cuboctahedra, edges with five equivalent Ti(6)Mg4Ti8 cuboctahedra,  a faceface with one Mg(1)Mg4Ti8 cuboctahedra,  a faceface with one Mg(2)Mg4Ti8 cuboctahedra,  a faceface with one Ti(3)Mg2Ti10 cuboctahedra,  a faceface with one Ti(4)Mg3Ti9 cuboctahedra, faces with two equivalent Mg(3)Mg4Ti8 cuboctahedra, faces with two equivalent Mg(4)Mg6Ti6 cuboctahedra, faces with two equivalent Ti(5)Mg3Ti9 cuboctahedra, faces with two equivalent Ti(1)Mg4Ti8 cuboctahedra, faces with two equivalent Ti(2)Mg4Ti8 cuboctahedra, faces with three equivalent Ti(7)Mg5Ti7 cuboctahedra, and faces with three equivalent Ti(8)Mg5Ti7 cuboctahedra. Both Mg(3)-Mg(4) bond lengths are 2.96 Å. The Mg(3)-Ti(3) bond length is 2.98 Å. The Mg(3)-Ti(4) bond length is 2.90 Å. The Mg(3)-Ti(7) bond length is 3.00 Å. The Mg(3)-Ti(8) bond length is 2.99 Å. Both Mg(3)-Ti(1) bond lengths are 2.96 Å. Both Mg(3)-Ti(2) bond lengths are 2.98 Å. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), one Ti(1), one Ti(2), one Ti(5), one Ti(6), one Ti(7), and one Ti(8) atom to form MgMg6Ti6 cuboctahedra that share  a cornercorner with one Mg(1)Mg4Ti8 cuboctahedra,  a cornercorner with one Ti(3)Mg2Ti10 cuboctahedra, corners with two equivalent Mg(3)Mg4Ti8 cuboctahedra, corners with two equivalent Ti(5)Mg3Ti9 cuboctahedra, corners with two equivalent Ti(2)Mg4Ti8 cuboctahedra, corners with two equivalent Ti(7)Mg5Ti7 cuboctahedra, corners with two equivalent Ti(8)Mg5Ti7 cuboctahedra, corners with three equivalent Ti(1)Mg4Ti8 cuboctahedra, corners with three equivalent Ti(6)Mg4Ti8 cuboctahedra,  an edgeedge with one Mg(1)Mg4Ti8 cuboctahedra,  an edgeedge with one Mg(2)Mg4Ti8 cuboctahedra,  an edgeedge with one Ti(5)Mg3Ti9 cuboctahedra, edges with two equivalent Ti(1)Mg4Ti8 cuboctahedra, edges with two equivalent Ti(6)Mg4Ti8 cuboctahedra, edges with three equivalent Ti(4)Mg3Ti9 cuboctahedra, edges with three equivalent Ti(2)Mg4Ti8 cuboctahedra, edges with five equivalent Ti(3)Mg2Ti10 cuboctahedra,  a faceface with one Ti(5)Mg3Ti9 cuboctahedra,  a faceface with one Ti(1)Mg4Ti8 cuboctahedra,  a faceface with one Ti(2)Mg4Ti8 cuboctahedra,  a faceface with one Ti(6)Mg4Ti8 cuboctahedra, faces with two equivalent Mg(1)Mg4Ti8 cuboctahedra, faces with two equivalent Mg(2)Mg4Ti8 cuboctahedra, faces with two equivalent Mg(3)Mg4Ti8 cuboctahedra, faces with two equivalent Mg(4)Mg6Ti6 cuboctahedra, faces with two equivalent Ti(4)Mg3Ti9 cuboctahedra, faces with three equivalent Ti(7)Mg5Ti7 cuboctahedra, and faces with three equivalent Ti(8)Mg5Ti7 cuboctahedra. The Mg(4)-Ti(1) bond length is 3.13 Å. The Mg(4)-Ti(2) bond length is 3.14 Å. The Mg(4)-Ti(5) bond length is 3.14 Å. The Mg(4)-Ti(6) bond length is 3.09 Å. The Mg(4)-Ti(7) bond length is 3.06 Å. The Mg(4)-Ti(8) bond length is 3.06 Å. There are eight inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one Mg(2), one Mg(4), two equivalent Mg(3), one Ti(2), one Ti(5), three equivalent Ti(3), and three equivalent Ti(8) atoms to form distorted TiMg4Ti8 cuboctahedra that share  a cornercorner with one Mg(3)Mg4Ti8 cuboctahedra,  a cornercorner with one Ti(6)Mg4Ti8 cuboctahedra, corners with two equivalent Mg(1)Mg4Ti8 cuboctahedra, corners with two equivalent Mg(2)Mg4Ti8 cuboctahedra, corners with two equivalent Ti(5)Mg3Ti9 cuboctahedra, corners with two equivalent Ti(2)Mg4Ti8 cuboctahedra, corners with two equivalent Ti(8)Mg5Ti7 cuboctahedra, corners with three equivalent Mg(4)Mg6Ti6 cuboctahedra, corners with three equivalent Ti(3)Mg2Ti10 cuboctahedra,  an edgeedge with one Mg(3)Mg4Ti8 cuboctahedra,  an edgeedge with one Ti(4)Mg3Ti9 cuboctahedra,  an edgeedge with one Ti(5)Mg3Ti9 cuboctahedra,  an edgeedge with one Ti(6)Mg4Ti8 cuboctahedra,  an edgeedge with one Ti(8)Mg5Ti7 cuboctahedra, edges with two equivalent Mg(1)Mg4Ti8 cuboctahedra, edges with two equivalent Mg(2)Mg4Ti8 cuboctahedra, edges with two equivalent Mg(4)Mg6Ti6 cuboctahedra, edges with three equivalent Ti(7)Mg5Ti7 cuboctahedra, edges with four equivalent Ti(1)Mg4Ti8 cuboctahedra,  a faceface with one Mg(4)Mg6Ti6 cuboctahedra,  a faceface with one Ti(2)Mg4Ti8 cuboctahedra, faces with two equivalent Mg(3)Mg4Ti8 cuboctahedra, faces with two equivalent Ti(4)Mg3Ti9 cuboctahedra, faces with two equivalent Ti(1)Mg4Ti8 cuboctahedra, faces with three equivalent Mg(2)Mg4Ti8 cuboctahedra, faces with three equivalent Ti(3)Mg2Ti10 cuboctahedra, faces with three equivalent Ti(5)Mg3Ti9 cuboctahedra, and faces with three equivalent Ti(8)Mg5Ti7 cuboctahedra. The Ti(1)-Ti(2) bond length is 3.12 Å. The Ti(1)-Ti(5) bond length is 2.84 Å. All Ti(1)-Ti(3) bond lengths are 2.86 Å. There are two shorter (2.93 Å) and one longer (3.09 Å) Ti(1)-Ti(8) bond length. In the second Ti site, Ti(2) is bonded to one Mg(1), one Mg(4), two equivalent Mg(3), one Ti(1), one Ti(5), one Ti(6), two equivalent Ti(4), and three equivalent Ti(7) atoms to form distorted TiMg4Ti8 cuboctahedra that share  a cornercorner with one Ti(4)Mg3Ti9 cuboctahedra,  a cornercorner with one Ti(8)Mg5Ti7 cuboctahedra, corners with two equivalent Mg(1)Mg4Ti8 cuboctahedra, corners with two equivalent Mg(2)Mg4Ti8 cuboctahedra, corners with two equivalent Mg(4)Mg6Ti6 cuboctahedra, corners with two equivalent Ti(1)Mg4Ti8 cuboctahedra, corners with two equivalent Ti(6)Mg4Ti8 cuboctahedra, corners with three equivalent Ti(5)Mg3Ti9 cuboctahedra, corners with three equivalent Ti(7)Mg5Ti7 cuboctahedra,  an edgeedge with one Mg(3)Mg4Ti8 cuboctahedra,  an edgeedge with one Ti(3)Mg2Ti10 cuboctahedra,  an edgeedge with one Ti(4)Mg3Ti9 cuboctahedra,  an edgeedge with one Ti(6)Mg4Ti8 cuboctahedra, edges with two equivalent Mg(1)Mg4Ti8 cuboctahedra, edges with two equivalent Ti(2)Mg4Ti8 cuboctahedra, edges with three equivalent Mg(4)Mg6Ti6 cuboctahedra, edges with three equivalent Ti(8)Mg5Ti7 cuboctahedra, edges with four equivalent Mg(2)Mg4Ti8 cuboctahedra,  a faceface with one Mg(4)Mg6Ti6 cuboctahedra,  a faceface with one Ti(5)Mg3Ti9 cuboctahedra,  a faceface with one Ti(1)Mg4Ti8 cuboctahedra, faces with two equivalent Mg(3)Mg4Ti8 cuboctahedra, faces with two equivalent Ti(3)Mg2Ti10 cuboctahedra, faces with two equivalent Ti(4)Mg3Ti9 cuboctahedra, faces with two equivalent Ti(2)Mg4Ti8 cuboctahedra, faces with three equivalent Mg(1)Mg4Ti8 cuboctahedra, faces with three equivalent Ti(6)Mg4Ti8 cuboctahedra, and faces with three equivalent Ti(7)Mg5Ti7 cuboctahedra. The Ti(2)-Ti(5) bond length is 2.86 Å. The Ti(2)-Ti(6) bond length is 2.81 Å. Both Ti(2)-Ti(4) bond lengths are 2.81 Å. There are two shorter (2.93 Å) and one longer (3.16 Å) Ti(2)-Ti(7) bond length. In the third Ti site, Ti(3) is bonded to one Mg(2), one Mg(3), one Ti(4), one Ti(8), two equivalent Ti(3), three equivalent Ti(1), and three equivalent Ti(5) atoms to form distorted TiMg2Ti10 cuboctahedra that share  a cornercorner with one Mg(1)Mg4Ti8 cuboctahedra,  a cornercorner with one Mg(4)Mg6Ti6 cuboctahedra, corners with two equivalent Mg(2)Mg4Ti8 cuboctahedra, corners with two equivalent Ti(4)Mg3Ti9 cuboctahedra, corners with two equivalent Ti(5)Mg3Ti9 cuboctahedra, corners with two equivalent Ti(6)Mg4Ti8 cuboctahedra, corners with two equivalent Ti(8)Mg5Ti7 cuboctahedra, corners with three equivalent Mg(3)Mg4Ti8 cuboctahedra, corners with three equivalent Ti(1)Mg4Ti8 cuboctahedra,  an edgeedge with one Mg(1)Mg4Ti8 cuboctahedra,  an edgeedge with one Mg(2)Mg4Ti8 cuboctahedra,  an edgeedge with one Ti(2)Mg4Ti8 cuboctahedra,  an edgeedge with one Ti(7)Mg5Ti7 cuboctahedra, edges with two equivalent Mg(3)Mg4Ti8 cuboctahedra, edges with two equivalent Ti(4)Mg3Ti9 cuboctahedra, edges with two equivalent Ti(6)Mg4Ti8 cuboctahedra, edges with three equivalent Ti(8)Mg5Ti7 cuboctahedra, edges with five equivalent Mg(4)Mg6Ti6 cuboctahedra,  a faceface with one Mg(3)Mg4Ti8 cuboctahedra,  a faceface with one Ti(4)Mg3Ti9 cuboctahedra, faces with two equivalent Ti(2)Mg4Ti8 cuboctahedra, faces with three equivalent Mg(2)Mg4Ti8 cuboctahedra, faces with three equivalent Ti(5)Mg3Ti9 cuboctahedra, faces with three equivalent Ti(1)Mg4Ti8 cuboctahedra, faces with three equivalent Ti(8)Mg5Ti7 cuboctahedra, and faces with four equivalent Ti(3)Mg2Ti10 cuboctahedra. The Ti(3)-Ti(4) bond length is 3.08 Å. The Ti(3)-Ti(8) bond length is 2.99 Å. Both Ti(3)-Ti(3) bond lengths are 2.87 Å. There are two shorter (2.90 Å) and one longer (2.94 Å) Ti(3)-Ti(5) bond length. In the fourth Ti site, Ti(4) is bonded to one Mg(1), one Mg(2), one Mg(3), one Ti(3), one Ti(7), two equivalent Ti(2), two equivalent Ti(5), and three equivalent Ti(6) atoms to form distorted TiMg3Ti9 cuboctahedra that share  a cornercorner with one Ti(2)Mg4Ti8 cuboctahedra,  a cornercorner with one Ti(8)Mg5Ti7 cuboctahedra, corners with two equivalent Mg(1)Mg4Ti8 cuboctahedra, corners with two equivalent Mg(3)Mg4Ti8 cuboctahedra, corners with two equivalent Ti(3)Mg2Ti10 cuboctahedra, corners with two equivalent Ti(5)Mg3Ti9 cuboctahedra, corners with two equivalent Ti(6)Mg4Ti8 cuboctahedra, corners with three equivalent Mg(2)Mg4Ti8 cuboctahedra, corners with three equivalent Ti(7)Mg5Ti7 cuboctahedra,  an edgeedge with one Mg(1)Mg4Ti8 cuboctahedra,  an edgeedge with one Mg(3)Mg4Ti8 cuboctahedra,  an edgeedge with one Ti(1)Mg4Ti8 cuboctahedra,  an edgeedge with one Ti(2)Mg4Ti8 cuboctahedra, edges with two equivalent Ti(3)Mg2Ti10 cuboctahedra, edges with two equivalent Ti(4)Mg3Ti9 cuboctahedra, edges with three equivalent Mg(4)Mg6Ti6 cuboctahedra, edges with three equivalent Ti(8)Mg5Ti7 cuboctahedra, edges with four equivalent Ti(7)Mg5Ti7 cuboctahedra,  a faceface with one Mg(2)Mg4Ti8 cuboctahedra,  a faceface with one Mg(3)Mg4Ti8 cuboctahedra,  a faceface with one Ti(3)Mg2Ti10 cuboctahedra,  a faceface with one Ti(7)Mg5Ti7 cuboctahedra, faces with two equivalent Mg(4)Mg6Ti6 cuboctahedra, faces with two equivalent Ti(4)Mg3Ti9 cuboctahedra, faces with two equivalent Ti(5)Mg3Ti9 cuboctahedra, faces with two equivalent Ti(1)Mg4Ti8 cuboctahedra, faces with two equivalent Ti(2)Mg4Ti8 cuboctahedra, faces with three equivalent Mg(1)Mg4Ti8 cuboctahedra, and faces with three equivalent Ti(6)Mg4Ti8 cuboctahedra. The Ti(4)-Ti(7) bond length is 2.93 Å. Both Ti(4)-Ti(5) bond lengths are 2.94 Å. There are two shorter (2.92 Å) and one longer (3.04 Å) Ti(4)-Ti(6) bond length. In the fifth Ti site, Ti(5) is bonded to one Mg(4), two equivalent Mg(2), one Ti(1), one Ti(2), one Ti(6), one Ti(8), two equivalent Ti(4), and three equivalent Ti(3) atoms to form distorted TiMg3Ti9 cuboctahedra that share  a cornercorner with one Mg(2)Mg4Ti8 cuboctahedra,  a cornercorner with one Ti(7)Mg5Ti7 cuboctahedra, corners with two equivalent Mg(4)Mg6Ti6 cuboctahedra, corners with two equivalent Ti(3)Mg2Ti10 cuboctahedra, corners with two equivalent Ti(4)Mg3Ti9 cuboctahedra, corners with two equivalent Ti(1)Mg4Ti8 cuboctahedra, corners with two equivalent Ti(6)Mg4Ti8 cuboctahedra, corners with three equivalent Ti(2)Mg4Ti8 cuboctahedra, corners with three equivalent Ti(8)Mg5Ti7 cuboctahedra,  an edgeedge with one Mg(1)Mg4Ti8 cuboctahedra,  an edgeedge with one Mg(2)Mg4Ti8 cuboctahedra,  an edgeedge with one Mg(4)Mg6Ti6 cuboctahedra,  an edgeedge with one Ti(1)Mg4Ti8 cuboctahedra, edges with two equivalent Ti(5)Mg3Ti9 cuboctahedra, edges with two equivalent Ti(6)Mg4Ti8 cuboctahedra, edges with three equivalent Mg(3)Mg4Ti8 cuboctahedra, edges with three equivalent Ti(7)Mg5Ti7 cuboctahedra, edges with four equivalent Ti(8)Mg5Ti7 cuboctahedra,  a faceface with one Mg(4)Mg6Ti6 cuboctahedra,  a faceface with one Ti(2)Mg4Ti8 cuboctahedra,  a faceface with one Ti(6)Mg4Ti8 cuboctahedra,  a faceface with one Ti(8)Mg5Ti7 cuboctahedra, faces with two equivalent Mg(1)Mg4Ti8 cuboctahedra, faces with two equivalent Mg(2)Mg4Ti8 cuboctahedra, faces with two equivalent Mg(3)Mg4Ti8 cuboctahedra, faces with two equivalent Ti(4)Mg3Ti9 cuboctahedra, faces with two equivalent Ti(5)Mg3Ti9 cuboctahedra, faces with three equivalent Ti(3)Mg2Ti10 cuboctahedra, and faces with three equivalent Ti(1)Mg4Ti8 cuboctahedra. The Ti(5)-Ti(6) bond length is 3.06 Å. The Ti(5)-Ti(8) bond length is 3.12 Å. In the sixth Ti site, Ti(6) is bonded to one Mg(4), three equivalent Mg(1), one Ti(2), one Ti(5), one Ti(7), two equivalent Ti(6), and three equivalent Ti(4) atoms to form distorted TiMg4Ti8 cuboctahedra that share  a cornercorner with one Mg(3)Mg4Ti8 cuboctahedra,  a cornercorner with one Ti(1)Mg4Ti8 cuboctahedra, corners with two equivalent Ti(3)Mg2Ti10 cuboctahedra, corners with two equivalent Ti(4)Mg3Ti9 cuboctahedra, corners with two equivalent Ti(5)Mg3Ti9 cuboctahedra, corners with two equivalent Ti(2)Mg4Ti8 cuboctahedra, corners with two equivalent Ti(7)Mg5Ti7 cuboctahedra, corners with three equivalent Mg(1)Mg4Ti8 cuboctahedra, corners with three equivalent Mg(4)Mg6Ti6 cuboctahedra,  an edgeedge with one Mg(2)Mg4Ti8 cuboctahedra,  an edgeedge with one Ti(1)Mg4Ti8 cuboctahedra,  an edgeedge with one Ti(2)Mg4Ti8 cuboctahedra,  an edgeedge with one Ti(8)Mg5Ti7 cuboctahedra, edges with two equivalent Mg(4)Mg6Ti6 cuboctahedra, edges with two equivalent Ti(3)Mg2Ti10 cuboctahedra, edges with two equivalent Ti(5)Mg3Ti9 cuboctahedra, edges with three equivalent Ti(7)Mg5Ti7 cuboctahedra, edges with five equivalent Mg(3)Mg4Ti8 cuboctahedra,  a faceface with one Mg(4)Mg6Ti6 cuboctahedra,  a faceface with one Ti(5)Mg3Ti9 cuboctahedra, faces with two equivalent Mg(2)Mg4Ti8 cuboctahedra, faces with three equivalent Mg(1)Mg4Ti8 cuboctahedra, faces with three equivalent Ti(4)Mg3Ti9 cuboctahedra, faces with three equivalent Ti(2)Mg4Ti8 cuboctahedra, faces with three equivalent Ti(7)Mg5Ti7 cuboctahedra, and faces with four equivalent Ti(6)Mg4Ti8 cuboctahedra. The Ti(6)-Ti(7) bond length is 3.08 Å. Both Ti(6)-Ti(6) bond lengths are 2.90 Å. In the seventh Ti site, Ti(7) is bonded to one Mg(3), one Mg(4), three equivalent Mg(1), one Ti(4), one Ti(6), two equivalent Ti(7), and three equivalent Ti(2) atoms to form distorted TiMg5Ti7 cuboctahedra that share  a cornercorner with one Mg(2)Mg4Ti8 cuboctahedra,  a cornercorner with one Ti(5)Mg3Ti9 cuboctahedra, corners with two equivalent Mg(1)Mg4Ti8 cuboctahedra, corners with two equivalent Mg(3)Mg4Ti8 cuboctahedra, corners with two equivalent Mg(4)Mg6Ti6 cuboctahedra, corners with two equivalent Ti(6)Mg4Ti8 cuboctahedra, corners with two equivalent Ti(8)Mg5Ti7 cuboctahedra, corners with three equivalent Ti(4)Mg3Ti9 cuboctahedra, corners with three equivalent Ti(2)Mg4Ti8 cuboctahedra,  an edgeedge with one Mg(1)Mg4Ti8 cuboctahedra,  an edgeedge with one Ti(3)Mg2Ti10 cuboctahedra, edges with three equivalent Mg(2)Mg4Ti8 cuboctahedra, edges with three equivalent Ti(5)Mg3Ti9 cuboctahedra, edges with three equivalent Ti(1)Mg4Ti8 cuboctahedra, edges with three equivalent Ti(6)Mg4Ti8 cuboctahedra, edges with four equivalent Ti(4)Mg3Ti9 cuboctahedra,  a faceface with one Ti(4)Mg3Ti9 cuboctahedra, faces with three equivalent Mg(1)Mg4Ti8 cuboctahedra, faces with three equivalent Mg(3)Mg4Ti8 cuboctahedra, faces with three equivalent Mg(4)Mg6Ti6 cuboctahedra, faces with three equivalent Ti(2)Mg4Ti8 cuboctahedra, faces with three equivalent Ti(6)Mg4Ti8 cuboctahedra, and faces with four equivalent Ti(7)Mg5Ti7 cuboctahedra. Both Ti(7)-Ti(7) bond lengths are 2.95 Å. In the eighth Ti site, Ti(8) is bonded to one Mg(3), one Mg(4), three equivalent Mg(2), one Ti(3), one Ti(5), two equivalent Ti(8), and three equivalent Ti(1) atoms to form distorted TiMg5Ti7 cuboctahedra that share  a cornercorner with one Ti(4)Mg3Ti9 cuboctahedra,  a cornercorner with one Ti(2)Mg4Ti8 cuboctahedra, corners with two equivalent Mg(3)Mg4Ti8 cuboctahedra, corners with two equivalent Mg(4)Mg6Ti6 cuboctahedra, corners with two equivalent Ti(3)Mg2Ti10 cuboctahedra, corners with two equivalent Ti(1)Mg4Ti8 cuboctahedra, corners with two equivalent Ti(7)Mg5Ti7 cuboctahedra, corners with three equivalent Mg(2)Mg4Ti8 cuboctahedra, corners with three equivalent Ti(5)Mg3Ti9 cuboctahedra,  an edgeedge with one Ti(1)Mg4Ti8 cuboctahedra,  an edgeedge with one Ti(6)Mg4Ti8 cuboctahedra, edges with three equivalent Mg(1)Mg4Ti8 cuboctahedra, edges with three equivalent Ti(3)Mg2Ti10 cuboctahedra, edges with three equivalent Ti(4)Mg3Ti9 cuboctahedra, edges with three equivalent Ti(2)Mg4Ti8 cuboctahedra, edges with four equivalent Ti(5)Mg3Ti9 cuboctahedra,  a faceface with one Ti(5)Mg3Ti9 cuboctahedra, faces with three equivalent Mg(2)Mg4Ti8 cuboctahedra, faces with three equivalent Mg(3)Mg4Ti8 cuboctahedra, faces with three equivalent Mg(4)Mg6Ti6 cuboctahedra, faces with three equivalent Ti(3)Mg2Ti10 cuboctahedra, faces with three equivalent Ti(1)Mg4Ti8 cuboctahedra, and faces with four equivalent Ti(8)Mg5Ti7 cuboctahedra. Both Ti(8)-Ti(8) bond lengths are 2.91 Å.