KMg14Ti crystallizes in the orthorhombic Amm2 space group. K(1) is bonded to two equivalent Mg(7); four Mg(3,3); four Mg(5,5,5); and two equivalent Ti(1) atoms to form KMg10Ti2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent K(1)Mg10Ti2 cuboctahedra; corners with eight Mg(4,4,4)Mg12 cuboctahedra; edges with two equivalent Ti(1)K2Mg10 cuboctahedra; edges with four Mg(3,3)K2Mg8Ti2 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; faces with two equivalent Ti(1)K2Mg10 cuboctahedra; faces with four Mg(3,3)K2Mg8Ti2 cuboctahedra; and faces with six equivalent Mg(6)Mg11Ti cuboctahedra. There are thirteen inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(2); two equivalent Mg(6); four Mg(4,4,4); and four Mg(5,5,5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent K(1)Mg10Ti2 cuboctahedra; corners with six equivalent Mg(1)Mg12 cuboctahedra; corners with eight Mg(3,3)K2Mg8Ti2 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with four equivalent Mg(6)Mg11Ti cuboctahedra; edges with four Mg(4,4,4)Mg12 cuboctahedra; faces with two equivalent Mg(6)Mg11Ti cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Ti(1)K2Mg10 cuboctahedra; faces with four Mg(4,4,4)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 Mg(4,4,4); and four Mg(5,5,5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Ti(1)K2Mg10 cuboctahedra; corners with six equivalent Mg(2)Mg12 cuboctahedra; corners with eight Mg(3,3)K2Mg8Ti2 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Mg(7)KMg11 cuboctahedra; edges with four Mg(4,4,4)Mg12 cuboctahedra; faces with two equivalent K(1)Mg10Ti2 cuboctahedra; faces with two equivalent Mg(7)KMg11 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with four Mg(4,4,4)Mg12 cuboctahedra; and faces with six equivalent Mg(6)Mg11Ti cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent K(1), two equivalent Mg(3), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and two equivalent Ti(1) atoms to form distorted MgK2Mg8Ti2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with six Mg(3,3)K2Mg8Ti2 cuboctahedra; edges with two equivalent K(1)Mg10Ti2 cuboctahedra; edges with two equivalent Mg(3)K2Mg8Ti2 cuboctahedra; edges with two equivalent Ti(1)K2Mg10 cuboctahedra; edges with four equivalent Mg(7)KMg11 cuboctahedra; edges with four equivalent Mg(6)Mg11Ti cuboctahedra; faces with two equivalent K(1)Mg10Ti2 cuboctahedra; faces with two equivalent Mg(3)K2Mg8Ti2 cuboctahedra; faces with two equivalent Mg(7)KMg11 cuboctahedra; faces with two equivalent Mg(6)Mg11Ti cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; and faces with two equivalent Ti(1)K2Mg10 cuboctahedra. 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)Mg10Ti2 cuboctahedra; corners with four equivalent Mg(3)K2Mg8Ti2 cuboctahedra; corners with four equivalent Ti(1)K2Mg10 cuboctahedra; corners with six Mg(4,4)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; edges with four equivalent Mg(6)Mg11Ti cuboctahedra; faces with two equivalent Mg(3)K2Mg8Ti2 cuboctahedra; faces with two equivalent Mg(7)KMg11 cuboctahedra; faces with two equivalent Mg(6)Mg11Ti 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(4) is bonded to two equivalent Mg(1); two equivalent Mg(2); two equivalent Mg(4); two Mg(5,5); two equivalent Mg(6); and two equivalent Mg(7) atoms to form MgMg12 cuboctahedra that share corners with four equivalent K(1)Mg10Ti2 cuboctahedra; corners with four equivalent Mg(3)K2Mg8Ti2 cuboctahedra; corners with four equivalent Ti(1)K2Mg10 cuboctahedra; corners with six Mg(4,4)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; edges with four equivalent Mg(6)Mg11Ti cuboctahedra; faces with two equivalent Mg(3)K2Mg8Ti2 cuboctahedra; faces with two equivalent Mg(7)KMg11 cuboctahedra; faces with two equivalent Mg(6)Mg11Ti 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 sixth 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 Ti(1) atom. In the seventh 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 Ti(1) atom. In the eighth Mg site, Mg(6) is bonded to one Mg(1); two equivalent Mg(3); two Mg(4,4); two equivalent Mg(7); four Mg(5,5,5,5); and one Ti(1) atom to form distorted MgMg11Ti cuboctahedra that share corners with four equivalent Mg(7)KMg11 cuboctahedra; corners with six equivalent Mg(6)Mg11Ti cuboctahedra; edges with two equivalent Mg(7)KMg11 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Ti(1)K2Mg10 cuboctahedra; edges with four Mg(3,3)K2Mg8Ti2 cuboctahedra; edges with four Mg(4,4,4)Mg12 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Ti(1)K2Mg10 cuboctahedra; faces with two equivalent Mg(3)K2Mg8Ti2 cuboctahedra; faces with two equivalent Mg(7)KMg11 cuboctahedra; faces with two equivalent Mg(6)Mg11Ti cuboctahedra; faces with two Mg(4,4)Mg12 cuboctahedra; faces with three equivalent K(1)Mg10Ti2 cuboctahedra; and faces with three equivalent Mg(2)Mg12 cuboctahedra. In the ninth Mg site, Mg(7) is bonded to one K(1); one Mg(2); two equivalent Mg(3); two Mg(4,4); two equivalent Mg(6); and four Mg(5,5,5,5) atoms to form distorted MgKMg11 cuboctahedra that share corners with four equivalent Mg(6)Mg11Ti cuboctahedra; corners with six equivalent Mg(7)KMg11 cuboctahedra; edges with two equivalent K(1)Mg10Ti2 cuboctahedra; edges with two equivalent Mg(6)Mg11Ti cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with four Mg(3,3)K2Mg8Ti2 cuboctahedra; edges with four Mg(4,4,4)Mg12 cuboctahedra;  a faceface with one K(1)Mg10Ti2 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra; faces with two equivalent Mg(3)K2Mg8Ti2 cuboctahedra; faces with two equivalent Mg(7)KMg11 cuboctahedra; faces with two equivalent Mg(6)Mg11Ti cuboctahedra; faces with two Mg(4,4)Mg12 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; and faces with three equivalent Ti(1)K2Mg10 cuboctahedra. In the tenth Mg site, Mg(3) is bonded to two equivalent K(1), two equivalent Mg(3), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and two equivalent Ti(1) atoms to form distorted MgK2Mg8Ti2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with six Mg(3,3)K2Mg8Ti2 cuboctahedra; edges with two equivalent K(1)Mg10Ti2 cuboctahedra; edges with two equivalent Mg(3)K2Mg8Ti2 cuboctahedra; edges with two equivalent Ti(1)K2Mg10 cuboctahedra; edges with four equivalent Mg(7)KMg11 cuboctahedra; edges with four equivalent Mg(6)Mg11Ti cuboctahedra; faces with two equivalent K(1)Mg10Ti2 cuboctahedra; faces with two equivalent Mg(3)K2Mg8Ti2 cuboctahedra; faces with two equivalent Mg(7)KMg11 cuboctahedra; faces with two equivalent Mg(6)Mg11Ti cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; and faces with two equivalent Ti(1)K2Mg10 cuboctahedra. In the eleventh 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)Mg10Ti2 cuboctahedra; corners with four equivalent Mg(3)K2Mg8Ti2 cuboctahedra; corners with four equivalent Ti(1)K2Mg10 cuboctahedra; corners with six Mg(4,4)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; edges with four equivalent Mg(6)Mg11Ti cuboctahedra; faces with two equivalent Mg(3)K2Mg8Ti2 cuboctahedra; faces with two equivalent Mg(7)KMg11 cuboctahedra; faces with two equivalent Mg(6)Mg11Ti 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 twelfth 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 Ti(1) atom. In the thirteenth 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 Ti(1) atom. Ti(1) is bonded to two equivalent K(1); two equivalent Mg(6); four Mg(3,3); and four Mg(5,5,5) atoms to form TiK2Mg10 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with six equivalent Ti(1)K2Mg10 cuboctahedra; corners with eight Mg(4,4,4)Mg12 cuboctahedra; edges with two equivalent K(1)Mg10Ti2 cuboctahedra; edges with four Mg(3,3)K2Mg8Ti2 cuboctahedra; edges with four equivalent Mg(6)Mg11Ti cuboctahedra; faces with two equivalent K(1)Mg10Ti2 cuboctahedra; faces with two equivalent Mg(6)Mg11Ti cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with four Mg(3,3)K2Mg8Ti2 cuboctahedra; and faces with six equivalent Mg(7)KMg11 cuboctahedra.
KMg14Ti crystallizes in the orthorhombic Amm2 space group. K(1) is bonded to two equivalent Mg(7); four Mg(3,3); four Mg(5,5,5); and two equivalent Ti(1) atoms to form KMg10Ti2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent K(1)Mg10Ti2 cuboctahedra; corners with eight Mg(4,4,4)Mg12 cuboctahedra; edges with two equivalent Ti(1)K2Mg10 cuboctahedra; edges with four Mg(3,3)K2Mg8Ti2 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; faces with two equivalent Ti(1)K2Mg10 cuboctahedra; faces with four Mg(3,3)K2Mg8Ti2 cuboctahedra; and faces with six equivalent Mg(6)Mg11Ti cuboctahedra. Both K(1)-Mg(7) bond lengths are 3.32 Å. All K(1)-Mg(3,3) bond lengths are 3.26 Å. All K(1)-Mg(5,5,5) bond lengths are 3.31 Å. Both K(1)-Ti(1) bond lengths are 3.31 Å. There are thirteen inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(2); two equivalent Mg(6); four Mg(4,4,4); and four Mg(5,5,5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent K(1)Mg10Ti2 cuboctahedra; corners with six equivalent Mg(1)Mg12 cuboctahedra; corners with eight Mg(3,3)K2Mg8Ti2 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with four equivalent Mg(6)Mg11Ti cuboctahedra; edges with four Mg(4,4,4)Mg12 cuboctahedra; faces with two equivalent Mg(6)Mg11Ti cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Ti(1)K2Mg10 cuboctahedra; faces with four Mg(4,4,4)Mg12 cuboctahedra; and faces with six equivalent Mg(7)KMg11 cuboctahedra. Both Mg(1)-Mg(2) bond lengths are 3.31 Å. Both Mg(1)-Mg(6) bond lengths are 3.24 Å. There are two shorter (3.24 Å) and two longer (3.28 Å) Mg(1)-Mg(4,4,4) bond lengths. All Mg(1)-Mg(5,5,5) bond lengths are 3.13 Å. In the second Mg site, Mg(2) is bonded to two equivalent Mg(1); two equivalent Mg(7); four Mg(4,4,4); and four Mg(5,5,5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Ti(1)K2Mg10 cuboctahedra; corners with six equivalent Mg(2)Mg12 cuboctahedra; corners with eight Mg(3,3)K2Mg8Ti2 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Mg(7)KMg11 cuboctahedra; edges with four Mg(4,4,4)Mg12 cuboctahedra; faces with two equivalent K(1)Mg10Ti2 cuboctahedra; faces with two equivalent Mg(7)KMg11 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with four Mg(4,4,4)Mg12 cuboctahedra; and faces with six equivalent Mg(6)Mg11Ti cuboctahedra. Both Mg(2)-Mg(7) bond lengths are 3.16 Å. There are two shorter (3.24 Å) and two longer (3.27 Å) Mg(2)-Mg(4,4,4) bond lengths. All Mg(2)-Mg(5,5,5) bond lengths are 3.21 Å. In the third Mg site, Mg(3) is bonded to two equivalent K(1), two equivalent Mg(3), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and two equivalent Ti(1) atoms to form distorted MgK2Mg8Ti2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with six Mg(3,3)K2Mg8Ti2 cuboctahedra; edges with two equivalent K(1)Mg10Ti2 cuboctahedra; edges with two equivalent Mg(3)K2Mg8Ti2 cuboctahedra; edges with two equivalent Ti(1)K2Mg10 cuboctahedra; edges with four equivalent Mg(7)KMg11 cuboctahedra; edges with four equivalent Mg(6)Mg11Ti cuboctahedra; faces with two equivalent K(1)Mg10Ti2 cuboctahedra; faces with two equivalent Mg(3)K2Mg8Ti2 cuboctahedra; faces with two equivalent Mg(7)KMg11 cuboctahedra; faces with two equivalent Mg(6)Mg11Ti cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; and faces with two equivalent Ti(1)K2Mg10 cuboctahedra. Both Mg(3)-Mg(3) bond lengths are 3.31 Å. Both Mg(3)-Mg(5) bond lengths are 3.23 Å. Both Mg(3)-Mg(6) bond lengths are 3.17 Å. Both Mg(3)-Mg(7) bond lengths are 3.30 Å. There is one shorter (3.13 Å) and one longer (3.39 Å) Mg(3)-Ti(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)Mg10Ti2 cuboctahedra; corners with four equivalent Mg(3)K2Mg8Ti2 cuboctahedra; corners with four equivalent Ti(1)K2Mg10 cuboctahedra; corners with six Mg(4,4)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; edges with four equivalent Mg(6)Mg11Ti cuboctahedra; faces with two equivalent Mg(3)K2Mg8Ti2 cuboctahedra; faces with two equivalent Mg(7)KMg11 cuboctahedra; faces with two equivalent Mg(6)Mg11Ti 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 (3.27 Å) and one longer (3.35 Å) Mg(4)-Mg(4) bond length. Both Mg(4)-Mg(5) bond lengths are 3.16 Å. Both Mg(4)-Mg(6) bond lengths are 3.28 Å. Both Mg(4)-Mg(7) bond lengths are 3.11 Å. In the fifth Mg site, Mg(4) is bonded to two equivalent Mg(1); two equivalent Mg(2); two equivalent Mg(4); two Mg(5,5); two equivalent Mg(6); and two equivalent Mg(7) atoms to form MgMg12 cuboctahedra that share corners with four equivalent K(1)Mg10Ti2 cuboctahedra; corners with four equivalent Mg(3)K2Mg8Ti2 cuboctahedra; corners with four equivalent Ti(1)K2Mg10 cuboctahedra; corners with six Mg(4,4)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; edges with four equivalent Mg(6)Mg11Ti cuboctahedra; faces with two equivalent Mg(3)K2Mg8Ti2 cuboctahedra; faces with two equivalent Mg(7)KMg11 cuboctahedra; faces with two equivalent Mg(6)Mg11Ti 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 (3.27 Å) and one longer (3.35 Å) Mg(4)-Mg(4) bond length. Both Mg(4)-Mg(5,5) bond lengths are 3.16 Å. Both Mg(4)-Mg(6) bond lengths are 3.28 Å. Both Mg(4)-Mg(7) bond lengths are 3.11 Å. In the sixth 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 Ti(1) atom. There is one shorter (3.14 Å) and one longer (3.47 Å) Mg(5)-Mg(5) bond length. There is one shorter (3.19 Å) and one longer (3.34 Å) Mg(5)-Mg(6) bond length. There is one shorter (3.15 Å) and one longer (3.37 Å) Mg(5)-Mg(7) bond length. The Mg(5)-Ti(1) bond length is 3.19 Å. In the seventh 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 Ti(1) atom. The Mg(5)-Mg(3) bond length is 3.23 Å. There is one shorter (3.14 Å) and one longer (3.47 Å) Mg(5)-Mg(5) bond length. There is one shorter (3.19 Å) and one longer (3.34 Å) Mg(5)-Mg(6) bond length. There is one shorter (3.15 Å) and one longer (3.37 Å) Mg(5)-Mg(7) bond length. The Mg(5)-Ti(1) bond length is 3.19 Å. In the eighth Mg site, Mg(6) is bonded to one Mg(1); two equivalent Mg(3); two Mg(4,4); two equivalent Mg(7); four Mg(5,5,5,5); and one Ti(1) atom to form distorted MgMg11Ti cuboctahedra that share corners with four equivalent Mg(7)KMg11 cuboctahedra; corners with six equivalent Mg(6)Mg11Ti cuboctahedra; edges with two equivalent Mg(7)KMg11 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Ti(1)K2Mg10 cuboctahedra; edges with four Mg(3,3)K2Mg8Ti2 cuboctahedra; edges with four Mg(4,4,4)Mg12 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Ti(1)K2Mg10 cuboctahedra; faces with two equivalent Mg(3)K2Mg8Ti2 cuboctahedra; faces with two equivalent Mg(7)KMg11 cuboctahedra; faces with two equivalent Mg(6)Mg11Ti cuboctahedra; faces with two Mg(4,4)Mg12 cuboctahedra; faces with three equivalent K(1)Mg10Ti2 cuboctahedra; and faces with three equivalent Mg(2)Mg12 cuboctahedra. The Mg(6)-Mg(4) bond length is 3.28 Å. Both Mg(6)-Mg(7) bond lengths are 3.32 Å. There is one shorter (3.19 Å) and one longer (3.34 Å) Mg(6)-Mg(5,5) bond length. The Mg(6)-Ti(1) bond length is 3.18 Å. In the ninth Mg site, Mg(7) is bonded to one K(1); one Mg(2); two equivalent Mg(3); two Mg(4,4); two equivalent Mg(6); and four Mg(5,5,5,5) atoms to form distorted MgKMg11 cuboctahedra that share corners with four equivalent Mg(6)Mg11Ti cuboctahedra; corners with six equivalent Mg(7)KMg11 cuboctahedra; edges with two equivalent K(1)Mg10Ti2 cuboctahedra; edges with two equivalent Mg(6)Mg11Ti cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with four Mg(3,3)K2Mg8Ti2 cuboctahedra; edges with four Mg(4,4,4)Mg12 cuboctahedra;  a faceface with one K(1)Mg10Ti2 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra; faces with two equivalent Mg(3)K2Mg8Ti2 cuboctahedra; faces with two equivalent Mg(7)KMg11 cuboctahedra; faces with two equivalent Mg(6)Mg11Ti cuboctahedra; faces with two Mg(4,4)Mg12 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; and faces with three equivalent Ti(1)K2Mg10 cuboctahedra. The Mg(7)-Mg(4) bond length is 3.11 Å. There is one shorter (3.15 Å) and one longer (3.37 Å) Mg(7)-Mg(5,5) bond length. In the tenth Mg site, Mg(3) is bonded to two equivalent K(1), two equivalent Mg(3), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and two equivalent Ti(1) atoms to form distorted MgK2Mg8Ti2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with six Mg(3,3)K2Mg8Ti2 cuboctahedra; edges with two equivalent K(1)Mg10Ti2 cuboctahedra; edges with two equivalent Mg(3)K2Mg8Ti2 cuboctahedra; edges with two equivalent Ti(1)K2Mg10 cuboctahedra; edges with four equivalent Mg(7)KMg11 cuboctahedra; edges with four equivalent Mg(6)Mg11Ti cuboctahedra; faces with two equivalent K(1)Mg10Ti2 cuboctahedra; faces with two equivalent Mg(3)K2Mg8Ti2 cuboctahedra; faces with two equivalent Mg(7)KMg11 cuboctahedra; faces with two equivalent Mg(6)Mg11Ti cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; and faces with two equivalent Ti(1)K2Mg10 cuboctahedra. Both Mg(3)-Mg(3) bond lengths are 3.31 Å. Both Mg(3)-Mg(5) bond lengths are 3.23 Å. Both Mg(3)-Mg(6) bond lengths are 3.17 Å. Both Mg(3)-Mg(7) bond lengths are 3.30 Å. There is one shorter (3.13 Å) and one longer (3.39 Å) Mg(3)-Ti(1) bond length. In the eleventh 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)Mg10Ti2 cuboctahedra; corners with four equivalent Mg(3)K2Mg8Ti2 cuboctahedra; corners with four equivalent Ti(1)K2Mg10 cuboctahedra; corners with six Mg(4,4)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; edges with four equivalent Mg(6)Mg11Ti cuboctahedra; faces with two equivalent Mg(3)K2Mg8Ti2 cuboctahedra; faces with two equivalent Mg(7)KMg11 cuboctahedra; faces with two equivalent Mg(6)Mg11Ti 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. Both Mg(4)-Mg(5) bond lengths are 3.16 Å. In the twelfth 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 Ti(1) atom. The Mg(5)-Ti(1) bond length is 3.19 Å. In the thirteenth 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 Ti(1) atom. The Mg(5)-K(1) bond length is 3.31 Å. The Mg(5)-Mg(1) bond length is 3.13 Å. The Mg(5)-Mg(2) bond length is 3.21 Å. The Mg(5)-Mg(3) bond length is 3.23 Å. The Mg(5)-Mg(4) bond length is 3.16 Å. The Mg(5)-Ti(1) bond length is 3.19 Å. Ti(1) is bonded to two equivalent K(1); two equivalent Mg(6); four Mg(3,3); and four Mg(5,5,5) atoms to form TiK2Mg10 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with six equivalent Ti(1)K2Mg10 cuboctahedra; corners with eight Mg(4,4,4)Mg12 cuboctahedra; edges with two equivalent K(1)Mg10Ti2 cuboctahedra; edges with four Mg(3,3)K2Mg8Ti2 cuboctahedra; edges with four equivalent Mg(6)Mg11Ti cuboctahedra; faces with two equivalent K(1)Mg10Ti2 cuboctahedra; faces with two equivalent Mg(6)Mg11Ti cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with four Mg(3,3)K2Mg8Ti2 cuboctahedra; and faces with six equivalent Mg(7)KMg11 cuboctahedra.