KMg14Hf crystallizes in the orthorhombic Amm2 space group. K(1) is bonded to two equivalent Mg(6); four Mg(3,3,3); four Mg(5,5); and two equivalent Hf(1) atoms to form KHf2Mg10 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with six equivalent K(1)Hf2Mg10 cuboctahedra; corners with eight Mg(4,4)Mg12 cuboctahedra; edges with two equivalent Hf(1)K2Mg10 cuboctahedra; edges with four Mg(3,3,3)K2Hf2Mg8 cuboctahedra; edges with four equivalent Mg(6)KMg11 cuboctahedra; faces with two equivalent Mg(6)KMg11 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Hf(1)K2Mg10 cuboctahedra; faces with four Mg(3,3,3)K2Hf2Mg8 cuboctahedra; and faces with six equivalent Mg(7)HfMg11 cuboctahedra. There are eleven 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); and four Mg(5,5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Hf(1)K2Mg10 cuboctahedra; corners with six equivalent Mg(1)Mg12 cuboctahedra; corners with eight Mg(3,3,3)K2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with four equivalent Mg(6)KMg11 cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra; faces with two equivalent K(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(6)KMg11 cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with four Mg(4,4)Mg12 cuboctahedra; and faces with six equivalent Mg(7)HfMg11 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(1); two equivalent Mg(7); four Mg(4,4); and four Mg(5,5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent K(1)Hf2Mg10 cuboctahedra; corners with six equivalent Mg(2)Mg12 cuboctahedra; corners with eight Mg(3,3,3)K2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Mg(7)HfMg11 cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Hf(1)K2Mg10 cuboctahedra; faces with four Mg(4,4)Mg12 cuboctahedra; and faces with six equivalent Mg(6)KMg11 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 Hf(1) atoms to form distorted MgK2Hf2Mg8 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)K2Hf2Mg8 cuboctahedra; edges with two equivalent K(1)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)K2Hf2Mg8 cuboctahedra; edges with two equivalent Hf(1)K2Mg10 cuboctahedra; edges with four equivalent Mg(7)HfMg11 cuboctahedra; edges with four equivalent Mg(6)KMg11 cuboctahedra; faces with two equivalent K(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(3)K2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(6)KMg11 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; and faces with two equivalent Hf(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)Hf2Mg10 cuboctahedra, corners with four equivalent Mg(3)K2Hf2Mg8 cuboctahedra, corners with four equivalent Hf(1)K2Mg10 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(7)HfMg11 cuboctahedra, edges with four equivalent Mg(6)KMg11 cuboctahedra, faces with two equivalent Mg(7)HfMg11 cuboctahedra, faces with two equivalent Mg(3)K2Hf2Mg8 cuboctahedra, faces with two equivalent Mg(6)KMg11 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(3) is bonded to two equivalent K(1); two equivalent Mg(3); two Mg(5,5); two equivalent Mg(6); two equivalent Mg(7); and two equivalent Hf(1) atoms to form distorted MgK2Hf2Mg8 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 equivalent Mg(3)K2Hf2Mg8 cuboctahedra, edges with two equivalent K(1)Hf2Mg10 cuboctahedra, edges with two equivalent Mg(3)K2Hf2Mg8 cuboctahedra, edges with two equivalent Hf(1)K2Mg10 cuboctahedra, edges with four equivalent Mg(7)HfMg11 cuboctahedra, edges with four equivalent Mg(6)KMg11 cuboctahedra, faces with two equivalent K(1)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(7)HfMg11 cuboctahedra, faces with two equivalent Mg(3)K2Hf2Mg8 cuboctahedra, faces with two equivalent Mg(6)KMg11 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, and faces with two equivalent Hf(1)K2Mg10 cuboctahedra. In the sixth 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)Hf2Mg10 cuboctahedra, corners with four equivalent Mg(3)K2Hf2Mg8 cuboctahedra, corners with four equivalent Hf(1)K2Mg10 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(7)HfMg11 cuboctahedra, edges with four equivalent Mg(6)KMg11 cuboctahedra, faces with two equivalent Mg(7)HfMg11 cuboctahedra, faces with two equivalent Mg(3)K2Hf2Mg8 cuboctahedra, faces with two equivalent Mg(6)KMg11 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 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 Hf(1) atom. In the eighth 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 Hf(1) atom. In the ninth Mg site, Mg(6) is bonded to one K(1); one Mg(1); two Mg(3,3); two Mg(4,4); two equivalent Mg(7); and four Mg(5,5) atoms to form distorted MgKMg11 cuboctahedra that share corners with four equivalent Mg(7)HfMg11 cuboctahedra; corners with six equivalent Mg(6)KMg11 cuboctahedra; edges with two equivalent K(1)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(7)HfMg11 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four Mg(3,3,3)K2Hf2Mg8 cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra;  a faceface with one K(1)Hf2Mg10 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two Mg(3,3)K2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(6)KMg11 cuboctahedra; faces with two Mg(4,4)Mg12 cuboctahedra; faces with three equivalent Mg(2)Mg12 cuboctahedra; and faces with three equivalent Hf(1)K2Mg10 cuboctahedra. In the tenth Mg site, Mg(7) is bonded to one Mg(2); two Mg(3,3); two Mg(4,4); two equivalent Mg(6); four Mg(5,5); and one Hf(1) atom to form MgHfMg11 cuboctahedra that share corners with four equivalent Mg(6)KMg11 cuboctahedra; corners with six equivalent Mg(7)HfMg11 cuboctahedra; edges with two equivalent Mg(6)KMg11 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Hf(1)K2Mg10 cuboctahedra; edges with four Mg(3,3,3)K2Hf2Mg8 cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Hf(1)K2Mg10 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two Mg(3,3)K2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(6)KMg11 cuboctahedra; faces with two Mg(4,4)Mg12 cuboctahedra; faces with three equivalent K(1)Hf2Mg10 cuboctahedra; and faces with three equivalent Mg(1)Mg12 cuboctahedra. In the eleventh 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 Hf(1) atoms to form distorted MgK2Hf2Mg8 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)K2Hf2Mg8 cuboctahedra; edges with two equivalent K(1)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)K2Hf2Mg8 cuboctahedra; edges with two equivalent Hf(1)K2Mg10 cuboctahedra; edges with four equivalent Mg(7)HfMg11 cuboctahedra; edges with four equivalent Mg(6)KMg11 cuboctahedra; faces with two equivalent K(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(3)K2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(6)KMg11 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; and faces with two equivalent Hf(1)K2Mg10 cuboctahedra. Hf(1) is bonded to two equivalent K(1); two equivalent Mg(7); four Mg(3,3,3); and four Mg(5,5) atoms to form distorted HfK2Mg10 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Hf(1)K2Mg10 cuboctahedra; corners with eight Mg(4,4)Mg12 cuboctahedra; edges with two equivalent K(1)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(7)HfMg11 cuboctahedra; edges with four Mg(3,3,3)K2Hf2Mg8 cuboctahedra; faces with two equivalent K(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with four Mg(3,3,3)K2Hf2Mg8 cuboctahedra; and faces with six equivalent Mg(6)KMg11 cuboctahedra.
KMg14Hf crystallizes in the orthorhombic Amm2 space group. K(1) is bonded to two equivalent Mg(6); four Mg(3,3,3); four Mg(5,5); and two equivalent Hf(1) atoms to form KHf2Mg10 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with six equivalent K(1)Hf2Mg10 cuboctahedra; corners with eight Mg(4,4)Mg12 cuboctahedra; edges with two equivalent Hf(1)K2Mg10 cuboctahedra; edges with four Mg(3,3,3)K2Hf2Mg8 cuboctahedra; edges with four equivalent Mg(6)KMg11 cuboctahedra; faces with two equivalent Mg(6)KMg11 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Hf(1)K2Mg10 cuboctahedra; faces with four Mg(3,3,3)K2Hf2Mg8 cuboctahedra; and faces with six equivalent Mg(7)HfMg11 cuboctahedra. Both K(1)-Mg(6) bond lengths are 3.32 Å. There are two shorter (3.26 Å) and two longer (3.28 Å) K(1)-Mg(3,3,3) bond lengths. All K(1)-Mg(5,5) bond lengths are 3.32 Å. Both K(1)-Hf(1) bond lengths are 3.32 Å. There are eleven 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); and four Mg(5,5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Hf(1)K2Mg10 cuboctahedra; corners with six equivalent Mg(1)Mg12 cuboctahedra; corners with eight Mg(3,3,3)K2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with four equivalent Mg(6)KMg11 cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra; faces with two equivalent K(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(6)KMg11 cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with four Mg(4,4)Mg12 cuboctahedra; and faces with six equivalent Mg(7)HfMg11 cuboctahedra. Both Mg(1)-Mg(2) bond lengths are 3.32 Å. Both Mg(1)-Mg(6) bond lengths are 3.17 Å. There are two shorter (3.26 Å) and two longer (3.28 Å) Mg(1)-Mg(4,4) bond lengths. All Mg(1)-Mg(5,5) bond lengths are 3.21 Å. In the second Mg site, Mg(2) is bonded to two equivalent Mg(1); two equivalent Mg(7); four Mg(4,4); and four Mg(5,5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent K(1)Hf2Mg10 cuboctahedra; corners with six equivalent Mg(2)Mg12 cuboctahedra; corners with eight Mg(3,3,3)K2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Mg(7)HfMg11 cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Hf(1)K2Mg10 cuboctahedra; faces with four Mg(4,4)Mg12 cuboctahedra; and faces with six equivalent Mg(6)KMg11 cuboctahedra. Both Mg(2)-Mg(7) bond lengths are 3.22 Å. There are two shorter (3.25 Å) and two longer (3.29 Å) Mg(2)-Mg(4,4) bond lengths. All Mg(2)-Mg(5,5) bond lengths are 3.13 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 Hf(1) atoms to form distorted MgK2Hf2Mg8 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)K2Hf2Mg8 cuboctahedra; edges with two equivalent K(1)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)K2Hf2Mg8 cuboctahedra; edges with two equivalent Hf(1)K2Mg10 cuboctahedra; edges with four equivalent Mg(7)HfMg11 cuboctahedra; edges with four equivalent Mg(6)KMg11 cuboctahedra; faces with two equivalent K(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(3)K2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(6)KMg11 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; and faces with two equivalent Hf(1)K2Mg10 cuboctahedra. There is one shorter (3.29 Å) and one longer (3.35 Å) Mg(3)-Mg(3) bond length. Both Mg(3)-Mg(5) bond lengths are 3.25 Å. Both Mg(3)-Mg(6) bond lengths are 3.30 Å. Both Mg(3)-Mg(7) bond lengths are 3.19 Å. There is one shorter (3.17 Å) and one longer (3.38 Å) Mg(3)-Hf(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)Hf2Mg10 cuboctahedra, corners with four equivalent Mg(3)K2Hf2Mg8 cuboctahedra, corners with four equivalent Hf(1)K2Mg10 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(7)HfMg11 cuboctahedra, edges with four equivalent Mg(6)KMg11 cuboctahedra, faces with two equivalent Mg(7)HfMg11 cuboctahedra, faces with two equivalent Mg(3)K2Hf2Mg8 cuboctahedra, faces with two equivalent Mg(6)KMg11 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 (3.29 Å) and one longer (3.35 Å) Mg(4)-Mg(4) bond length. Both Mg(4)-Mg(5) bond lengths are 3.15 Å. Both Mg(4)-Mg(6) bond lengths are 3.12 Å. Both Mg(4)-Mg(7) bond lengths are 3.26 Å. In the fifth Mg site, Mg(3) is bonded to two equivalent K(1); two equivalent Mg(3); two Mg(5,5); two equivalent Mg(6); two equivalent Mg(7); and two equivalent Hf(1) atoms to form distorted MgK2Hf2Mg8 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 equivalent Mg(3)K2Hf2Mg8 cuboctahedra, edges with two equivalent K(1)Hf2Mg10 cuboctahedra, edges with two equivalent Mg(3)K2Hf2Mg8 cuboctahedra, edges with two equivalent Hf(1)K2Mg10 cuboctahedra, edges with four equivalent Mg(7)HfMg11 cuboctahedra, edges with four equivalent Mg(6)KMg11 cuboctahedra, faces with two equivalent K(1)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(7)HfMg11 cuboctahedra, faces with two equivalent Mg(3)K2Hf2Mg8 cuboctahedra, faces with two equivalent Mg(6)KMg11 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, and faces with two equivalent Hf(1)K2Mg10 cuboctahedra. There is one shorter (3.29 Å) and one longer (3.35 Å) Mg(3)-Mg(3) bond length. Both Mg(3)-Mg(5,5) bond lengths are 3.25 Å. Both Mg(3)-Mg(6) bond lengths are 3.30 Å. Both Mg(3)-Mg(7) bond lengths are 3.19 Å. There is one shorter (3.17 Å) and one longer (3.38 Å) Mg(3)-Hf(1) bond length. In the sixth 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)Hf2Mg10 cuboctahedra, corners with four equivalent Mg(3)K2Hf2Mg8 cuboctahedra, corners with four equivalent Hf(1)K2Mg10 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(7)HfMg11 cuboctahedra, edges with four equivalent Mg(6)KMg11 cuboctahedra, faces with two equivalent Mg(7)HfMg11 cuboctahedra, faces with two equivalent Mg(3)K2Hf2Mg8 cuboctahedra, faces with two equivalent Mg(6)KMg11 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(5,5) bond lengths are 3.15 Å. Both Mg(4)-Mg(6) bond lengths are 3.12 Å. Both Mg(4)-Mg(7) bond lengths are 3.26 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 Hf(1) atom. There is one shorter (3.17 Å) and one longer (3.47 Å) Mg(5)-Mg(5) bond length. There is one shorter (3.16 Å) and one longer (3.38 Å) Mg(5)-Mg(6) bond length. There is one shorter (3.21 Å) and one longer (3.34 Å) Mg(5)-Mg(7) bond length. The Mg(5)-Hf(1) bond length is 3.21 Å. In the eighth 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 Hf(1) atom. There is one shorter (3.17 Å) and one longer (3.47 Å) Mg(5)-Mg(5) bond length. There is one shorter (3.16 Å) and one longer (3.38 Å) Mg(5)-Mg(6) bond length. There is one shorter (3.21 Å) and one longer (3.34 Å) Mg(5)-Mg(7) bond length. The Mg(5)-Hf(1) bond length is 3.21 Å. In the ninth Mg site, Mg(6) is bonded to one K(1); one Mg(1); two Mg(3,3); two Mg(4,4); two equivalent Mg(7); and four Mg(5,5) atoms to form distorted MgKMg11 cuboctahedra that share corners with four equivalent Mg(7)HfMg11 cuboctahedra; corners with six equivalent Mg(6)KMg11 cuboctahedra; edges with two equivalent K(1)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(7)HfMg11 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four Mg(3,3,3)K2Hf2Mg8 cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra;  a faceface with one K(1)Hf2Mg10 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two Mg(3,3)K2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(6)KMg11 cuboctahedra; faces with two Mg(4,4)Mg12 cuboctahedra; faces with three equivalent Mg(2)Mg12 cuboctahedra; and faces with three equivalent Hf(1)K2Mg10 cuboctahedra. Both Mg(6)-Mg(7) bond lengths are 3.32 Å. In the tenth Mg site, Mg(7) is bonded to one Mg(2); two Mg(3,3); two Mg(4,4); two equivalent Mg(6); four Mg(5,5); and one Hf(1) atom to form MgHfMg11 cuboctahedra that share corners with four equivalent Mg(6)KMg11 cuboctahedra; corners with six equivalent Mg(7)HfMg11 cuboctahedra; edges with two equivalent Mg(6)KMg11 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Hf(1)K2Mg10 cuboctahedra; edges with four Mg(3,3,3)K2Hf2Mg8 cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Hf(1)K2Mg10 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two Mg(3,3)K2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(6)KMg11 cuboctahedra; faces with two Mg(4,4)Mg12 cuboctahedra; faces with three equivalent K(1)Hf2Mg10 cuboctahedra; and faces with three equivalent Mg(1)Mg12 cuboctahedra. The Mg(7)-Hf(1) bond length is 3.21 Å. In the eleventh 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 Hf(1) atoms to form distorted MgK2Hf2Mg8 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)K2Hf2Mg8 cuboctahedra; edges with two equivalent K(1)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)K2Hf2Mg8 cuboctahedra; edges with two equivalent Hf(1)K2Mg10 cuboctahedra; edges with four equivalent Mg(7)HfMg11 cuboctahedra; edges with four equivalent Mg(6)KMg11 cuboctahedra; faces with two equivalent K(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(3)K2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(6)KMg11 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; and faces with two equivalent Hf(1)K2Mg10 cuboctahedra. Both Mg(3)-Mg(5) bond lengths are 3.25 Å. Both Mg(3)-Mg(6) bond lengths are 3.30 Å. Both Mg(3)-Mg(7) bond lengths are 3.19 Å. There is one shorter (3.17 Å) and one longer (3.38 Å) Mg(3)-Hf(1) bond length. Hf(1) is bonded to two equivalent K(1); two equivalent Mg(7); four Mg(3,3,3); and four Mg(5,5) atoms to form distorted HfK2Mg10 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Hf(1)K2Mg10 cuboctahedra; corners with eight Mg(4,4)Mg12 cuboctahedra; edges with two equivalent K(1)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(7)HfMg11 cuboctahedra; edges with four Mg(3,3,3)K2Hf2Mg8 cuboctahedra; faces with two equivalent K(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with four Mg(3,3,3)K2Hf2Mg8 cuboctahedra; and faces with six equivalent Mg(6)KMg11 cuboctahedra.