RbMg14HfO15 crystallizes in the orthorhombic Pmm2 space group. Rb(1) is bonded in a 5-coordinate geometry to one O(1), two equivalent O(10), and two equivalent O(6) atoms. There are ten inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one O(1), one O(2), two equivalent O(11), and two equivalent O(8) atoms to form MgO6 octahedra that share corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent Mg(2)O5 square pyramids, edges with two equivalent Mg(10)O6 octahedra, edges with two equivalent Mg(7)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, and edges with two equivalent Mg(5)O5 square pyramids. The corner-sharing octahedral tilt angles are 3°. In the second Mg site, Mg(2) is bonded to one O(3), two equivalent O(11), and two equivalent O(9) atoms to form MgO5 square pyramids that share corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent Mg(2)O5 square pyramids, edges with two equivalent Mg(10)O6 octahedra, edges with two equivalent Mg(8)O6 octahedra, and edges with four equivalent Mg(4)O6 octahedra. The corner-sharing octahedral tilt angles are 8°. In the third Mg site, Mg(3) is bonded to one O(5), one O(6), one O(7), and two equivalent O(10) atoms to form MgO5 square pyramids that share  a cornercorner with one Mg(4)O6 octahedra, corners with four equivalent Mg(3)O5 square pyramids,  an edgeedge with one Mg(7)O6 octahedra,  an edgeedge with one Mg(8)O6 octahedra, and edges with two equivalent Mg(10)O6 octahedra. The corner-sharing octahedral tilt angles are 4°. In the fourth Mg site, Mg(4) is bonded to one O(4), one O(5), one O(8), one O(9), and two equivalent O(11) atoms to form MgO6 octahedra that share corners with four equivalent Mg(4)O6 octahedra,  a cornercorner with one Mg(3)O5 square pyramid,  an edgeedge with one Mg(7)O6 octahedra,  an edgeedge with one Mg(8)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Mg(10)O6 octahedra,  an edgeedge with one Mg(5)O5 square pyramid, and edges with two equivalent Mg(2)O5 square pyramids. The corner-sharing octahedral tilt angles range from 1-9°. In the fifth Mg site, Mg(5) is bonded to one O(8), two equivalent O(1), and two equivalent O(4) atoms to form MgO5 square pyramids that share  a cornercorner with one Mg(7)O6 octahedra, corners with two equivalent Mg(5)O5 square pyramids, edges with two equivalent Mg(1)O6 octahedra, and edges with two equivalent Mg(4)O6 octahedra. The corner-sharing octahedra are not tilted. In the sixth Mg site, Mg(6) is bonded in a distorted T-shaped geometry to one O(9) and two equivalent O(4) atoms. In the seventh Mg site, Mg(7) is bonded to one O(6), one O(8), two equivalent O(2), and two equivalent O(5) atoms to form MgO6 octahedra that share corners with two equivalent Mg(7)O6 octahedra, corners with two equivalent Mg(8)O6 octahedra,  a cornercorner with one Mg(5)O5 square pyramid, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Mg(4)O6 octahedra, edges with four equivalent Mg(10)O6 octahedra, and edges with two equivalent Mg(3)O5 square pyramids. The corner-sharing octahedral tilt angles range from 4-12°. In the eighth Mg site, Mg(8) is bonded to one O(7), one O(9), two equivalent O(3), and two equivalent O(5) atoms to form MgO6 octahedra that share corners with two equivalent Mg(7)O6 octahedra, corners with two equivalent Mg(8)O6 octahedra, edges with two equivalent Mg(4)O6 octahedra, edges with four equivalent Mg(10)O6 octahedra, edges with two equivalent Mg(2)O5 square pyramids, and edges with two equivalent Mg(3)O5 square pyramids. The corner-sharing octahedral tilt angles range from 4-12°. In the ninth Mg site, Mg(9) is bonded in a rectangular see-saw-like geometry to one O(1), one O(11), and two equivalent O(4) atoms. In the tenth Mg site, Mg(10) is bonded to one O(10), one O(11), one O(2), one O(3), and two equivalent O(5) atoms to form MgO6 octahedra that share corners with four equivalent Mg(10)O6 octahedra,  an edgeedge with one Mg(1)O6 octahedra, edges with two equivalent Mg(4)O6 octahedra, edges with two equivalent Mg(7)O6 octahedra, edges with two equivalent Mg(8)O6 octahedra,  an edgeedge with one Mg(2)O5 square pyramid, and edges with two equivalent Mg(3)O5 square pyramids. The corner-sharing octahedral tilt angles range from 3-11°. Hf(1) is bonded in a 4-coordinate geometry to two equivalent O(10) and two equivalent O(7) atoms. There are eleven inequivalent O sites. In the first O site, O(1) is bonded to one Rb(1), one Mg(1), two equivalent Mg(5), and two equivalent Mg(9) atoms to form ORbMg5 octahedra that share corners with two equivalent O(1)RbMg5 octahedra,  a cornercorner with one O(2)Mg5 square pyramid, corners with two equivalent O(6)Rb2Mg3 trigonal bipyramids, corners with two equivalent O(10)RbHfMg3 trigonal bipyramids, edges with two equivalent O(11)Mg6 octahedra, edges with two equivalent O(8)Mg6 octahedra, and edges with four equivalent O(4)Mg5 square pyramids. The corner-sharing octahedral tilt angles are 6°. In the second O site, O(2) is bonded to one Mg(1), two equivalent Mg(10), and two equivalent Mg(7) atoms to form OMg5 square pyramids that share  a cornercorner with one O(1)RbMg5 octahedra, corners with two equivalent O(2)Mg5 square pyramids, corners with two equivalent O(3)Mg5 square pyramids, corners with two equivalent O(6)Rb2Mg3 trigonal bipyramids, corners with two equivalent O(10)RbHfMg3 trigonal bipyramids, edges with two equivalent O(11)Mg6 octahedra, edges with two equivalent O(8)Mg6 octahedra, and edges with four equivalent O(5)Mg6 octahedra. The corner-sharing octahedra are not tilted. In the third O site, O(3) is bonded to one Mg(2), two equivalent Mg(10), and two equivalent Mg(8) atoms to form OMg5 square pyramids that share corners with two equivalent O(2)Mg5 square pyramids, corners with two equivalent O(3)Mg5 square pyramids, corners with two equivalent O(7)Hf2Mg3 trigonal bipyramids, corners with two equivalent O(10)RbHfMg3 trigonal bipyramids, edges with two equivalent O(11)Mg6 octahedra, edges with two equivalent O(9)Mg6 octahedra, and edges with four equivalent O(5)Mg6 octahedra. In the fourth O site, O(4) is bonded to one Mg(4), one Mg(5), one Mg(6), and two equivalent Mg(9) atoms to form OMg5 square pyramids that share  a cornercorner with one O(5)Mg6 octahedra, corners with four equivalent O(4)Mg5 square pyramids,  an edgeedge with one O(8)Mg6 octahedra,  an edgeedge with one O(9)Mg6 octahedra, edges with two equivalent O(11)Mg6 octahedra, and edges with two equivalent O(1)RbMg5 octahedra. The corner-sharing octahedral tilt angles are 2°. In the fifth O site, O(5) is bonded to one Mg(3), one Mg(4), one Mg(7), one Mg(8), and two equivalent Mg(10) atoms to form OMg6 octahedra that share corners with four equivalent O(5)Mg6 octahedra,  a cornercorner with one O(4)Mg5 square pyramid,  an edgeedge with one O(8)Mg6 octahedra,  an edgeedge with one O(9)Mg6 octahedra, edges with two equivalent O(11)Mg6 octahedra, edges with two equivalent O(2)Mg5 square pyramids, edges with two equivalent O(3)Mg5 square pyramids,  an edgeedge with one O(7)Hf2Mg3 trigonal bipyramid,  an edgeedge with one O(6)Rb2Mg3 trigonal bipyramid, and edges with two equivalent O(10)RbHfMg3 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 2-6°. In the sixth O site, O(6) is bonded to two equivalent Rb(1), one Mg(7), and two equivalent Mg(3) atoms to form ORb2Mg3 trigonal bipyramids that share  a cornercorner with one O(8)Mg6 octahedra, corners with two equivalent O(1)RbMg5 octahedra, corners with two equivalent O(2)Mg5 square pyramids, corners with two equivalent O(7)Hf2Mg3 trigonal bipyramids, corners with two equivalent O(6)Rb2Mg3 trigonal bipyramids, edges with two equivalent O(5)Mg6 octahedra, and edges with four equivalent O(10)RbHfMg3 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 0-53°. In the seventh O site, O(7) is bonded to one Mg(8), two equivalent Mg(3), and two equivalent Hf(1) atoms to form OHf2Mg3 trigonal bipyramids that share  a cornercorner with one O(9)Mg6 octahedra, corners with two equivalent O(3)Mg5 square pyramids, corners with two equivalent O(7)Hf2Mg3 trigonal bipyramids, corners with two equivalent O(6)Rb2Mg3 trigonal bipyramids, edges with two equivalent O(5)Mg6 octahedra, and edges with four equivalent O(10)RbHfMg3 trigonal bipyramids. The corner-sharing octahedra are not tilted. In the eighth O site, O(8) is bonded to one Mg(5), one Mg(7), two equivalent Mg(1), and two equivalent Mg(4) atoms to form OMg6 octahedra that share corners with two equivalent O(8)Mg6 octahedra, corners with two equivalent O(9)Mg6 octahedra,  a cornercorner with one O(6)Rb2Mg3 trigonal bipyramid, edges with two equivalent O(5)Mg6 octahedra, edges with two equivalent O(1)RbMg5 octahedra, edges with four equivalent O(11)Mg6 octahedra, edges with two equivalent O(2)Mg5 square pyramids, and edges with two equivalent O(4)Mg5 square pyramids. The corner-sharing octahedral tilt angles range from 3-4°. In the ninth O site, O(9) is bonded to one Mg(6), one Mg(8), two equivalent Mg(2), and two equivalent Mg(4) atoms to form OMg6 octahedra that share corners with two equivalent O(8)Mg6 octahedra, corners with two equivalent O(9)Mg6 octahedra,  a cornercorner with one O(7)Hf2Mg3 trigonal bipyramid, edges with two equivalent O(5)Mg6 octahedra, edges with four equivalent O(11)Mg6 octahedra, edges with two equivalent O(3)Mg5 square pyramids, and edges with two equivalent O(4)Mg5 square pyramids. The corner-sharing octahedral tilt angles range from 4-16°. In the tenth O site, O(10) is bonded to one Rb(1), one Mg(10), two equivalent Mg(3), and one Hf(1) atom to form distorted ORbHfMg3 trigonal bipyramids that share  a cornercorner with one O(11)Mg6 octahedra,  a cornercorner with one O(1)RbMg5 octahedra,  a cornercorner with one O(2)Mg5 square pyramid,  a cornercorner with one O(3)Mg5 square pyramid, corners with four equivalent O(10)RbHfMg3 trigonal bipyramids, edges with two equivalent O(5)Mg6 octahedra, edges with two equivalent O(7)Hf2Mg3 trigonal bipyramids, and edges with two equivalent O(6)Rb2Mg3 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 9-60°. In the eleventh O site, O(11) is bonded to one Mg(1), one Mg(10), one Mg(2), one Mg(9), and two equivalent Mg(4) atoms to form OMg6 octahedra that share corners with four equivalent O(11)Mg6 octahedra,  a cornercorner with one O(10)RbHfMg3 trigonal bipyramid,  an edgeedge with one O(1)RbMg5 octahedra, edges with two equivalent O(5)Mg6 octahedra, edges with two equivalent O(8)Mg6 octahedra, edges with two equivalent O(9)Mg6 octahedra,  an edgeedge with one O(2)Mg5 square pyramid,  an edgeedge with one O(3)Mg5 square pyramid, and edges with two equivalent O(4)Mg5 square pyramids. The corner-sharing octahedral tilt angles range from 3-10°.
RbMg14HfO15 crystallizes in the orthorhombic Pmm2 space group. Rb(1) is bonded in a 5-coordinate geometry to one O(1), two equivalent O(10), and two equivalent O(6) atoms. The Rb(1)-O(1) bond length is 2.75 Å. Both Rb(1)-O(10) bond lengths are 2.75 Å. Both Rb(1)-O(6) bond lengths are 2.60 Å. There are ten inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one O(1), one O(2), two equivalent O(11), and two equivalent O(8) atoms to form MgO6 octahedra that share corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent Mg(2)O5 square pyramids, edges with two equivalent Mg(10)O6 octahedra, edges with two equivalent Mg(7)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, and edges with two equivalent Mg(5)O5 square pyramids. The corner-sharing octahedral tilt angles are 3°. The Mg(1)-O(1) bond length is 2.18 Å. The Mg(1)-O(2) bond length is 2.00 Å. Both Mg(1)-O(11) bond lengths are 2.16 Å. Both Mg(1)-O(8) bond lengths are 2.07 Å. In the second Mg site, Mg(2) is bonded to one O(3), two equivalent O(11), and two equivalent O(9) atoms to form MgO5 square pyramids that share corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent Mg(2)O5 square pyramids, edges with two equivalent Mg(10)O6 octahedra, edges with two equivalent Mg(8)O6 octahedra, and edges with four equivalent Mg(4)O6 octahedra. The corner-sharing octahedral tilt angles are 8°. The Mg(2)-O(3) bond length is 2.01 Å. Both Mg(2)-O(11) bond lengths are 2.07 Å. Both Mg(2)-O(9) bond lengths are 2.09 Å. In the third Mg site, Mg(3) is bonded to one O(5), one O(6), one O(7), and two equivalent O(10) atoms to form MgO5 square pyramids that share  a cornercorner with one Mg(4)O6 octahedra, corners with four equivalent Mg(3)O5 square pyramids,  an edgeedge with one Mg(7)O6 octahedra,  an edgeedge with one Mg(8)O6 octahedra, and edges with two equivalent Mg(10)O6 octahedra. The corner-sharing octahedral tilt angles are 4°. The Mg(3)-O(5) bond length is 2.09 Å. The Mg(3)-O(6) bond length is 1.98 Å. The Mg(3)-O(7) bond length is 2.24 Å. Both Mg(3)-O(10) bond lengths are 2.12 Å. In the fourth Mg site, Mg(4) is bonded to one O(4), one O(5), one O(8), one O(9), and two equivalent O(11) atoms to form MgO6 octahedra that share corners with four equivalent Mg(4)O6 octahedra,  a cornercorner with one Mg(3)O5 square pyramid,  an edgeedge with one Mg(7)O6 octahedra,  an edgeedge with one Mg(8)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Mg(10)O6 octahedra,  an edgeedge with one Mg(5)O5 square pyramid, and edges with two equivalent Mg(2)O5 square pyramids. The corner-sharing octahedral tilt angles range from 1-9°. The Mg(4)-O(4) bond length is 2.22 Å. The Mg(4)-O(5) bond length is 2.25 Å. The Mg(4)-O(8) bond length is 2.15 Å. The Mg(4)-O(9) bond length is 2.07 Å. Both Mg(4)-O(11) bond lengths are 2.07 Å. In the fifth Mg site, Mg(5) is bonded to one O(8), two equivalent O(1), and two equivalent O(4) atoms to form MgO5 square pyramids that share  a cornercorner with one Mg(7)O6 octahedra, corners with two equivalent Mg(5)O5 square pyramids, edges with two equivalent Mg(1)O6 octahedra, and edges with two equivalent Mg(4)O6 octahedra. The corner-sharing octahedra are not tilted. The Mg(5)-O(8) bond length is 2.03 Å. Both Mg(5)-O(1) bond lengths are 2.07 Å. Both Mg(5)-O(4) bond lengths are 2.09 Å. In the sixth Mg site, Mg(6) is bonded in a distorted T-shaped geometry to one O(9) and two equivalent O(4) atoms. The Mg(6)-O(9) bond length is 2.41 Å. Both Mg(6)-O(4) bond lengths are 2.17 Å. In the seventh Mg site, Mg(7) is bonded to one O(6), one O(8), two equivalent O(2), and two equivalent O(5) atoms to form MgO6 octahedra that share corners with two equivalent Mg(7)O6 octahedra, corners with two equivalent Mg(8)O6 octahedra,  a cornercorner with one Mg(5)O5 square pyramid, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Mg(4)O6 octahedra, edges with four equivalent Mg(10)O6 octahedra, and edges with two equivalent Mg(3)O5 square pyramids. The corner-sharing octahedral tilt angles range from 4-12°. The Mg(7)-O(6) bond length is 2.06 Å. The Mg(7)-O(8) bond length is 2.27 Å. Both Mg(7)-O(2) bond lengths are 2.08 Å. Both Mg(7)-O(5) bond lengths are 2.14 Å. In the eighth Mg site, Mg(8) is bonded to one O(7), one O(9), two equivalent O(3), and two equivalent O(5) atoms to form MgO6 octahedra that share corners with two equivalent Mg(7)O6 octahedra, corners with two equivalent Mg(8)O6 octahedra, edges with two equivalent Mg(4)O6 octahedra, edges with four equivalent Mg(10)O6 octahedra, edges with two equivalent Mg(2)O5 square pyramids, and edges with two equivalent Mg(3)O5 square pyramids. The corner-sharing octahedral tilt angles range from 4-12°. The Mg(8)-O(7) bond length is 2.16 Å. The Mg(8)-O(9) bond length is 2.53 Å. Both Mg(8)-O(3) bond lengths are 2.08 Å. Both Mg(8)-O(5) bond lengths are 2.08 Å. In the ninth Mg site, Mg(9) is bonded in a rectangular see-saw-like geometry to one O(1), one O(11), and two equivalent O(4) atoms. The Mg(9)-O(1) bond length is 2.04 Å. The Mg(9)-O(11) bond length is 2.10 Å. Both Mg(9)-O(4) bond lengths are 2.07 Å. In the tenth Mg site, Mg(10) is bonded to one O(10), one O(11), one O(2), one O(3), and two equivalent O(5) atoms to form MgO6 octahedra that share corners with four equivalent Mg(10)O6 octahedra,  an edgeedge with one Mg(1)O6 octahedra, edges with two equivalent Mg(4)O6 octahedra, edges with two equivalent Mg(7)O6 octahedra, edges with two equivalent Mg(8)O6 octahedra,  an edgeedge with one Mg(2)O5 square pyramid, and edges with two equivalent Mg(3)O5 square pyramids. The corner-sharing octahedral tilt angles range from 3-11°. The Mg(10)-O(10) bond length is 2.28 Å. The Mg(10)-O(11) bond length is 2.32 Å. The Mg(10)-O(2) bond length is 2.10 Å. The Mg(10)-O(3) bond length is 2.13 Å. Both Mg(10)-O(5) bond lengths are 2.07 Å. Hf(1) is bonded in a 4-coordinate geometry to two equivalent O(10) and two equivalent O(7) atoms. Both Hf(1)-O(10) bond lengths are 2.00 Å. Both Hf(1)-O(7) bond lengths are 2.21 Å. There are eleven inequivalent O sites. In the first O site, O(1) is bonded to one Rb(1), one Mg(1), two equivalent Mg(5), and two equivalent Mg(9) atoms to form ORbMg5 octahedra that share corners with two equivalent O(1)RbMg5 octahedra,  a cornercorner with one O(2)Mg5 square pyramid, corners with two equivalent O(6)Rb2Mg3 trigonal bipyramids, corners with two equivalent O(10)RbHfMg3 trigonal bipyramids, edges with two equivalent O(11)Mg6 octahedra, edges with two equivalent O(8)Mg6 octahedra, and edges with four equivalent O(4)Mg5 square pyramids. The corner-sharing octahedral tilt angles are 6°. In the second O site, O(2) is bonded to one Mg(1), two equivalent Mg(10), and two equivalent Mg(7) atoms to form OMg5 square pyramids that share  a cornercorner with one O(1)RbMg5 octahedra, corners with two equivalent O(2)Mg5 square pyramids, corners with two equivalent O(3)Mg5 square pyramids, corners with two equivalent O(6)Rb2Mg3 trigonal bipyramids, corners with two equivalent O(10)RbHfMg3 trigonal bipyramids, edges with two equivalent O(11)Mg6 octahedra, edges with two equivalent O(8)Mg6 octahedra, and edges with four equivalent O(5)Mg6 octahedra. The corner-sharing octahedra are not tilted. In the third O site, O(3) is bonded to one Mg(2), two equivalent Mg(10), and two equivalent Mg(8) atoms to form OMg5 square pyramids that share corners with two equivalent O(2)Mg5 square pyramids, corners with two equivalent O(3)Mg5 square pyramids, corners with two equivalent O(7)Hf2Mg3 trigonal bipyramids, corners with two equivalent O(10)RbHfMg3 trigonal bipyramids, edges with two equivalent O(11)Mg6 octahedra, edges with two equivalent O(9)Mg6 octahedra, and edges with four equivalent O(5)Mg6 octahedra. In the fourth O site, O(4) is bonded to one Mg(4), one Mg(5), one Mg(6), and two equivalent Mg(9) atoms to form OMg5 square pyramids that share  a cornercorner with one O(5)Mg6 octahedra, corners with four equivalent O(4)Mg5 square pyramids,  an edgeedge with one O(8)Mg6 octahedra,  an edgeedge with one O(9)Mg6 octahedra, edges with two equivalent O(11)Mg6 octahedra, and edges with two equivalent O(1)RbMg5 octahedra. The corner-sharing octahedral tilt angles are 2°. In the fifth O site, O(5) is bonded to one Mg(3), one Mg(4), one Mg(7), one Mg(8), and two equivalent Mg(10) atoms to form OMg6 octahedra that share corners with four equivalent O(5)Mg6 octahedra,  a cornercorner with one O(4)Mg5 square pyramid,  an edgeedge with one O(8)Mg6 octahedra,  an edgeedge with one O(9)Mg6 octahedra, edges with two equivalent O(11)Mg6 octahedra, edges with two equivalent O(2)Mg5 square pyramids, edges with two equivalent O(3)Mg5 square pyramids,  an edgeedge with one O(7)Hf2Mg3 trigonal bipyramid,  an edgeedge with one O(6)Rb2Mg3 trigonal bipyramid, and edges with two equivalent O(10)RbHfMg3 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 2-6°. In the sixth O site, O(6) is bonded to two equivalent Rb(1), one Mg(7), and two equivalent Mg(3) atoms to form ORb2Mg3 trigonal bipyramids that share  a cornercorner with one O(8)Mg6 octahedra, corners with two equivalent O(1)RbMg5 octahedra, corners with two equivalent O(2)Mg5 square pyramids, corners with two equivalent O(7)Hf2Mg3 trigonal bipyramids, corners with two equivalent O(6)Rb2Mg3 trigonal bipyramids, edges with two equivalent O(5)Mg6 octahedra, and edges with four equivalent O(10)RbHfMg3 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 0-53°. In the seventh O site, O(7) is bonded to one Mg(8), two equivalent Mg(3), and two equivalent Hf(1) atoms to form OHf2Mg3 trigonal bipyramids that share  a cornercorner with one O(9)Mg6 octahedra, corners with two equivalent O(3)Mg5 square pyramids, corners with two equivalent O(7)Hf2Mg3 trigonal bipyramids, corners with two equivalent O(6)Rb2Mg3 trigonal bipyramids, edges with two equivalent O(5)Mg6 octahedra, and edges with four equivalent O(10)RbHfMg3 trigonal bipyramids. The corner-sharing octahedra are not tilted. In the eighth O site, O(8) is bonded to one Mg(5), one Mg(7), two equivalent Mg(1), and two equivalent Mg(4) atoms to form OMg6 octahedra that share corners with two equivalent O(8)Mg6 octahedra, corners with two equivalent O(9)Mg6 octahedra,  a cornercorner with one O(6)Rb2Mg3 trigonal bipyramid, edges with two equivalent O(5)Mg6 octahedra, edges with two equivalent O(1)RbMg5 octahedra, edges with four equivalent O(11)Mg6 octahedra, edges with two equivalent O(2)Mg5 square pyramids, and edges with two equivalent O(4)Mg5 square pyramids. The corner-sharing octahedral tilt angles range from 3-4°. In the ninth O site, O(9) is bonded to one Mg(6), one Mg(8), two equivalent Mg(2), and two equivalent Mg(4) atoms to form OMg6 octahedra that share corners with two equivalent O(8)Mg6 octahedra, corners with two equivalent O(9)Mg6 octahedra,  a cornercorner with one O(7)Hf2Mg3 trigonal bipyramid, edges with two equivalent O(5)Mg6 octahedra, edges with four equivalent O(11)Mg6 octahedra, edges with two equivalent O(3)Mg5 square pyramids, and edges with two equivalent O(4)Mg5 square pyramids. The corner-sharing octahedral tilt angles range from 4-16°. In the tenth O site, O(10) is bonded to one Rb(1), one Mg(10), two equivalent Mg(3), and one Hf(1) atom to form distorted ORbHfMg3 trigonal bipyramids that share  a cornercorner with one O(11)Mg6 octahedra,  a cornercorner with one O(1)RbMg5 octahedra,  a cornercorner with one O(2)Mg5 square pyramid,  a cornercorner with one O(3)Mg5 square pyramid, corners with four equivalent O(10)RbHfMg3 trigonal bipyramids, edges with two equivalent O(5)Mg6 octahedra, edges with two equivalent O(7)Hf2Mg3 trigonal bipyramids, and edges with two equivalent O(6)Rb2Mg3 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 9-60°. In the eleventh O site, O(11) is bonded to one Mg(1), one Mg(10), one Mg(2), one Mg(9), and two equivalent Mg(4) atoms to form OMg6 octahedra that share corners with four equivalent O(11)Mg6 octahedra,  a cornercorner with one O(10)RbHfMg3 trigonal bipyramid,  an edgeedge with one O(1)RbMg5 octahedra, edges with two equivalent O(5)Mg6 octahedra, edges with two equivalent O(8)Mg6 octahedra, edges with two equivalent O(9)Mg6 octahedra,  an edgeedge with one O(2)Mg5 square pyramid,  an edgeedge with one O(3)Mg5 square pyramid, and edges with two equivalent O(4)Mg5 square pyramids. The corner-sharing octahedral tilt angles range from 3-10°.