K6Mg(BiO4)2 crystallizes in the triclinic P1 space group. There are six inequivalent K sites. In the first K site, K(1) is bonded in a rectangular see-saw-like geometry to one O(3), one O(4), one O(5), and one O(6) atom. In the second K site, K(2) is bonded in a 5-coordinate geometry to one O(1), one O(4), one O(5), one O(6), and one O(8) atom. In the third K site, K(3) is bonded in a 5-coordinate geometry to one O(2), one O(4), one O(5), one O(6), and one O(8) atom. In the fourth K site, K(4) is bonded in a 5-coordinate geometry to one O(2), one O(3), one O(5), one O(7), and one O(8) atom. In the fifth K site, K(5) is bonded in a 5-coordinate geometry to one O(1), one O(3), one O(4), one O(6), and one O(7) atom. In the sixth K site, K(6) is bonded in a 5-coordinate geometry to one O(1), one O(2), one O(4), one O(6), and one O(7) atom. Mg(1) is bonded to one O(1), one O(2), one O(3), and one O(8) atom to form distorted MgO4 tetrahedra that share  an edgeedge with one Bi(1)O5 trigonal bipyramid. There are two inequivalent Bi sites. In the first Bi site, Bi(1) is bonded to one O(2), one O(4), one O(6), one O(7), and one O(8) atom to form BiO5 trigonal bipyramids that share  an edgeedge with one Mg(1)O4 tetrahedra. In the second Bi site, Bi(2) is bonded in a 4-coordinate geometry to one O(1), one O(2), one O(3), and one O(5) atom. There are eight inequivalent O sites. In the first O site, O(1) is bonded to one K(2), one K(5), one K(6), one Mg(1), and one Bi(2) atom to form distorted OK3MgBi trigonal bipyramids that share corners with three equivalent O(4)K5Bi octahedra and corners with two equivalent O(7)K3Bi tetrahedra. The corner-sharing octahedral tilt angles range from 22-63°. In the second O site, O(2) is bonded in a 6-coordinate geometry to one K(3), one K(4), one K(6), one Mg(1), one Bi(1), and one Bi(2) atom. In the third O site, O(3) is bonded in a 5-coordinate geometry to one K(1), one K(4), one K(5), one Mg(1), and one Bi(2) atom. In the fourth O site, O(4) is bonded to one K(1), one K(2), one K(3), one K(5), one K(6), and one Bi(1) atom to form distorted OK5Bi octahedra that share  a cornercorner with one O(7)K3Bi tetrahedra, corners with three equivalent O(1)K3MgBi trigonal bipyramids, and  an edgeedge with one O(7)K3Bi tetrahedra. In the fifth O site, O(5) is bonded in a 5-coordinate geometry to one K(1), one K(2), one K(3), one K(4), and one Bi(2) atom. In the sixth O site, O(6) is bonded in a 6-coordinate geometry to one K(1), one K(2), one K(3), one K(5), one K(6), and one Bi(1) atom. In the seventh O site, O(7) is bonded to one K(4), one K(5), one K(6), and one Bi(1) atom to form distorted OK3Bi tetrahedra that share  a cornercorner with one O(4)K5Bi octahedra, corners with two equivalent O(1)K3MgBi trigonal bipyramids, and  an edgeedge with one O(4)K5Bi octahedra. The corner-sharing octahedral tilt angles are 76°. In the eighth O site, O(8) is bonded in a 5-coordinate geometry to one K(2), one K(3), one K(4), one Mg(1), and one Bi(1) atom.
K6Mg(BiO4)2 crystallizes in the triclinic P1 space group. There are six inequivalent K sites. In the first K site, K(1) is bonded in a rectangular see-saw-like geometry to one O(3), one O(4), one O(5), and one O(6) atom. The K(1)-O(3) bond length is 2.64 Å. The K(1)-O(4) bond length is 2.60 Å. The K(1)-O(5) bond length is 2.68 Å. The K(1)-O(6) bond length is 2.60 Å. In the second K site, K(2) is bonded in a 5-coordinate geometry to one O(1), one O(4), one O(5), one O(6), and one O(8) atom. The K(2)-O(1) bond length is 2.67 Å. The K(2)-O(4) bond length is 2.83 Å. The K(2)-O(5) bond length is 2.60 Å. The K(2)-O(6) bond length is 2.73 Å. The K(2)-O(8) bond length is 2.95 Å. In the third K site, K(3) is bonded in a 5-coordinate geometry to one O(2), one O(4), one O(5), one O(6), and one O(8) atom. The K(3)-O(2) bond length is 3.06 Å. The K(3)-O(4) bond length is 2.68 Å. The K(3)-O(5) bond length is 2.76 Å. The K(3)-O(6) bond length is 2.75 Å. The K(3)-O(8) bond length is 3.09 Å. In the fourth K site, K(4) is bonded in a 5-coordinate geometry to one O(2), one O(3), one O(5), one O(7), and one O(8) atom. The K(4)-O(2) bond length is 2.77 Å. The K(4)-O(3) bond length is 3.03 Å. The K(4)-O(5) bond length is 2.86 Å. The K(4)-O(7) bond length is 2.79 Å. The K(4)-O(8) bond length is 2.83 Å. In the fifth K site, K(5) is bonded in a 5-coordinate geometry to one O(1), one O(3), one O(4), one O(6), and one O(7) atom. The K(5)-O(1) bond length is 2.71 Å. The K(5)-O(3) bond length is 2.84 Å. The K(5)-O(4) bond length is 2.93 Å. The K(5)-O(6) bond length is 3.16 Å. The K(5)-O(7) bond length is 2.62 Å. In the sixth K site, K(6) is bonded in a 5-coordinate geometry to one O(1), one O(2), one O(4), one O(6), and one O(7) atom. The K(6)-O(1) bond length is 3.10 Å. The K(6)-O(2) bond length is 2.86 Å. The K(6)-O(4) bond length is 2.91 Å. The K(6)-O(6) bond length is 2.95 Å. The K(6)-O(7) bond length is 2.65 Å. Mg(1) is bonded to one O(1), one O(2), one O(3), and one O(8) atom to form distorted MgO4 tetrahedra that share  an edgeedge with one Bi(1)O5 trigonal bipyramid. The Mg(1)-O(1) bond length is 2.03 Å. The Mg(1)-O(2) bond length is 2.04 Å. The Mg(1)-O(3) bond length is 1.98 Å. The Mg(1)-O(8) bond length is 2.05 Å. There are two inequivalent Bi sites. In the first Bi site, Bi(1) is bonded to one O(2), one O(4), one O(6), one O(7), and one O(8) atom to form BiO5 trigonal bipyramids that share  an edgeedge with one Mg(1)O4 tetrahedra. The Bi(1)-O(2) bond length is 2.20 Å. The Bi(1)-O(4) bond length is 2.11 Å. The Bi(1)-O(6) bond length is 2.09 Å. The Bi(1)-O(7) bond length is 2.09 Å. The Bi(1)-O(8) bond length is 2.15 Å. In the second Bi site, Bi(2) is bonded in a 4-coordinate geometry to one O(1), one O(2), one O(3), and one O(5) atom. The Bi(2)-O(1) bond length is 2.19 Å. The Bi(2)-O(2) bond length is 2.63 Å. The Bi(2)-O(3) bond length is 2.26 Å. The Bi(2)-O(5) bond length is 2.10 Å. There are eight inequivalent O sites. In the first O site, O(1) is bonded to one K(2), one K(5), one K(6), one Mg(1), and one Bi(2) atom to form distorted OK3MgBi trigonal bipyramids that share corners with three equivalent O(4)K5Bi octahedra and corners with two equivalent O(7)K3Bi tetrahedra. The corner-sharing octahedral tilt angles range from 22-63°. In the second O site, O(2) is bonded in a 6-coordinate geometry to one K(3), one K(4), one K(6), one Mg(1), one Bi(1), and one Bi(2) atom. In the third O site, O(3) is bonded in a 5-coordinate geometry to one K(1), one K(4), one K(5), one Mg(1), and one Bi(2) atom. In the fourth O site, O(4) is bonded to one K(1), one K(2), one K(3), one K(5), one K(6), and one Bi(1) atom to form distorted OK5Bi octahedra that share  a cornercorner with one O(7)K3Bi tetrahedra, corners with three equivalent O(1)K3MgBi trigonal bipyramids, and  an edgeedge with one O(7)K3Bi tetrahedra. In the fifth O site, O(5) is bonded in a 5-coordinate geometry to one K(1), one K(2), one K(3), one K(4), and one Bi(2) atom. In the sixth O site, O(6) is bonded in a 6-coordinate geometry to one K(1), one K(2), one K(3), one K(5), one K(6), and one Bi(1) atom. In the seventh O site, O(7) is bonded to one K(4), one K(5), one K(6), and one Bi(1) atom to form distorted OK3Bi tetrahedra that share  a cornercorner with one O(4)K5Bi octahedra, corners with two equivalent O(1)K3MgBi trigonal bipyramids, and  an edgeedge with one O(4)K5Bi octahedra. The corner-sharing octahedral tilt angles are 76°. In the eighth O site, O(8) is bonded in a 5-coordinate geometry to one K(2), one K(3), one K(4), one Mg(1), and one Bi(1) atom.