K4MgMo2(SO3)2 crystallizes in the triclinic P1 space group. There are four inequivalent K sites. In the first K site, K(1) is bonded in a 4-coordinate geometry to one S(1), one S(2), one O(1), and one O(3) atom. In the second K site, K(2) is bonded to one S(2), one O(2), one O(3), one O(4), one O(5), and one O(6) atom to form distorted KSO5 pentagonal pyramids that share  a cornercorner with one Mg(1)SO3 tetrahedra, corners with two equivalent Mo(1)SO3 tetrahedra, corners with two equivalent Mo(2)SO3 tetrahedra,  an edgeedge with one Mg(1)SO3 tetrahedra, and  an edgeedge with one Mo(2)SO3 tetrahedra. In the third K site, K(3) is bonded in a 6-coordinate geometry to two equivalent S(2), one O(1), one O(2), one O(4), and one O(5) atom. In the fourth K site, K(4) is bonded in a 6-coordinate geometry to two equivalent S(1), one O(1), one O(2), one O(3), and one O(6) atom. Mg(1) is bonded to one S(1), one O(4), one O(5), and one O(6) atom to form distorted MgSO3 tetrahedra that share  a cornercorner with one K(2)SO5 pentagonal pyramid, corners with two equivalent Mo(2)SO3 tetrahedra,  an edgeedge with one K(2)SO5 pentagonal pyramid, and  an edgeedge with one Mo(1)SO3 tetrahedra. There are two inequivalent Mo sites. In the first Mo site, Mo(1) is bonded to one S(1), one O(1), one O(3), and one O(4) atom to form distorted MoSO3 tetrahedra that share corners with two equivalent K(2)SO5 pentagonal pyramids and  an edgeedge with one Mg(1)SO3 tetrahedra. In the second Mo site, Mo(2) is bonded to one S(2), one O(2), one O(5), and one O(6) atom to form distorted MoSO3 tetrahedra that share corners with two equivalent K(2)SO5 pentagonal pyramids, corners with two equivalent Mg(1)SO3 tetrahedra, and  an edgeedge with one K(2)SO5 pentagonal pyramid. There are two inequivalent S sites. In the first S site, S(1) is bonded to one K(1), two equivalent K(4), one Mg(1), and one Mo(1) atom to form distorted corner-sharing SK3MgMo square pyramids. In the second S site, S(2) is bonded in a 5-coordinate geometry to one K(1), one K(2), two equivalent K(3), and one Mo(2) atom. There are six inequivalent O sites. In the first O site, O(1) is bonded in a distorted rectangular see-saw-like geometry to one K(1), one K(3), one K(4), and one Mo(1) atom. In the second O site, O(2) is bonded in a 4-coordinate geometry to one K(2), one K(3), one K(4), and one Mo(2) atom. In the third O site, O(3) is bonded in a 4-coordinate geometry to one K(1), one K(2), one K(4), and one Mo(1) atom. In the fourth O site, O(4) is bonded in a distorted rectangular see-saw-like geometry to one K(2), one K(3), one Mg(1), and one Mo(1) atom. In the fifth O site, O(5) is bonded in a 4-coordinate geometry to one K(2), one K(3), one Mg(1), and one Mo(2) atom. In the sixth O site, O(6) is bonded in a 4-coordinate geometry to one K(2), one K(4), one Mg(1), and one Mo(2) atom.
K4MgMo2(SO3)2 crystallizes in the triclinic P1 space group. There are four inequivalent K sites. In the first K site, K(1) is bonded in a 4-coordinate geometry to one S(1), one S(2), one O(1), and one O(3) atom. The K(1)-S(1) bond length is 3.18 Å. The K(1)-S(2) bond length is 3.16 Å. The K(1)-O(1) bond length is 2.62 Å. The K(1)-O(3) bond length is 2.64 Å. In the second K site, K(2) is bonded to one S(2), one O(2), one O(3), one O(4), one O(5), and one O(6) atom to form distorted KSO5 pentagonal pyramids that share  a cornercorner with one Mg(1)SO3 tetrahedra, corners with two equivalent Mo(1)SO3 tetrahedra, corners with two equivalent Mo(2)SO3 tetrahedra,  an edgeedge with one Mg(1)SO3 tetrahedra, and  an edgeedge with one Mo(2)SO3 tetrahedra. The K(2)-S(2) bond length is 3.17 Å. The K(2)-O(2) bond length is 3.03 Å. The K(2)-O(3) bond length is 2.75 Å. The K(2)-O(4) bond length is 2.78 Å. The K(2)-O(5) bond length is 2.96 Å. The K(2)-O(6) bond length is 2.92 Å. In the third K site, K(3) is bonded in a 6-coordinate geometry to two equivalent S(2), one O(1), one O(2), one O(4), and one O(5) atom. There is one shorter (3.18 Å) and one longer (3.27 Å) K(3)-S(2) bond length. The K(3)-O(1) bond length is 2.78 Å. The K(3)-O(2) bond length is 2.70 Å. The K(3)-O(4) bond length is 2.79 Å. The K(3)-O(5) bond length is 3.07 Å. In the fourth K site, K(4) is bonded in a 6-coordinate geometry to two equivalent S(1), one O(1), one O(2), one O(3), and one O(6) atom. There is one shorter (3.12 Å) and one longer (3.20 Å) K(4)-S(1) bond length. The K(4)-O(1) bond length is 2.87 Å. The K(4)-O(2) bond length is 2.92 Å. The K(4)-O(3) bond length is 2.91 Å. The K(4)-O(6) bond length is 3.01 Å. Mg(1) is bonded to one S(1), one O(4), one O(5), and one O(6) atom to form distorted MgSO3 tetrahedra that share  a cornercorner with one K(2)SO5 pentagonal pyramid, corners with two equivalent Mo(2)SO3 tetrahedra,  an edgeedge with one K(2)SO5 pentagonal pyramid, and  an edgeedge with one Mo(1)SO3 tetrahedra. The Mg(1)-S(1) bond length is 2.55 Å. The Mg(1)-O(4) bond length is 2.00 Å. The Mg(1)-O(5) bond length is 2.02 Å. The Mg(1)-O(6) bond length is 1.97 Å. There are two inequivalent Mo sites. In the first Mo site, Mo(1) is bonded to one S(1), one O(1), one O(3), and one O(4) atom to form distorted MoSO3 tetrahedra that share corners with two equivalent K(2)SO5 pentagonal pyramids and  an edgeedge with one Mg(1)SO3 tetrahedra. The Mo(1)-S(1) bond length is 2.36 Å. The Mo(1)-O(1) bond length is 1.82 Å. The Mo(1)-O(3) bond length is 1.81 Å. The Mo(1)-O(4) bond length is 1.92 Å. In the second Mo site, Mo(2) is bonded to one S(2), one O(2), one O(5), and one O(6) atom to form distorted MoSO3 tetrahedra that share corners with two equivalent K(2)SO5 pentagonal pyramids, corners with two equivalent Mg(1)SO3 tetrahedra, and  an edgeedge with one K(2)SO5 pentagonal pyramid. The Mo(2)-S(2) bond length is 2.33 Å. The Mo(2)-O(2) bond length is 1.80 Å. The Mo(2)-O(5) bond length is 1.87 Å. The Mo(2)-O(6) bond length is 1.91 Å. There are two inequivalent S sites. In the first S site, S(1) is bonded to one K(1), two equivalent K(4), one Mg(1), and one Mo(1) atom to form distorted corner-sharing SK3MgMo square pyramids. In the second S site, S(2) is bonded in a 5-coordinate geometry to one K(1), one K(2), two equivalent K(3), and one Mo(2) atom. There are six inequivalent O sites. In the first O site, O(1) is bonded in a distorted rectangular see-saw-like geometry to one K(1), one K(3), one K(4), and one Mo(1) atom. In the second O site, O(2) is bonded in a 4-coordinate geometry to one K(2), one K(3), one K(4), and one Mo(2) atom. In the third O site, O(3) is bonded in a 4-coordinate geometry to one K(1), one K(2), one K(4), and one Mo(1) atom. In the fourth O site, O(4) is bonded in a distorted rectangular see-saw-like geometry to one K(2), one K(3), one Mg(1), and one Mo(1) atom. In the fifth O site, O(5) is bonded in a 4-coordinate geometry to one K(2), one K(3), one Mg(1), and one Mo(2) atom. In the sixth O site, O(6) is bonded in a 4-coordinate geometry to one K(2), one K(4), one Mg(1), and one Mo(2) atom.