Lu2CoTe2(SO7)2 crystallizes in the triclinic P-1 space group. Lu(1) is bonded to one O(1), one O(2), one O(3), one O(5), one O(6), and two equivalent O(7) atoms to form distorted LuO7 pentagonal bipyramids that share corners with three equivalent S(1)O4 tetrahedra,  an edgeedge with one Co(1)O6 octahedra, and  an edgeedge with one Lu(1)O7 pentagonal bipyramid. Co(1) is bonded to two equivalent O(4), two equivalent O(5), and two equivalent O(6) atoms to form CoO6 octahedra that share corners with two equivalent S(1)O4 tetrahedra and edges with two equivalent Lu(1)O7 pentagonal bipyramids. Te(1) is bonded in a distorted T-shaped geometry to one O(5), one O(6), and one O(7) atom. S(1) is bonded to one O(1), one O(2), one O(3), and one O(4) atom to form SO4 tetrahedra that share  a cornercorner with one Co(1)O6 octahedra and corners with three equivalent Lu(1)O7 pentagonal bipyramids. The corner-sharing octahedral tilt angles are 50°. There are seven inequivalent O sites. In the first O site, O(1) is bonded in a bent 150 degrees geometry to one Lu(1) and one S(1) atom. In the second O site, O(2) is bonded in a bent 150 degrees geometry to one Lu(1) and one S(1) atom. In the third O site, O(3) is bonded in a bent 120 degrees geometry to one Lu(1) and one S(1) atom. In the fourth O site, O(4) is bonded in a distorted bent 120 degrees geometry to one Co(1) and one S(1) atom. In the fifth O site, O(5) is bonded in a 3-coordinate geometry to one Lu(1), one Co(1), and one Te(1) atom. In the sixth O site, O(6) is bonded in a distorted trigonal non-coplanar geometry to one Lu(1), one Co(1), and one Te(1) atom. In the seventh O site, O(7) is bonded in a trigonal non-coplanar geometry to two equivalent Lu(1) and one Te(1) atom.
Lu2CoTe2(SO7)2 crystallizes in the triclinic P-1 space group. Lu(1) is bonded to one O(1), one O(2), one O(3), one O(5), one O(6), and two equivalent O(7) atoms to form distorted LuO7 pentagonal bipyramids that share corners with three equivalent S(1)O4 tetrahedra,  an edgeedge with one Co(1)O6 octahedra, and  an edgeedge with one Lu(1)O7 pentagonal bipyramid. The Lu(1)-O(1) bond length is 2.27 Å. The Lu(1)-O(2) bond length is 2.23 Å. The Lu(1)-O(3) bond length is 2.26 Å. The Lu(1)-O(5) bond length is 2.52 Å. The Lu(1)-O(6) bond length is 2.19 Å. There is one shorter (2.22 Å) and one longer (2.31 Å) Lu(1)-O(7) bond length. Co(1) is bonded to two equivalent O(4), two equivalent O(5), and two equivalent O(6) atoms to form CoO6 octahedra that share corners with two equivalent S(1)O4 tetrahedra and edges with two equivalent Lu(1)O7 pentagonal bipyramids. Both Co(1)-O(4) bond lengths are 2.14 Å. Both Co(1)-O(5) bond lengths are 2.05 Å. Both Co(1)-O(6) bond lengths are 2.11 Å. Te(1) is bonded in a distorted T-shaped geometry to one O(5), one O(6), and one O(7) atom. The Te(1)-O(5) bond length is 1.92 Å. The Te(1)-O(6) bond length is 1.90 Å. The Te(1)-O(7) bond length is 1.90 Å. S(1) is bonded to one O(1), one O(2), one O(3), and one O(4) atom to form SO4 tetrahedra that share  a cornercorner with one Co(1)O6 octahedra and corners with three equivalent Lu(1)O7 pentagonal bipyramids. The corner-sharing octahedral tilt angles are 50°. The S(1)-O(1) bond length is 1.49 Å. The S(1)-O(2) bond length is 1.49 Å. The S(1)-O(3) bond length is 1.49 Å. The S(1)-O(4) bond length is 1.48 Å. There are seven inequivalent O sites. In the first O site, O(1) is bonded in a bent 150 degrees geometry to one Lu(1) and one S(1) atom. In the second O site, O(2) is bonded in a bent 150 degrees geometry to one Lu(1) and one S(1) atom. In the third O site, O(3) is bonded in a bent 120 degrees geometry to one Lu(1) and one S(1) atom. In the fourth O site, O(4) is bonded in a distorted bent 120 degrees geometry to one Co(1) and one S(1) atom. In the fifth O site, O(5) is bonded in a 3-coordinate geometry to one Lu(1), one Co(1), and one Te(1) atom. In the sixth O site, O(6) is bonded in a distorted trigonal non-coplanar geometry to one Lu(1), one Co(1), and one Te(1) atom. In the seventh O site, O(7) is bonded in a trigonal non-coplanar geometry to two equivalent Lu(1) and one Te(1) atom.