MgDy4(CuO4)2 crystallizes in the triclinic P1 space group. Mg(1) is bonded in a distorted see-saw-like geometry to one O(1), one O(2), one O(4), and one O(5) atom. There are four inequivalent Dy sites. In the first Dy site, Dy(1) is bonded to one O(1), one O(2), one O(3), one O(5), one O(6), and one O(8) atom to form edge-sharing DyO6 octahedra. In the second Dy site, Dy(2) is bonded to one O(1), one O(3), one O(4), one O(6), one O(7), and one O(8) atom to form edge-sharing DyO6 octahedra. In the third Dy site, Dy(3) is bonded in a 6-coordinate geometry to one O(2), one O(3), one O(4), one O(5), one O(6), and one O(7) atom. In the fourth Dy site, Dy(4) is bonded in a 5-coordinate geometry to one O(2), one O(3), one O(4), one O(6), and one O(7) atom. There are two inequivalent Cu sites. In the first Cu site, Cu(1) is bonded in a 3-coordinate geometry to one O(5), one O(7), and one O(8) atom. In the second Cu site, Cu(2) is bonded in a linear geometry to one O(1) and one O(8) atom. There are eight inequivalent O sites. In the first O site, O(1) is bonded to one Mg(1), one Dy(1), one Dy(2), and one Cu(2) atom to form distorted ODy2MgCu tetrahedra that share  a cornercorner with one O(8)Dy2Cu2 tetrahedra, corners with two equivalent O(3)Dy4 tetrahedra,  a cornercorner with one O(7)Dy3Cu trigonal pyramid, corners with two equivalent O(2)Dy3Mg trigonal pyramids,  an edgeedge with one O(8)Dy2Cu2 tetrahedra, and  an edgeedge with one O(5)Dy2MgCu trigonal pyramid. In the second O site, O(2) is bonded to one Mg(1), one Dy(1), one Dy(3), and one Dy(4) atom to form distorted ODy3Mg trigonal pyramids that share  a cornercorner with one O(8)Dy2Cu2 tetrahedra,  a cornercorner with one O(3)Dy4 tetrahedra, corners with two equivalent O(1)Dy2MgCu tetrahedra, corners with three equivalent O(5)Dy2MgCu trigonal pyramids,  an edgeedge with one O(3)Dy4 tetrahedra, and  an edgeedge with one O(7)Dy3Cu trigonal pyramid. In the third O site, O(3) is bonded to one Dy(1), one Dy(2), one Dy(3), and one Dy(4) atom to form ODy4 tetrahedra that share corners with two equivalent O(8)Dy2Cu2 tetrahedra, corners with two equivalent O(1)Dy2MgCu tetrahedra,  a cornercorner with one O(2)Dy3Mg trigonal pyramid, corners with two equivalent O(5)Dy2MgCu trigonal pyramids, corners with three equivalent O(7)Dy3Cu trigonal pyramids, and  an edgeedge with one O(2)Dy3Mg trigonal pyramid. In the fourth O site, O(4) is bonded in a rectangular see-saw-like geometry to one Mg(1), one Dy(2), one Dy(3), and one Dy(4) atom. In the fifth O site, O(5) is bonded to one Mg(1), one Dy(1), one Dy(3), and one Cu(1) atom to form distorted ODy2MgCu trigonal pyramids that share corners with two equivalent O(8)Dy2Cu2 tetrahedra, corners with two equivalent O(3)Dy4 tetrahedra, corners with two equivalent O(7)Dy3Cu trigonal pyramids, corners with three equivalent O(2)Dy3Mg trigonal pyramids, and  an edgeedge with one O(1)Dy2MgCu tetrahedra. In the sixth O site, O(6) is bonded in a distorted rectangular see-saw-like geometry to one Dy(1), one Dy(2), one Dy(3), and one Dy(4) atom. In the seventh O site, O(7) is bonded to one Dy(2), one Dy(3), one Dy(4), and one Cu(1) atom to form distorted ODy3Cu trigonal pyramids that share  a cornercorner with one O(1)Dy2MgCu tetrahedra, corners with two equivalent O(8)Dy2Cu2 tetrahedra, corners with three equivalent O(3)Dy4 tetrahedra, corners with two equivalent O(5)Dy2MgCu trigonal pyramids, and  an edgeedge with one O(2)Dy3Mg trigonal pyramid. In the eighth O site, O(8) is bonded to one Dy(1), one Dy(2), one Cu(1), and one Cu(2) atom to form distorted ODy2Cu2 tetrahedra that share  a cornercorner with one O(1)Dy2MgCu tetrahedra, corners with two equivalent O(3)Dy4 tetrahedra,  a cornercorner with one O(2)Dy3Mg trigonal pyramid, corners with two equivalent O(5)Dy2MgCu trigonal pyramids, corners with two equivalent O(7)Dy3Cu trigonal pyramids, and  an edgeedge with one O(1)Dy2MgCu tetrahedra.
MgDy4(CuO4)2 crystallizes in the triclinic P1 space group. Mg(1) is bonded in a distorted see-saw-like geometry to one O(1), one O(2), one O(4), and one O(5) atom. The Mg(1)-O(1) bond length is 1.96 Å. The Mg(1)-O(2) bond length is 2.03 Å. The Mg(1)-O(4) bond length is 2.00 Å. The Mg(1)-O(5) bond length is 2.03 Å. There are four inequivalent Dy sites. In the first Dy site, Dy(1) is bonded to one O(1), one O(2), one O(3), one O(5), one O(6), and one O(8) atom to form edge-sharing DyO6 octahedra. The Dy(1)-O(1) bond length is 2.30 Å. The Dy(1)-O(2) bond length is 2.30 Å. The Dy(1)-O(3) bond length is 2.38 Å. The Dy(1)-O(5) bond length is 2.28 Å. The Dy(1)-O(6) bond length is 2.28 Å. The Dy(1)-O(8) bond length is 2.18 Å. In the second Dy site, Dy(2) is bonded to one O(1), one O(3), one O(4), one O(6), one O(7), and one O(8) atom to form edge-sharing DyO6 octahedra. The Dy(2)-O(1) bond length is 2.22 Å. The Dy(2)-O(3) bond length is 2.31 Å. The Dy(2)-O(4) bond length is 2.41 Å. The Dy(2)-O(6) bond length is 2.36 Å. The Dy(2)-O(7) bond length is 2.29 Å. The Dy(2)-O(8) bond length is 2.20 Å. In the third Dy site, Dy(3) is bonded in a 6-coordinate geometry to one O(2), one O(3), one O(4), one O(5), one O(6), and one O(7) atom. The Dy(3)-O(2) bond length is 2.36 Å. The Dy(3)-O(3) bond length is 2.30 Å. The Dy(3)-O(4) bond length is 2.41 Å. The Dy(3)-O(5) bond length is 2.21 Å. The Dy(3)-O(6) bond length is 2.36 Å. The Dy(3)-O(7) bond length is 2.34 Å. In the fourth Dy site, Dy(4) is bonded in a 5-coordinate geometry to one O(2), one O(3), one O(4), one O(6), and one O(7) atom. The Dy(4)-O(2) bond length is 2.27 Å. The Dy(4)-O(3) bond length is 2.25 Å. The Dy(4)-O(4) bond length is 2.27 Å. The Dy(4)-O(6) bond length is 2.44 Å. The Dy(4)-O(7) bond length is 2.39 Å. There are two inequivalent Cu sites. In the first Cu site, Cu(1) is bonded in a 3-coordinate geometry to one O(5), one O(7), and one O(8) atom. The Cu(1)-O(5) bond length is 1.92 Å. The Cu(1)-O(7) bond length is 1.94 Å. The Cu(1)-O(8) bond length is 2.11 Å. In the second Cu site, Cu(2) is bonded in a linear geometry to one O(1) and one O(8) atom. The Cu(2)-O(1) bond length is 1.80 Å. The Cu(2)-O(8) bond length is 1.80 Å. There are eight inequivalent O sites. In the first O site, O(1) is bonded to one Mg(1), one Dy(1), one Dy(2), and one Cu(2) atom to form distorted ODy2MgCu tetrahedra that share  a cornercorner with one O(8)Dy2Cu2 tetrahedra, corners with two equivalent O(3)Dy4 tetrahedra,  a cornercorner with one O(7)Dy3Cu trigonal pyramid, corners with two equivalent O(2)Dy3Mg trigonal pyramids,  an edgeedge with one O(8)Dy2Cu2 tetrahedra, and  an edgeedge with one O(5)Dy2MgCu trigonal pyramid. In the second O site, O(2) is bonded to one Mg(1), one Dy(1), one Dy(3), and one Dy(4) atom to form distorted ODy3Mg trigonal pyramids that share  a cornercorner with one O(8)Dy2Cu2 tetrahedra,  a cornercorner with one O(3)Dy4 tetrahedra, corners with two equivalent O(1)Dy2MgCu tetrahedra, corners with three equivalent O(5)Dy2MgCu trigonal pyramids,  an edgeedge with one O(3)Dy4 tetrahedra, and  an edgeedge with one O(7)Dy3Cu trigonal pyramid. In the third O site, O(3) is bonded to one Dy(1), one Dy(2), one Dy(3), and one Dy(4) atom to form ODy4 tetrahedra that share corners with two equivalent O(8)Dy2Cu2 tetrahedra, corners with two equivalent O(1)Dy2MgCu tetrahedra,  a cornercorner with one O(2)Dy3Mg trigonal pyramid, corners with two equivalent O(5)Dy2MgCu trigonal pyramids, corners with three equivalent O(7)Dy3Cu trigonal pyramids, and  an edgeedge with one O(2)Dy3Mg trigonal pyramid. In the fourth O site, O(4) is bonded in a rectangular see-saw-like geometry to one Mg(1), one Dy(2), one Dy(3), and one Dy(4) atom. In the fifth O site, O(5) is bonded to one Mg(1), one Dy(1), one Dy(3), and one Cu(1) atom to form distorted ODy2MgCu trigonal pyramids that share corners with two equivalent O(8)Dy2Cu2 tetrahedra, corners with two equivalent O(3)Dy4 tetrahedra, corners with two equivalent O(7)Dy3Cu trigonal pyramids, corners with three equivalent O(2)Dy3Mg trigonal pyramids, and  an edgeedge with one O(1)Dy2MgCu tetrahedra. In the sixth O site, O(6) is bonded in a distorted rectangular see-saw-like geometry to one Dy(1), one Dy(2), one Dy(3), and one Dy(4) atom. In the seventh O site, O(7) is bonded to one Dy(2), one Dy(3), one Dy(4), and one Cu(1) atom to form distorted ODy3Cu trigonal pyramids that share  a cornercorner with one O(1)Dy2MgCu tetrahedra, corners with two equivalent O(8)Dy2Cu2 tetrahedra, corners with three equivalent O(3)Dy4 tetrahedra, corners with two equivalent O(5)Dy2MgCu trigonal pyramids, and  an edgeedge with one O(2)Dy3Mg trigonal pyramid. In the eighth O site, O(8) is bonded to one Dy(1), one Dy(2), one Cu(1), and one Cu(2) atom to form distorted ODy2Cu2 tetrahedra that share  a cornercorner with one O(1)Dy2MgCu tetrahedra, corners with two equivalent O(3)Dy4 tetrahedra,  a cornercorner with one O(2)Dy3Mg trigonal pyramid, corners with two equivalent O(5)Dy2MgCu trigonal pyramids, corners with two equivalent O(7)Dy3Cu trigonal pyramids, and  an edgeedge with one O(1)Dy2MgCu tetrahedra.