MgHo2Ag2(WO4)4 crystallizes in the triclinic P1 space group. Mg(1) is bonded to one O(10), one O(15), one O(16), one O(5), and one O(7) atom to form distorted MgO5 trigonal bipyramids that share  a cornercorner with one Ho(2)O6 octahedra,  a cornercorner with one W(2)O6 octahedra,  an edgeedge with one W(1)O6 octahedra, and  an edgeedge with one W(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 54-65°. There are two inequivalent Ho sites. In the first Ho site, Ho(1) is bonded in a 6-coordinate geometry to one O(1), one O(11), one O(3), one O(5), one O(7), and one O(9) atom. In the second Ho site, Ho(2) is bonded to one O(10), one O(12), one O(2), one O(4), one O(6), and one O(8) atom to form HoO6 octahedra that share corners with two equivalent W(1)O6 octahedra, corners with two equivalent W(2)O6 octahedra, corners with two equivalent W(3)O6 octahedra, corners with two equivalent W(4)O6 octahedra, and  a cornercorner with one Mg(1)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 36-59°. There are four inequivalent W sites. In the first W site, W(1) is bonded to one O(1), one O(10), one O(11), one O(13), one O(16), and one O(4) atom to form distorted WO6 octahedra that share corners with two equivalent Ho(2)O6 octahedra,  an edgeedge with one W(3)O6 octahedra,  an edgeedge with one W(4)O6 octahedra, and  an edgeedge with one Mg(1)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 44-59°. In the second W site, W(2) is bonded to one O(12), one O(14), one O(15), one O(2), one O(3), and one O(9) atom to form distorted WO6 octahedra that share corners with two equivalent Ho(2)O6 octahedra,  a cornercorner with one Mg(1)O5 trigonal bipyramid,  an edgeedge with one W(3)O6 octahedra, and  an edgeedge with one W(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 36-56°. In the third W site, W(3) is bonded to one O(13), one O(14), one O(2), one O(4), one O(5), and one O(7) atom to form WO6 octahedra that share corners with two equivalent Ho(2)O6 octahedra,  an edgeedge with one W(1)O6 octahedra,  an edgeedge with one W(2)O6 octahedra,  an edgeedge with one W(4)O6 octahedra, and  an edgeedge with one Mg(1)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 44-52°. In the fourth W site, W(4) is bonded to one O(1), one O(13), one O(14), one O(3), one O(6), and one O(8) atom to form distorted WO6 octahedra that share corners with two equivalent Ho(2)O6 octahedra,  an edgeedge with one W(1)O6 octahedra,  an edgeedge with one W(2)O6 octahedra, and  an edgeedge with one W(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 40-41°. There are two inequivalent Ag sites. In the first Ag site, Ag(1) is bonded in a 5-coordinate geometry to one O(13), one O(16), one O(2), one O(6), and one O(9) atom. In the second Ag site, Ag(2) is bonded in a 5-coordinate geometry to one O(11), one O(14), one O(15), one O(4), and one O(8) atom. There are sixteen inequivalent O sites. In the first O site, O(1) is bonded in a distorted trigonal planar geometry to one Ho(1), one W(1), and one W(4) atom. In the second O site, O(2) is bonded to one Ho(2), one W(2), one W(3), and one Ag(1) atom to form distorted edge-sharing OHoAgW2 trigonal pyramids. In the third O site, O(3) is bonded in a distorted trigonal planar geometry to one Ho(1), one W(2), and one W(4) atom. In the fourth O site, O(4) is bonded in a 4-coordinate geometry to one Ho(2), one W(1), one W(3), and one Ag(2) atom. In the fifth O site, O(5) is bonded in a 3-coordinate geometry to one Mg(1), one Ho(1), and one W(3) atom. In the sixth O site, O(6) is bonded in a 3-coordinate geometry to one Ho(2), one W(4), and one Ag(1) atom. In the seventh O site, O(7) is bonded in a 3-coordinate geometry to one Mg(1), one Ho(1), and one W(3) atom. In the eighth O site, O(8) is bonded in a 3-coordinate geometry to one Ho(2), one W(4), and one Ag(2) atom. In the ninth O site, O(9) is bonded in a distorted T-shaped geometry to one Ho(1), one W(2), and one Ag(1) atom. In the tenth O site, O(10) is bonded in a distorted trigonal planar geometry to one Mg(1), one Ho(2), and one W(1) atom. In the eleventh O site, O(11) is bonded in a distorted trigonal non-coplanar geometry to one Ho(1), one W(1), and one Ag(2) atom. In the twelfth O site, O(12) is bonded in a bent 150 degrees geometry to one Ho(2) and one W(2) atom. In the thirteenth O site, O(13) is bonded to one W(1), one W(3), one W(4), and one Ag(1) atom to form OAgW3 trigonal pyramids that share  an edgeedge with one O(14)AgW3 trigonal pyramid and  an edgeedge with one O(2)HoAgW2 trigonal pyramid. In the fourteenth O site, O(14) is bonded to one W(2), one W(3), one W(4), and one Ag(2) atom to form distorted OAgW3 trigonal pyramids that share  an edgeedge with one O(13)AgW3 trigonal pyramid and  an edgeedge with one O(2)HoAgW2 trigonal pyramid. In the fifteenth O site, O(15) is bonded in a 3-coordinate geometry to one Mg(1), one W(2), and one Ag(2) atom. In the sixteenth O site, O(16) is bonded in a distorted trigonal non-coplanar geometry to one Mg(1), one W(1), and one Ag(1) atom.
MgHo2Ag2(WO4)4 crystallizes in the triclinic P1 space group. Mg(1) is bonded to one O(10), one O(15), one O(16), one O(5), and one O(7) atom to form distorted MgO5 trigonal bipyramids that share  a cornercorner with one Ho(2)O6 octahedra,  a cornercorner with one W(2)O6 octahedra,  an edgeedge with one W(1)O6 octahedra, and  an edgeedge with one W(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 54-65°. The Mg(1)-O(10) bond length is 2.03 Å. The Mg(1)-O(15) bond length is 2.09 Å. The Mg(1)-O(16) bond length is 2.04 Å. The Mg(1)-O(5) bond length is 2.07 Å. The Mg(1)-O(7) bond length is 2.18 Å. There are two inequivalent Ho sites. In the first Ho site, Ho(1) is bonded in a 6-coordinate geometry to one O(1), one O(11), one O(3), one O(5), one O(7), and one O(9) atom. The Ho(1)-O(1) bond length is 2.38 Å. The Ho(1)-O(11) bond length is 2.29 Å. The Ho(1)-O(3) bond length is 2.33 Å. The Ho(1)-O(5) bond length is 2.24 Å. The Ho(1)-O(7) bond length is 2.41 Å. The Ho(1)-O(9) bond length is 2.34 Å. In the second Ho site, Ho(2) is bonded to one O(10), one O(12), one O(2), one O(4), one O(6), and one O(8) atom to form HoO6 octahedra that share corners with two equivalent W(1)O6 octahedra, corners with two equivalent W(2)O6 octahedra, corners with two equivalent W(3)O6 octahedra, corners with two equivalent W(4)O6 octahedra, and  a cornercorner with one Mg(1)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 36-59°. The Ho(2)-O(10) bond length is 2.18 Å. The Ho(2)-O(12) bond length is 2.26 Å. The Ho(2)-O(2) bond length is 2.42 Å. The Ho(2)-O(4) bond length is 2.40 Å. The Ho(2)-O(6) bond length is 2.27 Å. The Ho(2)-O(8) bond length is 2.29 Å. There are four inequivalent W sites. In the first W site, W(1) is bonded to one O(1), one O(10), one O(11), one O(13), one O(16), and one O(4) atom to form distorted WO6 octahedra that share corners with two equivalent Ho(2)O6 octahedra,  an edgeedge with one W(3)O6 octahedra,  an edgeedge with one W(4)O6 octahedra, and  an edgeedge with one Mg(1)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 44-59°. The W(1)-O(1) bond length is 2.20 Å. The W(1)-O(10) bond length is 2.02 Å. The W(1)-O(11) bond length is 1.87 Å. The W(1)-O(13) bond length is 2.13 Å. The W(1)-O(16) bond length is 1.92 Å. The W(1)-O(4) bond length is 2.11 Å. In the second W site, W(2) is bonded to one O(12), one O(14), one O(15), one O(2), one O(3), and one O(9) atom to form distorted WO6 octahedra that share corners with two equivalent Ho(2)O6 octahedra,  a cornercorner with one Mg(1)O5 trigonal bipyramid,  an edgeedge with one W(3)O6 octahedra, and  an edgeedge with one W(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 36-56°. The W(2)-O(12) bond length is 1.83 Å. The W(2)-O(14) bond length is 2.08 Å. The W(2)-O(15) bond length is 1.87 Å. The W(2)-O(2) bond length is 2.11 Å. The W(2)-O(3) bond length is 2.16 Å. The W(2)-O(9) bond length is 1.85 Å. In the third W site, W(3) is bonded to one O(13), one O(14), one O(2), one O(4), one O(5), and one O(7) atom to form WO6 octahedra that share corners with two equivalent Ho(2)O6 octahedra,  an edgeedge with one W(1)O6 octahedra,  an edgeedge with one W(2)O6 octahedra,  an edgeedge with one W(4)O6 octahedra, and  an edgeedge with one Mg(1)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 44-52°. The W(3)-O(13) bond length is 2.10 Å. The W(3)-O(14) bond length is 2.11 Å. The W(3)-O(2) bond length is 2.07 Å. The W(3)-O(4) bond length is 2.10 Å. The W(3)-O(5) bond length is 1.97 Å. The W(3)-O(7) bond length is 1.86 Å. In the fourth W site, W(4) is bonded to one O(1), one O(13), one O(14), one O(3), one O(6), and one O(8) atom to form distorted WO6 octahedra that share corners with two equivalent Ho(2)O6 octahedra,  an edgeedge with one W(1)O6 octahedra,  an edgeedge with one W(2)O6 octahedra, and  an edgeedge with one W(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 40-41°. The W(4)-O(1) bond length is 1.95 Å. The W(4)-O(13) bond length is 2.12 Å. The W(4)-O(14) bond length is 2.16 Å. The W(4)-O(3) bond length is 1.99 Å. The W(4)-O(6) bond length is 1.83 Å. The W(4)-O(8) bond length is 1.83 Å. There are two inequivalent Ag sites. In the first Ag site, Ag(1) is bonded in a 5-coordinate geometry to one O(13), one O(16), one O(2), one O(6), and one O(9) atom. The Ag(1)-O(13) bond length is 2.46 Å. The Ag(1)-O(16) bond length is 2.19 Å. The Ag(1)-O(2) bond length is 2.61 Å. The Ag(1)-O(6) bond length is 2.54 Å. The Ag(1)-O(9) bond length is 2.30 Å. In the second Ag site, Ag(2) is bonded in a 5-coordinate geometry to one O(11), one O(14), one O(15), one O(4), and one O(8) atom. The Ag(2)-O(11) bond length is 2.30 Å. The Ag(2)-O(14) bond length is 2.49 Å. The Ag(2)-O(15) bond length is 2.27 Å. The Ag(2)-O(4) bond length is 2.62 Å. The Ag(2)-O(8) bond length is 2.45 Å. There are sixteen inequivalent O sites. In the first O site, O(1) is bonded in a distorted trigonal planar geometry to one Ho(1), one W(1), and one W(4) atom. In the second O site, O(2) is bonded to one Ho(2), one W(2), one W(3), and one Ag(1) atom to form distorted edge-sharing OHoAgW2 trigonal pyramids. In the third O site, O(3) is bonded in a distorted trigonal planar geometry to one Ho(1), one W(2), and one W(4) atom. In the fourth O site, O(4) is bonded in a 4-coordinate geometry to one Ho(2), one W(1), one W(3), and one Ag(2) atom. In the fifth O site, O(5) is bonded in a 3-coordinate geometry to one Mg(1), one Ho(1), and one W(3) atom. In the sixth O site, O(6) is bonded in a 3-coordinate geometry to one Ho(2), one W(4), and one Ag(1) atom. In the seventh O site, O(7) is bonded in a 3-coordinate geometry to one Mg(1), one Ho(1), and one W(3) atom. In the eighth O site, O(8) is bonded in a 3-coordinate geometry to one Ho(2), one W(4), and one Ag(2) atom. In the ninth O site, O(9) is bonded in a distorted T-shaped geometry to one Ho(1), one W(2), and one Ag(1) atom. In the tenth O site, O(10) is bonded in a distorted trigonal planar geometry to one Mg(1), one Ho(2), and one W(1) atom. In the eleventh O site, O(11) is bonded in a distorted trigonal non-coplanar geometry to one Ho(1), one W(1), and one Ag(2) atom. In the twelfth O site, O(12) is bonded in a bent 150 degrees geometry to one Ho(2) and one W(2) atom. In the thirteenth O site, O(13) is bonded to one W(1), one W(3), one W(4), and one Ag(1) atom to form OAgW3 trigonal pyramids that share  an edgeedge with one O(14)AgW3 trigonal pyramid and  an edgeedge with one O(2)HoAgW2 trigonal pyramid. In the fourteenth O site, O(14) is bonded to one W(2), one W(3), one W(4), and one Ag(2) atom to form distorted OAgW3 trigonal pyramids that share  an edgeedge with one O(13)AgW3 trigonal pyramid and  an edgeedge with one O(2)HoAgW2 trigonal pyramid. In the fifteenth O site, O(15) is bonded in a 3-coordinate geometry to one Mg(1), one W(2), and one Ag(2) atom. In the sixteenth O site, O(16) is bonded in a distorted trigonal non-coplanar geometry to one Mg(1), one W(1), and one Ag(1) atom.