MgAg20(BiO4)4 crystallizes in the triclinic P1 space group. Mg(1) is bonded in a 3-coordinate geometry to one O(1), one O(11), and one O(15) atom. There are twenty inequivalent Ag sites. In the first Ag site, Ag(1) is bonded in a linear geometry to one O(16) and one O(9) atom. In the second Ag site, Ag(2) is bonded in a linear geometry to one O(5) and one O(8) atom. In the third Ag site, Ag(3) is bonded in a linear geometry to one O(1) and one O(3) atom. In the fourth Ag site, Ag(4) is bonded in a linear geometry to one O(2) and one O(4) atom. In the fifth Ag site, Ag(5) is bonded in a distorted T-shaped geometry to one O(14), one O(4), and one O(5) atom. In the sixth Ag site, Ag(6) is bonded in a 3-coordinate geometry to one O(13), one O(3), and one O(6) atom. In the seventh Ag site, Ag(7) is bonded in a 3-coordinate geometry to one O(12), one O(15), and one O(2) atom. In the eighth Ag site, Ag(8) is bonded in a 2-coordinate geometry to one O(1) and one O(16) atom. In the ninth Ag site, Ag(9) is bonded in a distorted linear geometry to one O(11), one O(15), and one O(2) atom. In the tenth Ag site, Ag(10) is bonded in a 1-coordinate geometry to one O(12) atom. In the eleventh Ag site, Ag(11) is bonded in a linear geometry to one O(13) and one O(4) atom. In the twelfth Ag site, Ag(12) is bonded in a linear geometry to one O(14) and one O(3) atom. In the thirteenth Ag site, Ag(13) is bonded in a linear geometry to one O(11) and one O(13) atom. In the fourteenth Ag site, Ag(14) is bonded in a linear geometry to one O(12) and one O(14) atom. In the fifteenth Ag site, Ag(15) is bonded in a linear geometry to one O(6) and one O(7) atom. In the sixteenth Ag site, Ag(16) is bonded in a linear geometry to one O(5) and one O(8) atom. In the seventeenth Ag site, Ag(17) is bonded in a linear geometry to one O(16) and one O(9) atom. In the eighteenth Ag site, Ag(18) is bonded in a linear geometry to one O(10) and one O(15) atom. In the nineteenth Ag site, Ag(19) is bonded in a linear geometry to one O(6) and one O(7) atom. In the twentieth Ag site, Ag(20) is bonded in a linear geometry to one O(10) and one O(15) atom. There are four inequivalent Bi sites. In the first Bi site, Bi(1) is bonded to one O(10), one O(14), one O(4), one O(6), and one O(8) atom to form edge-sharing BiO5 square pyramids. In the second Bi site, Bi(2) is bonded in a distorted square pyramidal geometry to one O(13), one O(3), one O(5), one O(7), and one O(9) atom. In the third Bi site, Bi(3) is bonded to one O(10), one O(12), one O(16), one O(2), and one O(8) atom to form edge-sharing BiO5 square pyramids. In the fourth Bi site, Bi(4) is bonded in a rectangular see-saw-like geometry to one O(1), one O(11), one O(7), and one O(9) atom. There are sixteen inequivalent O sites. In the first O site, O(1) is bonded to one Mg(1), one Ag(3), one Ag(8), and one Bi(4) atom to form OMgAg2Bi tetrahedra that share  a cornercorner with one O(7)Ag2Bi2 tetrahedra and  a cornercorner with one O(3)Ag3Bi tetrahedra. In the second O site, O(2) is bonded to one Ag(4), one Ag(7), one Ag(9), and one Bi(3) atom to form OAg3Bi tetrahedra that share  a cornercorner with one O(10)Ag2Bi2 tetrahedra,  a cornercorner with one O(8)Ag2Bi2 tetrahedra,  a cornercorner with one O(4)Ag3Bi tetrahedra, and corners with two equivalent O(12)Ag3Bi tetrahedra. In the third O site, O(3) is bonded to one Ag(12), one Ag(3), one Ag(6), and one Bi(2) atom to form distorted OAg3Bi tetrahedra that share  a cornercorner with one O(7)Ag2Bi2 tetrahedra,  a cornercorner with one O(14)Ag3Bi tetrahedra,  a cornercorner with one O(5)Ag3Bi tetrahedra,  a cornercorner with one O(6)Ag3Bi tetrahedra,  a cornercorner with one O(1)MgAg2Bi tetrahedra, and corners with two equivalent O(13)Ag3Bi tetrahedra. In the fourth O site, O(4) is bonded to one Ag(11), one Ag(4), one Ag(5), and one Bi(1) atom to form distorted OAg3Bi tetrahedra that share  a cornercorner with one O(10)Ag2Bi2 tetrahedra,  a cornercorner with one O(8)Ag2Bi2 tetrahedra,  a cornercorner with one O(13)Ag3Bi tetrahedra,  a cornercorner with one O(2)Ag3Bi tetrahedra,  a cornercorner with one O(5)Ag3Bi tetrahedra,  a cornercorner with one O(6)Ag3Bi tetrahedra, and corners with two equivalent O(14)Ag3Bi tetrahedra. In the fifth O site, O(5) is bonded to one Ag(16), one Ag(2), one Ag(5), and one Bi(2) atom to form OAg3Bi tetrahedra that share  a cornercorner with one O(7)Ag2Bi2 tetrahedra,  a cornercorner with one O(13)Ag3Bi tetrahedra,  a cornercorner with one O(14)Ag3Bi tetrahedra,  a cornercorner with one O(3)Ag3Bi tetrahedra,  a cornercorner with one O(4)Ag3Bi tetrahedra, and corners with two equivalent O(8)Ag2Bi2 tetrahedra. In the sixth O site, O(6) is bonded to one Ag(15), one Ag(19), one Ag(6), and one Bi(1) atom to form OAg3Bi tetrahedra that share  a cornercorner with one O(10)Ag2Bi2 tetrahedra,  a cornercorner with one O(8)Ag2Bi2 tetrahedra,  a cornercorner with one O(13)Ag3Bi tetrahedra,  a cornercorner with one O(14)Ag3Bi tetrahedra,  a cornercorner with one O(3)Ag3Bi tetrahedra,  a cornercorner with one O(4)Ag3Bi tetrahedra, and corners with two equivalent O(7)Ag2Bi2 tetrahedra. In the seventh O site, O(7) is bonded to one Ag(15), one Ag(19), one Bi(2), and one Bi(4) atom to form distorted OAg2Bi2 tetrahedra that share  a cornercorner with one O(13)Ag3Bi tetrahedra,  a cornercorner with one O(3)Ag3Bi tetrahedra,  a cornercorner with one O(5)Ag3Bi tetrahedra,  a cornercorner with one O(1)MgAg2Bi tetrahedra, and corners with two equivalent O(6)Ag3Bi tetrahedra. In the eighth O site, O(8) is bonded to one Ag(16), one Ag(2), one Bi(1), and one Bi(3) atom to form OAg2Bi2 tetrahedra that share  a cornercorner with one O(12)Ag3Bi tetrahedra,  a cornercorner with one O(14)Ag3Bi tetrahedra,  a cornercorner with one O(2)Ag3Bi tetrahedra,  a cornercorner with one O(4)Ag3Bi tetrahedra,  a cornercorner with one O(6)Ag3Bi tetrahedra, corners with two equivalent O(5)Ag3Bi tetrahedra, and  an edgeedge with one O(10)Ag2Bi2 tetrahedra. In the ninth O site, O(9) is bonded in a distorted rectangular see-saw-like geometry to one Ag(1), one Ag(17), one Bi(2), and one Bi(4) atom. In the tenth O site, O(10) is bonded to one Ag(18), one Ag(20), one Bi(1), and one Bi(3) atom to form OAg2Bi2 tetrahedra that share  a cornercorner with one O(12)Ag3Bi tetrahedra,  a cornercorner with one O(14)Ag3Bi tetrahedra,  a cornercorner with one O(2)Ag3Bi tetrahedra,  a cornercorner with one O(4)Ag3Bi tetrahedra,  a cornercorner with one O(6)Ag3Bi tetrahedra, and  an edgeedge with one O(8)Ag2Bi2 tetrahedra. In the eleventh O site, O(11) is bonded in a distorted see-saw-like geometry to one Mg(1), one Ag(13), one Ag(9), and one Bi(4) atom. In the twelfth O site, O(12) is bonded to one Ag(10), one Ag(14), one Ag(7), and one Bi(3) atom to form OAg3Bi tetrahedra that share  a cornercorner with one O(10)Ag2Bi2 tetrahedra,  a cornercorner with one O(8)Ag2Bi2 tetrahedra,  a cornercorner with one O(14)Ag3Bi tetrahedra, and corners with two equivalent O(2)Ag3Bi tetrahedra. In the thirteenth O site, O(13) is bonded to one Ag(11), one Ag(13), one Ag(6), and one Bi(2) atom to form OAg3Bi tetrahedra that share  a cornercorner with one O(7)Ag2Bi2 tetrahedra,  a cornercorner with one O(4)Ag3Bi tetrahedra,  a cornercorner with one O(5)Ag3Bi tetrahedra,  a cornercorner with one O(6)Ag3Bi tetrahedra, and corners with two equivalent O(3)Ag3Bi tetrahedra. In the fourteenth O site, O(14) is bonded to one Ag(12), one Ag(14), one Ag(5), and one Bi(1) atom to form OAg3Bi tetrahedra that share  a cornercorner with one O(10)Ag2Bi2 tetrahedra,  a cornercorner with one O(8)Ag2Bi2 tetrahedra,  a cornercorner with one O(12)Ag3Bi tetrahedra,  a cornercorner with one O(3)Ag3Bi tetrahedra,  a cornercorner with one O(5)Ag3Bi tetrahedra,  a cornercorner with one O(6)Ag3Bi tetrahedra, and corners with two equivalent O(4)Ag3Bi tetrahedra. In the fifteenth O site, O(15) is bonded in a 5-coordinate geometry to one Mg(1), one Ag(18), one Ag(20), one Ag(7), and one Ag(9) atom. In the sixteenth O site, O(16) is bonded in a 4-coordinate geometry to one Ag(1), one Ag(17), one Ag(8), and one Bi(3) atom.
MgAg20(BiO4)4 crystallizes in the triclinic P1 space group. Mg(1) is bonded in a 3-coordinate geometry to one O(1), one O(11), and one O(15) atom. The Mg(1)-O(1) bond length is 2.00 Å. The Mg(1)-O(11) bond length is 2.05 Å. The Mg(1)-O(15) bond length is 2.00 Å. There are twenty inequivalent Ag sites. In the first Ag site, Ag(1) is bonded in a linear geometry to one O(16) and one O(9) atom. The Ag(1)-O(16) bond length is 2.06 Å. The Ag(1)-O(9) bond length is 2.12 Å. In the second Ag site, Ag(2) is bonded in a linear geometry to one O(5) and one O(8) atom. The Ag(2)-O(5) bond length is 2.11 Å. The Ag(2)-O(8) bond length is 2.10 Å. In the third Ag site, Ag(3) is bonded in a linear geometry to one O(1) and one O(3) atom. The Ag(3)-O(1) bond length is 2.12 Å. The Ag(3)-O(3) bond length is 2.12 Å. In the fourth Ag site, Ag(4) is bonded in a linear geometry to one O(2) and one O(4) atom. The Ag(4)-O(2) bond length is 2.14 Å. The Ag(4)-O(4) bond length is 2.15 Å. In the fifth Ag site, Ag(5) is bonded in a distorted T-shaped geometry to one O(14), one O(4), and one O(5) atom. The Ag(5)-O(14) bond length is 2.21 Å. The Ag(5)-O(4) bond length is 2.61 Å. The Ag(5)-O(5) bond length is 2.21 Å. In the sixth Ag site, Ag(6) is bonded in a 3-coordinate geometry to one O(13), one O(3), and one O(6) atom. The Ag(6)-O(13) bond length is 2.28 Å. The Ag(6)-O(3) bond length is 2.74 Å. The Ag(6)-O(6) bond length is 2.23 Å. In the seventh Ag site, Ag(7) is bonded in a 3-coordinate geometry to one O(12), one O(15), and one O(2) atom. The Ag(7)-O(12) bond length is 2.21 Å. The Ag(7)-O(15) bond length is 2.20 Å. The Ag(7)-O(2) bond length is 2.59 Å. In the eighth Ag site, Ag(8) is bonded in a 2-coordinate geometry to one O(1) and one O(16) atom. The Ag(8)-O(1) bond length is 2.29 Å. The Ag(8)-O(16) bond length is 2.44 Å. In the ninth Ag site, Ag(9) is bonded in a distorted linear geometry to one O(11), one O(15), and one O(2) atom. The Ag(9)-O(11) bond length is 2.32 Å. The Ag(9)-O(15) bond length is 2.72 Å. The Ag(9)-O(2) bond length is 2.20 Å. In the tenth Ag site, Ag(10) is bonded in a 1-coordinate geometry to one O(12) atom. The Ag(10)-O(12) bond length is 2.40 Å. In the eleventh Ag site, Ag(11) is bonded in a linear geometry to one O(13) and one O(4) atom. The Ag(11)-O(13) bond length is 2.22 Å. The Ag(11)-O(4) bond length is 2.13 Å. In the twelfth Ag site, Ag(12) is bonded in a linear geometry to one O(14) and one O(3) atom. The Ag(12)-O(14) bond length is 2.20 Å. The Ag(12)-O(3) bond length is 2.15 Å. In the thirteenth Ag site, Ag(13) is bonded in a linear geometry to one O(11) and one O(13) atom. The Ag(13)-O(11) bond length is 2.23 Å. The Ag(13)-O(13) bond length is 2.23 Å. In the fourteenth Ag site, Ag(14) is bonded in a linear geometry to one O(12) and one O(14) atom. The Ag(14)-O(12) bond length is 2.17 Å. The Ag(14)-O(14) bond length is 2.19 Å. In the fifteenth Ag site, Ag(15) is bonded in a linear geometry to one O(6) and one O(7) atom. The Ag(15)-O(6) bond length is 2.10 Å. The Ag(15)-O(7) bond length is 2.12 Å. In the sixteenth Ag site, Ag(16) is bonded in a linear geometry to one O(5) and one O(8) atom. The Ag(16)-O(5) bond length is 2.14 Å. The Ag(16)-O(8) bond length is 2.12 Å. In the seventeenth Ag site, Ag(17) is bonded in a linear geometry to one O(16) and one O(9) atom. The Ag(17)-O(16) bond length is 2.13 Å. The Ag(17)-O(9) bond length is 2.16 Å. In the eighteenth Ag site, Ag(18) is bonded in a linear geometry to one O(10) and one O(15) atom. The Ag(18)-O(10) bond length is 2.22 Å. The Ag(18)-O(15) bond length is 2.29 Å. In the nineteenth Ag site, Ag(19) is bonded in a linear geometry to one O(6) and one O(7) atom. The Ag(19)-O(6) bond length is 2.15 Å. The Ag(19)-O(7) bond length is 2.18 Å. In the twentieth Ag site, Ag(20) is bonded in a linear geometry to one O(10) and one O(15) atom. The Ag(20)-O(10) bond length is 2.10 Å. The Ag(20)-O(15) bond length is 2.09 Å. There are four inequivalent Bi sites. In the first Bi site, Bi(1) is bonded to one O(10), one O(14), one O(4), one O(6), and one O(8) atom to form edge-sharing BiO5 square pyramids. The Bi(1)-O(10) bond length is 2.24 Å. The Bi(1)-O(14) bond length is 2.21 Å. The Bi(1)-O(4) bond length is 2.25 Å. The Bi(1)-O(6) bond length is 2.41 Å. The Bi(1)-O(8) bond length is 2.45 Å. In the second Bi site, Bi(2) is bonded in a distorted square pyramidal geometry to one O(13), one O(3), one O(5), one O(7), and one O(9) atom. The Bi(2)-O(13) bond length is 2.21 Å. The Bi(2)-O(3) bond length is 2.16 Å. The Bi(2)-O(5) bond length is 2.31 Å. The Bi(2)-O(7) bond length is 2.57 Å. The Bi(2)-O(9) bond length is 2.39 Å. In the third Bi site, Bi(3) is bonded to one O(10), one O(12), one O(16), one O(2), and one O(8) atom to form edge-sharing BiO5 square pyramids. The Bi(3)-O(10) bond length is 2.52 Å. The Bi(3)-O(12) bond length is 2.18 Å. The Bi(3)-O(16) bond length is 2.31 Å. The Bi(3)-O(2) bond length is 2.22 Å. The Bi(3)-O(8) bond length is 2.37 Å. In the fourth Bi site, Bi(4) is bonded in a rectangular see-saw-like geometry to one O(1), one O(11), one O(7), and one O(9) atom. The Bi(4)-O(1) bond length is 2.28 Å. The Bi(4)-O(11) bond length is 2.19 Å. The Bi(4)-O(7) bond length is 2.17 Å. The Bi(4)-O(9) bond length is 2.35 Å. There are sixteen inequivalent O sites. In the first O site, O(1) is bonded to one Mg(1), one Ag(3), one Ag(8), and one Bi(4) atom to form OMgAg2Bi tetrahedra that share  a cornercorner with one O(7)Ag2Bi2 tetrahedra and  a cornercorner with one O(3)Ag3Bi tetrahedra. In the second O site, O(2) is bonded to one Ag(4), one Ag(7), one Ag(9), and one Bi(3) atom to form OAg3Bi tetrahedra that share  a cornercorner with one O(10)Ag2Bi2 tetrahedra,  a cornercorner with one O(8)Ag2Bi2 tetrahedra,  a cornercorner with one O(4)Ag3Bi tetrahedra, and corners with two equivalent O(12)Ag3Bi tetrahedra. In the third O site, O(3) is bonded to one Ag(12), one Ag(3), one Ag(6), and one Bi(2) atom to form distorted OAg3Bi tetrahedra that share  a cornercorner with one O(7)Ag2Bi2 tetrahedra,  a cornercorner with one O(14)Ag3Bi tetrahedra,  a cornercorner with one O(5)Ag3Bi tetrahedra,  a cornercorner with one O(6)Ag3Bi tetrahedra,  a cornercorner with one O(1)MgAg2Bi tetrahedra, and corners with two equivalent O(13)Ag3Bi tetrahedra. In the fourth O site, O(4) is bonded to one Ag(11), one Ag(4), one Ag(5), and one Bi(1) atom to form distorted OAg3Bi tetrahedra that share  a cornercorner with one O(10)Ag2Bi2 tetrahedra,  a cornercorner with one O(8)Ag2Bi2 tetrahedra,  a cornercorner with one O(13)Ag3Bi tetrahedra,  a cornercorner with one O(2)Ag3Bi tetrahedra,  a cornercorner with one O(5)Ag3Bi tetrahedra,  a cornercorner with one O(6)Ag3Bi tetrahedra, and corners with two equivalent O(14)Ag3Bi tetrahedra. In the fifth O site, O(5) is bonded to one Ag(16), one Ag(2), one Ag(5), and one Bi(2) atom to form OAg3Bi tetrahedra that share  a cornercorner with one O(7)Ag2Bi2 tetrahedra,  a cornercorner with one O(13)Ag3Bi tetrahedra,  a cornercorner with one O(14)Ag3Bi tetrahedra,  a cornercorner with one O(3)Ag3Bi tetrahedra,  a cornercorner with one O(4)Ag3Bi tetrahedra, and corners with two equivalent O(8)Ag2Bi2 tetrahedra. In the sixth O site, O(6) is bonded to one Ag(15), one Ag(19), one Ag(6), and one Bi(1) atom to form OAg3Bi tetrahedra that share  a cornercorner with one O(10)Ag2Bi2 tetrahedra,  a cornercorner with one O(8)Ag2Bi2 tetrahedra,  a cornercorner with one O(13)Ag3Bi tetrahedra,  a cornercorner with one O(14)Ag3Bi tetrahedra,  a cornercorner with one O(3)Ag3Bi tetrahedra,  a cornercorner with one O(4)Ag3Bi tetrahedra, and corners with two equivalent O(7)Ag2Bi2 tetrahedra. In the seventh O site, O(7) is bonded to one Ag(15), one Ag(19), one Bi(2), and one Bi(4) atom to form distorted OAg2Bi2 tetrahedra that share  a cornercorner with one O(13)Ag3Bi tetrahedra,  a cornercorner with one O(3)Ag3Bi tetrahedra,  a cornercorner with one O(5)Ag3Bi tetrahedra,  a cornercorner with one O(1)MgAg2Bi tetrahedra, and corners with two equivalent O(6)Ag3Bi tetrahedra. In the eighth O site, O(8) is bonded to one Ag(16), one Ag(2), one Bi(1), and one Bi(3) atom to form OAg2Bi2 tetrahedra that share  a cornercorner with one O(12)Ag3Bi tetrahedra,  a cornercorner with one O(14)Ag3Bi tetrahedra,  a cornercorner with one O(2)Ag3Bi tetrahedra,  a cornercorner with one O(4)Ag3Bi tetrahedra,  a cornercorner with one O(6)Ag3Bi tetrahedra, corners with two equivalent O(5)Ag3Bi tetrahedra, and  an edgeedge with one O(10)Ag2Bi2 tetrahedra. In the ninth O site, O(9) is bonded in a distorted rectangular see-saw-like geometry to one Ag(1), one Ag(17), one Bi(2), and one Bi(4) atom. In the tenth O site, O(10) is bonded to one Ag(18), one Ag(20), one Bi(1), and one Bi(3) atom to form OAg2Bi2 tetrahedra that share  a cornercorner with one O(12)Ag3Bi tetrahedra,  a cornercorner with one O(14)Ag3Bi tetrahedra,  a cornercorner with one O(2)Ag3Bi tetrahedra,  a cornercorner with one O(4)Ag3Bi tetrahedra,  a cornercorner with one O(6)Ag3Bi tetrahedra, and  an edgeedge with one O(8)Ag2Bi2 tetrahedra. In the eleventh O site, O(11) is bonded in a distorted see-saw-like geometry to one Mg(1), one Ag(13), one Ag(9), and one Bi(4) atom. In the twelfth O site, O(12) is bonded to one Ag(10), one Ag(14), one Ag(7), and one Bi(3) atom to form OAg3Bi tetrahedra that share  a cornercorner with one O(10)Ag2Bi2 tetrahedra,  a cornercorner with one O(8)Ag2Bi2 tetrahedra,  a cornercorner with one O(14)Ag3Bi tetrahedra, and corners with two equivalent O(2)Ag3Bi tetrahedra. In the thirteenth O site, O(13) is bonded to one Ag(11), one Ag(13), one Ag(6), and one Bi(2) atom to form OAg3Bi tetrahedra that share  a cornercorner with one O(7)Ag2Bi2 tetrahedra,  a cornercorner with one O(4)Ag3Bi tetrahedra,  a cornercorner with one O(5)Ag3Bi tetrahedra,  a cornercorner with one O(6)Ag3Bi tetrahedra, and corners with two equivalent O(3)Ag3Bi tetrahedra. In the fourteenth O site, O(14) is bonded to one Ag(12), one Ag(14), one Ag(5), and one Bi(1) atom to form OAg3Bi tetrahedra that share  a cornercorner with one O(10)Ag2Bi2 tetrahedra,  a cornercorner with one O(8)Ag2Bi2 tetrahedra,  a cornercorner with one O(12)Ag3Bi tetrahedra,  a cornercorner with one O(3)Ag3Bi tetrahedra,  a cornercorner with one O(5)Ag3Bi tetrahedra,  a cornercorner with one O(6)Ag3Bi tetrahedra, and corners with two equivalent O(4)Ag3Bi tetrahedra. In the fifteenth O site, O(15) is bonded in a 5-coordinate geometry to one Mg(1), one Ag(18), one Ag(20), one Ag(7), and one Ag(9) atom. In the sixteenth O site, O(16) is bonded in a 4-coordinate geometry to one Ag(1), one Ag(17), one Ag(8), and one Bi(3) atom.