Ba3Sr2Ca4Mg3(SiO4)6 crystallizes in the trigonal P3 space group. There are three inequivalent Ba sites. In the first Ba site, Ba(1) is bonded to three equivalent O(1), three equivalent O(10), three equivalent O(4), and three equivalent O(7) atoms to form BaO12 cuboctahedra that share corners with three equivalent Ca(3)O7 trigonal pyramids, edges with six equivalent Ba(1)O12 cuboctahedra, edges with three equivalent Si(1)O4 tetrahedra, edges with three equivalent Si(4)O4 tetrahedra, edges with three equivalent Ca(2)O4 trigonal pyramids,  a faceface with one Mg(1)O6 octahedra, and  a faceface with one Mg(2)O6 octahedra. In the second Ba site, Ba(2) is bonded to three equivalent O(11), three equivalent O(2), three equivalent O(5), and three equivalent O(8) atoms to form BaO12 cuboctahedra that share edges with six equivalent Ba(2)O12 cuboctahedra, edges with three equivalent Si(2)O4 tetrahedra, edges with three equivalent Si(5)O4 tetrahedra, edges with three equivalent Ca(3)O7 trigonal pyramids,  a faceface with one Mg(2)O6 octahedra, and  a faceface with one Mg(3)O6 octahedra. In the third Ba site, Ba(3) is bonded to three equivalent O(12), three equivalent O(3), three equivalent O(6), and three equivalent O(9) atoms to form BaO12 cuboctahedra that share edges with six equivalent Ba(3)O12 cuboctahedra, edges with three equivalent Si(3)O4 tetrahedra, edges with three equivalent Si(6)O4 tetrahedra,  a faceface with one Mg(1)O6 octahedra, and  a faceface with one Mg(3)O6 octahedra. There are two inequivalent Sr sites. In the first Sr site, Sr(1) is bonded in a 10-coordinate geometry to one O(1), three equivalent O(8), and six equivalent O(10) atoms. In the second Sr site, Sr(2) is bonded in a 10-coordinate geometry to one O(2), three equivalent O(9), and six equivalent O(11) atoms. There are four inequivalent Ca sites. In the first Ca site, Ca(1) is bonded in a 4-coordinate geometry to one O(3) and three equivalent O(12) atoms. In the second Ca site, Ca(2) is bonded to one O(4) and three equivalent O(7) atoms to form distorted CaO4 trigonal pyramids that share corners with three equivalent Mg(1)O6 octahedra,  a cornercorner with one Si(4)O4 tetrahedra, corners with three equivalent Si(1)O4 tetrahedra, and edges with three equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 83°. In the third Ca site, Ca(3) is bonded to one O(5), three equivalent O(10), and three equivalent O(8) atoms to form distorted CaO7 trigonal pyramids that share corners with three equivalent Ba(1)O12 cuboctahedra,  a cornercorner with one Si(5)O4 tetrahedra, corners with three equivalent Si(2)O4 tetrahedra, edges with three equivalent Ba(2)O12 cuboctahedra, edges with three equivalent Mg(2)O6 octahedra, and  a faceface with one Si(4)O4 tetrahedra. In the fourth Ca site, Ca(4) is bonded in a 4-coordinate geometry to one O(6), three equivalent O(11), and three equivalent O(9) atoms. There are three inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to three equivalent O(12) and three equivalent O(7) atoms to form MgO6 octahedra that share corners with three equivalent Si(1)O4 tetrahedra, corners with three equivalent Si(6)O4 tetrahedra, corners with three equivalent Ca(2)O4 trigonal pyramids,  a faceface with one Ba(1)O12 cuboctahedra, and  a faceface with one Ba(3)O12 cuboctahedra. In the second Mg site, Mg(2) is bonded to three equivalent O(10) and three equivalent O(8) atoms to form MgO6 octahedra that share corners with three equivalent Si(2)O4 tetrahedra, corners with three equivalent Si(4)O4 tetrahedra, edges with three equivalent Ca(3)O7 trigonal pyramids,  a faceface with one Ba(1)O12 cuboctahedra, and  a faceface with one Ba(2)O12 cuboctahedra. In the third Mg site, Mg(3) is bonded to three equivalent O(11) and three equivalent O(9) atoms to form MgO6 octahedra that share corners with three equivalent Si(3)O4 tetrahedra, corners with three equivalent Si(5)O4 tetrahedra,  a faceface with one Ba(2)O12 cuboctahedra, and  a faceface with one Ba(3)O12 cuboctahedra. There are six inequivalent Si sites. In the first Si site, Si(1) is bonded to one O(1) and three equivalent O(7) atoms to form SiO4 tetrahedra that share corners with three equivalent Mg(1)O6 octahedra, corners with three equivalent Ca(2)O4 trigonal pyramids, and edges with three equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 25°. In the second Si site, Si(2) is bonded to one O(2) and three equivalent O(8) atoms to form SiO4 tetrahedra that share corners with three equivalent Mg(2)O6 octahedra, corners with three equivalent Ca(3)O7 trigonal pyramids, and edges with three equivalent Ba(2)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 24°. In the third Si site, Si(3) is bonded to one O(3) and three equivalent O(9) atoms to form SiO4 tetrahedra that share corners with three equivalent Mg(3)O6 octahedra and edges with three equivalent Ba(3)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 23°. In the fourth Si site, Si(4) is bonded to one O(4) and three equivalent O(10) atoms to form SiO4 tetrahedra that share corners with three equivalent Mg(2)O6 octahedra,  a cornercorner with one Ca(2)O4 trigonal pyramid, edges with three equivalent Ba(1)O12 cuboctahedra, and  a faceface with one Ca(3)O7 trigonal pyramid. The corner-sharing octahedral tilt angles are 15°. In the fifth Si site, Si(5) is bonded to one O(5) and three equivalent O(11) atoms to form SiO4 tetrahedra that share corners with three equivalent Mg(3)O6 octahedra,  a cornercorner with one Ca(3)O7 trigonal pyramid, and edges with three equivalent Ba(2)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 15°. In the sixth Si site, Si(6) is bonded to one O(6) and three equivalent O(12) atoms to form SiO4 tetrahedra that share corners with three equivalent Mg(1)O6 octahedra and edges with three equivalent Ba(3)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 25°. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a distorted linear geometry to three equivalent Ba(1), one Sr(1), and one Si(1) atom. In the second O site, O(2) is bonded in a distorted linear geometry to three equivalent Ba(2), one Sr(2), and one Si(2) atom. In the third O site, O(3) is bonded in a distorted linear geometry to three equivalent Ba(3), one Ca(1), and one Si(3) atom. In the fourth O site, O(4) is bonded in a distorted linear geometry to three equivalent Ba(1), one Ca(2), and one Si(4) atom. In the fifth O site, O(5) is bonded in a distorted linear geometry to three equivalent Ba(2), one Ca(3), and one Si(5) atom. In the sixth O site, O(6) is bonded in a distorted linear geometry to three equivalent Ba(3), one Ca(4), and one Si(6) atom. In the seventh O site, O(7) is bonded in a 3-coordinate geometry to one Ba(1), one Ca(2), one Mg(1), and one Si(1) atom. In the eighth O site, O(8) is bonded in a 3-coordinate geometry to one Ba(2), one Sr(1), one Ca(3), one Mg(2), and one Si(2) atom. In the ninth O site, O(9) is bonded in a 3-coordinate geometry to one Ba(3), one Sr(2), one Ca(4), one Mg(3), and one Si(3) atom. In the tenth O site, O(10) is bonded in a 6-coordinate geometry to one Ba(1), two equivalent Sr(1), one Ca(3), one Mg(2), and one Si(4) atom. In the eleventh O site, O(11) is bonded in a 6-coordinate geometry to one Ba(2), two equivalent Sr(2), one Ca(4), one Mg(3), and one Si(5) atom. In the twelfth O site, O(12) is bonded in a 3-coordinate geometry to one Ba(3), one Ca(1), one Mg(1), and one Si(6) atom.
Ba3Sr2Ca4Mg3(SiO4)6 crystallizes in the trigonal P3 space group. There are three inequivalent Ba sites. In the first Ba site, Ba(1) is bonded to three equivalent O(1), three equivalent O(10), three equivalent O(4), and three equivalent O(7) atoms to form BaO12 cuboctahedra that share corners with three equivalent Ca(3)O7 trigonal pyramids, edges with six equivalent Ba(1)O12 cuboctahedra, edges with three equivalent Si(1)O4 tetrahedra, edges with three equivalent Si(4)O4 tetrahedra, edges with three equivalent Ca(2)O4 trigonal pyramids,  a faceface with one Mg(1)O6 octahedra, and  a faceface with one Mg(2)O6 octahedra. All Ba(1)-O(1) bond lengths are 3.19 Å. All Ba(1)-O(10) bond lengths are 2.81 Å. All Ba(1)-O(4) bond lengths are 3.19 Å. All Ba(1)-O(7) bond lengths are 2.86 Å. In the second Ba site, Ba(2) is bonded to three equivalent O(11), three equivalent O(2), three equivalent O(5), and three equivalent O(8) atoms to form BaO12 cuboctahedra that share edges with six equivalent Ba(2)O12 cuboctahedra, edges with three equivalent Si(2)O4 tetrahedra, edges with three equivalent Si(5)O4 tetrahedra, edges with three equivalent Ca(3)O7 trigonal pyramids,  a faceface with one Mg(2)O6 octahedra, and  a faceface with one Mg(3)O6 octahedra. All Ba(2)-O(11) bond lengths are 2.81 Å. All Ba(2)-O(2) bond lengths are 3.19 Å. All Ba(2)-O(5) bond lengths are 3.19 Å. All Ba(2)-O(8) bond lengths are 2.83 Å. In the third Ba site, Ba(3) is bonded to three equivalent O(12), three equivalent O(3), three equivalent O(6), and three equivalent O(9) atoms to form BaO12 cuboctahedra that share edges with six equivalent Ba(3)O12 cuboctahedra, edges with three equivalent Si(3)O4 tetrahedra, edges with three equivalent Si(6)O4 tetrahedra,  a faceface with one Mg(1)O6 octahedra, and  a faceface with one Mg(3)O6 octahedra. All Ba(3)-O(12) bond lengths are 2.81 Å. All Ba(3)-O(3) bond lengths are 3.19 Å. All Ba(3)-O(6) bond lengths are 3.19 Å. All Ba(3)-O(9) bond lengths are 2.81 Å. There are two inequivalent Sr sites. In the first Sr site, Sr(1) is bonded in a 10-coordinate geometry to one O(1), three equivalent O(8), and six equivalent O(10) atoms. The Sr(1)-O(1) bond length is 2.38 Å. All Sr(1)-O(8) bond lengths are 2.82 Å. There are three shorter (2.63 Å) and three longer (2.89 Å) Sr(1)-O(10) bond lengths. In the second Sr site, Sr(2) is bonded in a 10-coordinate geometry to one O(2), three equivalent O(9), and six equivalent O(11) atoms. The Sr(2)-O(2) bond length is 2.37 Å. All Sr(2)-O(9) bond lengths are 2.81 Å. There are three shorter (2.64 Å) and three longer (2.89 Å) Sr(2)-O(11) bond lengths. There are four inequivalent Ca sites. In the first Ca site, Ca(1) is bonded in a 4-coordinate geometry to one O(3) and three equivalent O(12) atoms. The Ca(1)-O(3) bond length is 2.26 Å. All Ca(1)-O(12) bond lengths are 2.42 Å. In the second Ca site, Ca(2) is bonded to one O(4) and three equivalent O(7) atoms to form distorted CaO4 trigonal pyramids that share corners with three equivalent Mg(1)O6 octahedra,  a cornercorner with one Si(4)O4 tetrahedra, corners with three equivalent Si(1)O4 tetrahedra, and edges with three equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 83°. The Ca(2)-O(4) bond length is 2.28 Å. All Ca(2)-O(7) bond lengths are 2.41 Å. In the third Ca site, Ca(3) is bonded to one O(5), three equivalent O(10), and three equivalent O(8) atoms to form distorted CaO7 trigonal pyramids that share corners with three equivalent Ba(1)O12 cuboctahedra,  a cornercorner with one Si(5)O4 tetrahedra, corners with three equivalent Si(2)O4 tetrahedra, edges with three equivalent Ba(2)O12 cuboctahedra, edges with three equivalent Mg(2)O6 octahedra, and  a faceface with one Si(4)O4 tetrahedra. The Ca(3)-O(5) bond length is 2.28 Å. All Ca(3)-O(10) bond lengths are 2.86 Å. All Ca(3)-O(8) bond lengths are 2.44 Å. In the fourth Ca site, Ca(4) is bonded in a 4-coordinate geometry to one O(6), three equivalent O(11), and three equivalent O(9) atoms. The Ca(4)-O(6) bond length is 2.24 Å. All Ca(4)-O(11) bond lengths are 2.84 Å. All Ca(4)-O(9) bond lengths are 2.45 Å. There are three inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to three equivalent O(12) and three equivalent O(7) atoms to form MgO6 octahedra that share corners with three equivalent Si(1)O4 tetrahedra, corners with three equivalent Si(6)O4 tetrahedra, corners with three equivalent Ca(2)O4 trigonal pyramids,  a faceface with one Ba(1)O12 cuboctahedra, and  a faceface with one Ba(3)O12 cuboctahedra. All Mg(1)-O(12) bond lengths are 2.12 Å. All Mg(1)-O(7) bond lengths are 2.11 Å. In the second Mg site, Mg(2) is bonded to three equivalent O(10) and three equivalent O(8) atoms to form MgO6 octahedra that share corners with three equivalent Si(2)O4 tetrahedra, corners with three equivalent Si(4)O4 tetrahedra, edges with three equivalent Ca(3)O7 trigonal pyramids,  a faceface with one Ba(1)O12 cuboctahedra, and  a faceface with one Ba(2)O12 cuboctahedra. All Mg(2)-O(10) bond lengths are 2.09 Å. All Mg(2)-O(8) bond lengths are 2.12 Å. In the third Mg site, Mg(3) is bonded to three equivalent O(11) and three equivalent O(9) atoms to form MgO6 octahedra that share corners with three equivalent Si(3)O4 tetrahedra, corners with three equivalent Si(5)O4 tetrahedra,  a faceface with one Ba(2)O12 cuboctahedra, and  a faceface with one Ba(3)O12 cuboctahedra. All Mg(3)-O(11) bond lengths are 2.09 Å. All Mg(3)-O(9) bond lengths are 2.13 Å. There are six inequivalent Si sites. In the first Si site, Si(1) is bonded to one O(1) and three equivalent O(7) atoms to form SiO4 tetrahedra that share corners with three equivalent Mg(1)O6 octahedra, corners with three equivalent Ca(2)O4 trigonal pyramids, and edges with three equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 25°. The Si(1)-O(1) bond length is 1.61 Å. All Si(1)-O(7) bond lengths are 1.66 Å. In the second Si site, Si(2) is bonded to one O(2) and three equivalent O(8) atoms to form SiO4 tetrahedra that share corners with three equivalent Mg(2)O6 octahedra, corners with three equivalent Ca(3)O7 trigonal pyramids, and edges with three equivalent Ba(2)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 24°. The Si(2)-O(2) bond length is 1.61 Å. All Si(2)-O(8) bond lengths are 1.66 Å. In the third Si site, Si(3) is bonded to one O(3) and three equivalent O(9) atoms to form SiO4 tetrahedra that share corners with three equivalent Mg(3)O6 octahedra and edges with three equivalent Ba(3)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 23°. The Si(3)-O(3) bond length is 1.61 Å. All Si(3)-O(9) bond lengths are 1.67 Å. In the fourth Si site, Si(4) is bonded to one O(4) and three equivalent O(10) atoms to form SiO4 tetrahedra that share corners with three equivalent Mg(2)O6 octahedra,  a cornercorner with one Ca(2)O4 trigonal pyramid, edges with three equivalent Ba(1)O12 cuboctahedra, and  a faceface with one Ca(3)O7 trigonal pyramid. The corner-sharing octahedral tilt angles are 15°. The Si(4)-O(4) bond length is 1.63 Å. All Si(4)-O(10) bond lengths are 1.66 Å. In the fifth Si site, Si(5) is bonded to one O(5) and three equivalent O(11) atoms to form SiO4 tetrahedra that share corners with three equivalent Mg(3)O6 octahedra,  a cornercorner with one Ca(3)O7 trigonal pyramid, and edges with three equivalent Ba(2)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 15°. The Si(5)-O(5) bond length is 1.63 Å. All Si(5)-O(11) bond lengths are 1.66 Å. In the sixth Si site, Si(6) is bonded to one O(6) and three equivalent O(12) atoms to form SiO4 tetrahedra that share corners with three equivalent Mg(1)O6 octahedra and edges with three equivalent Ba(3)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 25°. The Si(6)-O(6) bond length is 1.63 Å. All Si(6)-O(12) bond lengths are 1.66 Å. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a distorted linear geometry to three equivalent Ba(1), one Sr(1), and one Si(1) atom. In the second O site, O(2) is bonded in a distorted linear geometry to three equivalent Ba(2), one Sr(2), and one Si(2) atom. In the third O site, O(3) is bonded in a distorted linear geometry to three equivalent Ba(3), one Ca(1), and one Si(3) atom. In the fourth O site, O(4) is bonded in a distorted linear geometry to three equivalent Ba(1), one Ca(2), and one Si(4) atom. In the fifth O site, O(5) is bonded in a distorted linear geometry to three equivalent Ba(2), one Ca(3), and one Si(5) atom. In the sixth O site, O(6) is bonded in a distorted linear geometry to three equivalent Ba(3), one Ca(4), and one Si(6) atom. In the seventh O site, O(7) is bonded in a 3-coordinate geometry to one Ba(1), one Ca(2), one Mg(1), and one Si(1) atom. In the eighth O site, O(8) is bonded in a 3-coordinate geometry to one Ba(2), one Sr(1), one Ca(3), one Mg(2), and one Si(2) atom. In the ninth O site, O(9) is bonded in a 3-coordinate geometry to one Ba(3), one Sr(2), one Ca(4), one Mg(3), and one Si(3) atom. In the tenth O site, O(10) is bonded in a 6-coordinate geometry to one Ba(1), two equivalent Sr(1), one Ca(3), one Mg(2), and one Si(4) atom. In the eleventh O site, O(11) is bonded in a 6-coordinate geometry to one Ba(2), two equivalent Sr(2), one Ca(4), one Mg(3), and one Si(5) atom. In the twelfth O site, O(12) is bonded in a 3-coordinate geometry to one Ba(3), one Ca(1), one Mg(1), and one Si(6) atom.