Ba2Sr3CaMg2(SiO4)4 crystallizes in the trigonal P3m1 space group. There are two inequivalent Ba sites. In the first Ba site, Ba(1) is bonded to three equivalent O(1), three equivalent O(3), three equivalent O(5), and three equivalent O(7) atoms to form BaO12 cuboctahedra that share edges with six equivalent Ba(1)O12 cuboctahedra, edges with three equivalent Si(1)O4 tetrahedra, edges with three equivalent Si(3)O4 tetrahedra,  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(2), three equivalent O(4), three equivalent O(6), 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(4)O4 tetrahedra,  a faceface with one Mg(1)O6 octahedra, and  a faceface with one Mg(2)O6 octahedra. There are three inequivalent Sr sites. In the first Sr site, Sr(1) is bonded in a 10-coordinate geometry to one O(2), three equivalent O(5), and six equivalent O(8) atoms. In the second Sr site, Sr(2) is bonded in a 10-coordinate geometry to one O(3), three equivalent O(8), and six equivalent O(5) atoms. In the third Sr site, Sr(3) is bonded in a 10-coordinate geometry to one O(4), three equivalent O(7), and six equivalent O(6) atoms. Ca(1) is bonded in a 10-coordinate geometry to one O(1), three equivalent O(6), and six equivalent O(7) atoms. There are two inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to three equivalent O(5) and three equivalent O(8) atoms to form MgO6 octahedra that share corners with three equivalent Si(1)O4 tetrahedra, corners with three equivalent Si(4)O4 tetrahedra,  a faceface with one Ba(1)O12 cuboctahedra, and  a faceface with one Ba(2)O12 cuboctahedra. In the second Mg site, Mg(2) is bonded to three equivalent O(6) and three equivalent O(7) atoms to form MgO6 octahedra that share corners with three equivalent Si(2)O4 tetrahedra, corners with three equivalent Si(3)O4 tetrahedra,  a faceface with one Ba(1)O12 cuboctahedra, and  a faceface with one Ba(2)O12 cuboctahedra. There are four inequivalent Si sites. In the first Si site, Si(1) is bonded to one O(1) and three equivalent O(5) atoms to form SiO4 tetrahedra that share corners with three equivalent Mg(1)O6 octahedra and edges with three equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 13°. In the second Si site, Si(2) is bonded to one O(2) and three equivalent O(6) atoms to form SiO4 tetrahedra that share corners with three equivalent Mg(2)O6 octahedra and edges with three equivalent Ba(2)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 13°. In the third Si site, Si(3) is bonded to one O(3) and three equivalent O(7) atoms to form SiO4 tetrahedra that share corners with three equivalent Mg(2)O6 octahedra and edges with three equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 13°. In the fourth Si site, Si(4) is bonded to one O(4) and three equivalent O(8) atoms to form SiO4 tetrahedra that share corners with three equivalent Mg(1)O6 octahedra and edges with three equivalent Ba(2)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 13°. There are eight inequivalent O sites. In the first O site, O(1) is bonded in a distorted linear geometry to three equivalent Ba(1), one Ca(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(1), and one Si(2) atom. In the third O site, O(3) is bonded in a distorted linear geometry to three equivalent Ba(1), one Sr(2), and one Si(3) atom. In the fourth O site, O(4) is bonded in a distorted linear geometry to three equivalent Ba(2), one Sr(3), and one Si(4) atom. In the fifth O site, O(5) is bonded in a 2-coordinate geometry to one Ba(1), one Sr(1), two equivalent Sr(2), one Mg(1), and one Si(1) atom. In the sixth O site, O(6) is bonded in a 2-coordinate geometry to one Ba(2), two equivalent Sr(3), one Ca(1), one Mg(2), and one Si(2) atom. In the seventh O site, O(7) is bonded in a 2-coordinate geometry to one Ba(1), one Sr(3), two equivalent Ca(1), one Mg(2), and one Si(3) atom. In the eighth O site, O(8) is bonded in a 2-coordinate geometry to one Ba(2), one Sr(2), two equivalent Sr(1), one Mg(1), and one Si(4) atom.
Ba2Sr3CaMg2(SiO4)4 crystallizes in the trigonal P3m1 space group. There are two inequivalent Ba sites. In the first Ba site, Ba(1) is bonded to three equivalent O(1), three equivalent O(3), three equivalent O(5), and three equivalent O(7) atoms to form BaO12 cuboctahedra that share edges with six equivalent Ba(1)O12 cuboctahedra, edges with three equivalent Si(1)O4 tetrahedra, edges with three equivalent Si(3)O4 tetrahedra,  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 3.20 Å. All Ba(1)-O(3) bond lengths are 3.20 Å. All Ba(1)-O(5) bond lengths are 2.83 Å. All Ba(1)-O(7) bond lengths are 2.81 Å. In the second Ba site, Ba(2) is bonded to three equivalent O(2), three equivalent O(4), three equivalent O(6), 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(4)O4 tetrahedra,  a faceface with one Mg(1)O6 octahedra, and  a faceface with one Mg(2)O6 octahedra. All Ba(2)-O(2) bond lengths are 3.20 Å. All Ba(2)-O(4) bond lengths are 3.20 Å. All Ba(2)-O(6) bond lengths are 2.84 Å. All Ba(2)-O(8) bond lengths are 2.84 Å. There are three inequivalent Sr sites. In the first Sr site, Sr(1) is bonded in a 10-coordinate geometry to one O(2), three equivalent O(5), and six equivalent O(8) atoms. The Sr(1)-O(2) bond length is 2.40 Å. All Sr(1)-O(5) bond lengths are 2.85 Å. All Sr(1)-O(8) bond lengths are 2.78 Å. In the second Sr site, Sr(2) is bonded in a 10-coordinate geometry to one O(3), three equivalent O(8), and six equivalent O(5) atoms. The Sr(2)-O(3) bond length is 2.37 Å. All Sr(2)-O(8) bond lengths are 2.83 Å. All Sr(2)-O(5) bond lengths are 2.78 Å. In the third Sr site, Sr(3) is bonded in a 10-coordinate geometry to one O(4), three equivalent O(7), and six equivalent O(6) atoms. The Sr(3)-O(4) bond length is 2.39 Å. All Sr(3)-O(7) bond lengths are 2.82 Å. All Sr(3)-O(6) bond lengths are 2.78 Å. Ca(1) is bonded in a 10-coordinate geometry to one O(1), three equivalent O(6), and six equivalent O(7) atoms. The Ca(1)-O(1) bond length is 2.28 Å. All Ca(1)-O(6) bond lengths are 2.85 Å. All Ca(1)-O(7) bond lengths are 2.77 Å. There are two inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to three equivalent O(5) and three equivalent O(8) atoms to form MgO6 octahedra that share corners with three equivalent Si(1)O4 tetrahedra, corners with three equivalent Si(4)O4 tetrahedra,  a faceface with one Ba(1)O12 cuboctahedra, and  a faceface with one Ba(2)O12 cuboctahedra. All Mg(1)-O(5) bond lengths are 2.10 Å. All Mg(1)-O(8) bond lengths are 2.09 Å. In the second Mg site, Mg(2) is bonded to three equivalent O(6) and three equivalent O(7) atoms to form MgO6 octahedra that share corners with three equivalent Si(2)O4 tetrahedra, corners with three equivalent Si(3)O4 tetrahedra,  a faceface with one Ba(1)O12 cuboctahedra, and  a faceface with one Ba(2)O12 cuboctahedra. All Mg(2)-O(6) bond lengths are 2.09 Å. All Mg(2)-O(7) bond lengths are 2.09 Å. There are four inequivalent Si sites. In the first Si site, Si(1) is bonded to one O(1) and three equivalent O(5) atoms to form SiO4 tetrahedra that share corners with three equivalent Mg(1)O6 octahedra and edges with three equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 13°. The Si(1)-O(1) bond length is 1.63 Å. All Si(1)-O(5) bond lengths are 1.66 Å. In the second Si site, Si(2) is bonded to one O(2) and three equivalent O(6) atoms to form SiO4 tetrahedra that share corners with three equivalent Mg(2)O6 octahedra and edges with three equivalent Ba(2)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 13°. The Si(2)-O(2) bond length is 1.62 Å. All Si(2)-O(6) bond lengths are 1.66 Å. In the third Si site, Si(3) is bonded to one O(3) and three equivalent O(7) atoms to form SiO4 tetrahedra that share corners with three equivalent Mg(2)O6 octahedra and edges with three equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 13°. The Si(3)-O(3) bond length is 1.61 Å. All Si(3)-O(7) bond lengths are 1.66 Å. In the fourth Si site, Si(4) is bonded to one O(4) and three equivalent O(8) atoms to form SiO4 tetrahedra that share corners with three equivalent Mg(1)O6 octahedra and edges with three equivalent Ba(2)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 13°. The Si(4)-O(4) bond length is 1.62 Å. All Si(4)-O(8) bond lengths are 1.66 Å. There are eight inequivalent O sites. In the first O site, O(1) is bonded in a distorted linear geometry to three equivalent Ba(1), one Ca(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(1), and one Si(2) atom. In the third O site, O(3) is bonded in a distorted linear geometry to three equivalent Ba(1), one Sr(2), and one Si(3) atom. In the fourth O site, O(4) is bonded in a distorted linear geometry to three equivalent Ba(2), one Sr(3), and one Si(4) atom. In the fifth O site, O(5) is bonded in a 2-coordinate geometry to one Ba(1), one Sr(1), two equivalent Sr(2), one Mg(1), and one Si(1) atom. In the sixth O site, O(6) is bonded in a 2-coordinate geometry to one Ba(2), two equivalent Sr(3), one Ca(1), one Mg(2), and one Si(2) atom. In the seventh O site, O(7) is bonded in a 2-coordinate geometry to one Ba(1), one Sr(3), two equivalent Ca(1), one Mg(2), and one Si(3) atom. In the eighth O site, O(8) is bonded in a 2-coordinate geometry to one Ba(2), one Sr(2), two equivalent Sr(1), one Mg(1), and one Si(4) atom.