Ca8Mn4Al4O21 crystallizes in the tetragonal P4/mmm space group. There are two inequivalent Ca sites. In the first Ca site, Ca(1) is bonded in a distorted q6 geometry to two equivalent O(1), four equivalent O(4), and four equivalent O(5) atoms. In the second Ca site, Ca(2) is bonded in a distorted q6 geometry to one O(3), two equivalent O(2), four equivalent O(4), and four equivalent O(5) atoms. Mn(1) is bonded to one O(1), one O(2), two equivalent O(4), and two equivalent O(5) atoms to form MnO6 octahedra that share corners with two equivalent Mn(1)O6 octahedra and corners with two equivalent Al(2)O5 square pyramids. The corner-sharing octahedra are not tilted. There are two inequivalent Al sites. In the first Al site, Al(1) is bonded in a rectangular see-saw-like geometry to four equivalent O(4) atoms. In the second Al site, Al(2) is bonded to one O(3) and four equivalent O(5) atoms to form AlO5 square pyramids that share corners with four equivalent Mn(1)O6 octahedra and  a cornercorner with one Al(2)O5 square pyramid. The corner-sharing octahedral tilt angles are 12°. There are five inequivalent O sites. In the first O site, O(1) is bonded in a distorted linear geometry to four equivalent Ca(1) and two equivalent Mn(1) atoms. In the second O site, O(2) is bonded in a distorted linear geometry to four equivalent Ca(2) and two equivalent Mn(1) atoms. In the third O site, O(3) is bonded to four equivalent Ca(2) and two equivalent Al(2) atoms to form distorted face-sharing OCa4Al2 octahedra. In the fourth O site, O(4) is bonded in a distorted linear geometry to two equivalent Ca(1), two equivalent Ca(2), one Mn(1), and one Al(1) atom. In the fifth O site, O(5) is bonded to two equivalent Ca(1), two equivalent Ca(2), one Mn(1), and one Al(2) atom to form distorted OCa4MnAl octahedra that share corners with six equivalent O(5)Ca4MnAl octahedra, edges with two equivalent O(5)Ca4MnAl octahedra,  a faceface with one O(3)Ca4Al2 octahedra, and faces with two equivalent O(5)Ca4MnAl octahedra. The corner-sharing octahedral tilt angles range from 7-63°.
Ca8Mn4Al4O21 crystallizes in the tetragonal P4/mmm space group. There are two inequivalent Ca sites. In the first Ca site, Ca(1) is bonded in a distorted q6 geometry to two equivalent O(1), four equivalent O(4), and four equivalent O(5) atoms. Both Ca(1)-O(1) bond lengths are 2.69 Å. All Ca(1)-O(4) bond lengths are 2.71 Å. All Ca(1)-O(5) bond lengths are 2.53 Å. In the second Ca site, Ca(2) is bonded in a distorted q6 geometry to one O(3), two equivalent O(2), four equivalent O(4), and four equivalent O(5) atoms. The Ca(2)-O(3) bond length is 2.56 Å. Both Ca(2)-O(2) bond lengths are 2.70 Å. All Ca(2)-O(4) bond lengths are 2.74 Å. All Ca(2)-O(5) bond lengths are 2.72 Å. Mn(1) is bonded to one O(1), one O(2), two equivalent O(4), and two equivalent O(5) atoms to form MnO6 octahedra that share corners with two equivalent Mn(1)O6 octahedra and corners with two equivalent Al(2)O5 square pyramids. The corner-sharing octahedra are not tilted. The Mn(1)-O(1) bond length is 1.84 Å. The Mn(1)-O(2) bond length is 1.90 Å. Both Mn(1)-O(4) bond lengths are 2.00 Å. Both Mn(1)-O(5) bond lengths are 1.98 Å. There are two inequivalent Al sites. In the first Al site, Al(1) is bonded in a rectangular see-saw-like geometry to four equivalent O(4) atoms. All Al(1)-O(4) bond lengths are 1.80 Å. In the second Al site, Al(2) is bonded to one O(3) and four equivalent O(5) atoms to form AlO5 square pyramids that share corners with four equivalent Mn(1)O6 octahedra and  a cornercorner with one Al(2)O5 square pyramid. The corner-sharing octahedral tilt angles are 12°. The Al(2)-O(3) bond length is 1.75 Å. All Al(2)-O(5) bond lengths are 1.85 Å. There are five inequivalent O sites. In the first O site, O(1) is bonded in a distorted linear geometry to four equivalent Ca(1) and two equivalent Mn(1) atoms. In the second O site, O(2) is bonded in a distorted linear geometry to four equivalent Ca(2) and two equivalent Mn(1) atoms. In the third O site, O(3) is bonded to four equivalent Ca(2) and two equivalent Al(2) atoms to form distorted face-sharing OCa4Al2 octahedra. In the fourth O site, O(4) is bonded in a distorted linear geometry to two equivalent Ca(1), two equivalent Ca(2), one Mn(1), and one Al(1) atom. In the fifth O site, O(5) is bonded to two equivalent Ca(1), two equivalent Ca(2), one Mn(1), and one Al(2) atom to form distorted OCa4MnAl octahedra that share corners with six equivalent O(5)Ca4MnAl octahedra, edges with two equivalent O(5)Ca4MnAl octahedra,  a faceface with one O(3)Ca4Al2 octahedra, and faces with two equivalent O(5)Ca4MnAl octahedra. The corner-sharing octahedral tilt angles range from 7-63°.