Ca8Cr2Mn6O21 crystallizes in the monoclinic Pm space group. There are four inequivalent Ca sites. In the first Ca site, Ca(1) is bonded in a distorted q6 geometry to one O(10), one O(14), one O(15), one O(16), one O(17), one O(2), one O(7), one O(8), and one O(9) atom. In the second Ca site, Ca(2) is bonded in a 7-coordinate geometry to one O(10), one O(15), one O(17), one O(3), one O(5), one O(6), and one O(8) atom. In the third Ca site, Ca(3) is bonded in a 9-coordinate geometry to one O(11), one O(12), one O(13), one O(14), one O(15), one O(16), one O(17), one O(2), and one O(4) atom. In the fourth Ca site, Ca(4) is bonded in a 9-coordinate geometry to one O(1), one O(11), one O(13), one O(15), one O(16), one O(17), one O(3), one O(5), and one O(6) atom. There are two inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(1), one O(7), and two equivalent O(14) atoms to form CrO4 tetrahedra that share corners with two equivalent Mn(2)O6 octahedra,  a cornercorner with one Mn(1)O5 square pyramid, and  a cornercorner with one Cr(2)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles are 40°. In the second Cr site, Cr(2) is bonded to one O(4), one O(5), one O(7), and two equivalent O(16) atoms to form CrO5 trigonal bipyramids that share corners with two equivalent Mn(4)O6 octahedra, corners with two equivalent Mn(5)O5 square pyramids, and  a cornercorner with one Cr(1)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 14-34°. There are six inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to one O(1), one O(11), one O(8), and two equivalent O(15) atoms to form MnO5 square pyramids that share corners with two equivalent Mn(3)O6 octahedra, corners with two equivalent Mn(4)O6 octahedra, and  a cornercorner with one Cr(1)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 2-4°. In the second Mn site, Mn(2) is bonded to one O(12), one O(2), one O(3), one O(9), and two equivalent O(14) atoms to form distorted MnO6 octahedra that share corners with two equivalent Mn(3)O6 octahedra, corners with two equivalent Mn(5)O5 square pyramids, and corners with two equivalent Cr(1)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 6-7°. In the third Mn site, Mn(3) is bonded to one O(10), one O(13), one O(2), one O(3), and two equivalent O(15) atoms to form MnO6 octahedra that share corners with two equivalent Mn(2)O6 octahedra, corners with two equivalent Mn(1)O5 square pyramids, and corners with two equivalent Mn(6)O5 square pyramids. The corner-sharing octahedral tilt angles range from 6-7°. In the fourth Mn site, Mn(4) is bonded to one O(11), one O(4), one O(5), one O(8), and two equivalent O(17) atoms to form MnO6 octahedra that share corners with two equivalent Mn(1)O5 square pyramids, corners with two equivalent Mn(6)O5 square pyramids, and corners with two equivalent Cr(2)O5 trigonal bipyramids. In the fifth Mn site, Mn(5) is bonded to one O(12), one O(6), one O(9), and two equivalent O(16) atoms to form MnO5 square pyramids that share corners with two equivalent Mn(2)O6 octahedra,  a cornercorner with one Mn(6)O5 square pyramid, and corners with two equivalent Cr(2)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 14-17°. In the sixth Mn site, Mn(6) is bonded to one O(10), one O(13), one O(6), and two equivalent O(17) atoms to form MnO5 square pyramids that share corners with two equivalent Mn(3)O6 octahedra, corners with two equivalent Mn(4)O6 octahedra, and  a cornercorner with one Mn(5)O5 square pyramid. The corner-sharing octahedral tilt angles range from 2-7°. There are seventeen inequivalent O sites. In the first O site, O(1) is bonded in a distorted rectangular see-saw-like geometry to two equivalent Ca(4), one Cr(1), and one Mn(1) atom. In the second O site, O(2) is bonded in a distorted linear geometry to two equivalent Ca(1), two equivalent Ca(3), one Mn(2), and one Mn(3) atom. In the third O site, O(3) is bonded in a distorted linear geometry to two equivalent Ca(2), two equivalent Ca(4), one Mn(2), and one Mn(3) atom. In the fourth O site, O(4) is bonded to two equivalent Ca(3), one Cr(2), and one Mn(4) atom to form distorted OCa2MnCr tetrahedra that share  a cornercorner with one O(8)Ca4Mn2 octahedra, corners with two equivalent O(13)Ca4Mn2 octahedra, corners with two equivalent O(15)Ca4Mn2 octahedra,  a cornercorner with one O(7)Ca2Cr2 tetrahedra, edges with two equivalent O(17)Ca4Mn2 octahedra, and  a faceface with one O(11)Ca4Mn2 octahedra. The corner-sharing octahedral tilt angles range from 48-76°. In the fifth O site, O(5) is bonded in a 6-coordinate geometry to two equivalent Ca(2), two equivalent Ca(4), one Cr(2), and one Mn(4) atom. In the sixth O site, O(6) is bonded in a 6-coordinate geometry to two equivalent Ca(2), two equivalent Ca(4), one Mn(5), and one Mn(6) atom. In the seventh O site, O(7) is bonded to two equivalent Ca(1), one Cr(1), and one Cr(2) atom to form distorted OCa2Cr2 tetrahedra that share corners with two equivalent O(10)Ca4Mn2 octahedra, corners with two equivalent O(15)Ca4Mn2 octahedra, corners with two equivalent O(17)Ca4Mn2 octahedra,  a cornercorner with one O(4)Ca2MnCr tetrahedra, and  an edgeedge with one O(8)Ca4Mn2 octahedra. The corner-sharing octahedral tilt angles range from 12-72°. In the eighth O site, O(8) is bonded to two equivalent Ca(1), two equivalent Ca(2), one Mn(1), and one Mn(4) atom to form distorted OCa4Mn2 octahedra that share corners with two equivalent O(11)Ca4Mn2 octahedra,  a cornercorner with one O(4)Ca2MnCr tetrahedra, edges with two equivalent O(10)Ca4Mn2 octahedra,  an edgeedge with one O(7)Ca2Cr2 tetrahedra, faces with two equivalent O(15)Ca4Mn2 octahedra, and faces with two equivalent O(17)Ca4Mn2 octahedra. The corner-sharing octahedral tilt angles range from 3-8°. In the ninth O site, O(9) is bonded in a distorted rectangular see-saw-like geometry to two equivalent Ca(1), one Mn(2), and one Mn(5) atom. In the tenth O site, O(10) is bonded to two equivalent Ca(1), two equivalent Ca(2), one Mn(3), and one Mn(6) atom to form distorted OCa4Mn2 octahedra that share corners with two equivalent O(13)Ca4Mn2 octahedra, corners with two equivalent O(7)Ca2Cr2 tetrahedra, edges with two equivalent O(8)Ca4Mn2 octahedra, faces with two equivalent O(15)Ca4Mn2 octahedra, and faces with two equivalent O(17)Ca4Mn2 octahedra. The corner-sharing octahedral tilt angles are 4°. In the eleventh O site, O(11) is bonded to two equivalent Ca(3), two equivalent Ca(4), one Mn(1), and one Mn(4) atom to form distorted OCa4Mn2 octahedra that share corners with two equivalent O(8)Ca4Mn2 octahedra, edges with two equivalent O(13)Ca4Mn2 octahedra, faces with two equivalent O(15)Ca4Mn2 octahedra, faces with two equivalent O(17)Ca4Mn2 octahedra, and  a faceface with one O(4)Ca2MnCr tetrahedra. The corner-sharing octahedral tilt angles range from 3-8°. In the twelfth O site, O(12) is bonded in a 4-coordinate geometry to two equivalent Ca(3), one Mn(2), and one Mn(5) atom. In the thirteenth O site, O(13) is bonded to two equivalent Ca(3), two equivalent Ca(4), one Mn(3), and one Mn(6) atom to form distorted OCa4Mn2 octahedra that share corners with two equivalent O(10)Ca4Mn2 octahedra, corners with two equivalent O(4)Ca2MnCr tetrahedra, edges with two equivalent O(11)Ca4Mn2 octahedra, faces with two equivalent O(15)Ca4Mn2 octahedra, and faces with two equivalent O(17)Ca4Mn2 octahedra. The corner-sharing octahedral tilt angles are 4°. In the fourteenth O site, O(14) is bonded in a 4-coordinate geometry to one Ca(1), one Ca(3), one Cr(1), and one Mn(2) atom. In the fifteenth O site, O(15) is bonded to one Ca(1), one Ca(2), one Ca(3), one Ca(4), one Mn(1), and one Mn(3) atom to form distorted OCa4Mn2 octahedra that share corners with two equivalent O(15)Ca4Mn2 octahedra,  a cornercorner with one O(7)Ca2Cr2 tetrahedra,  a cornercorner with one O(4)Ca2MnCr tetrahedra, edges with two equivalent O(17)Ca4Mn2 octahedra,  a faceface with one O(10)Ca4Mn2 octahedra,  a faceface with one O(11)Ca4Mn2 octahedra,  a faceface with one O(13)Ca4Mn2 octahedra, and  a faceface with one O(8)Ca4Mn2 octahedra. The corner-sharing octahedral tilt angles range from 3-6°. In the sixteenth O site, O(16) is bonded in a 2-coordinate geometry to one Ca(1), one Ca(3), one Ca(4), one Cr(2), and one Mn(5) atom. In the seventeenth O site, O(17) is bonded to one Ca(1), one Ca(2), one Ca(3), one Ca(4), one Mn(4), and one Mn(6) atom to form distorted OCa4Mn2 octahedra that share corners with two equivalent O(17)Ca4Mn2 octahedra,  a cornercorner with one O(7)Ca2Cr2 tetrahedra, edges with two equivalent O(15)Ca4Mn2 octahedra,  an edgeedge with one O(4)Ca2MnCr tetrahedra,  a faceface with one O(10)Ca4Mn2 octahedra,  a faceface with one O(11)Ca4Mn2 octahedra,  a faceface with one O(13)Ca4Mn2 octahedra, and  a faceface with one O(8)Ca4Mn2 octahedra. The corner-sharing octahedral tilt angles range from 6-11°.
Ca8Cr2Mn6O21 crystallizes in the monoclinic Pm space group. There are four inequivalent Ca sites. In the first Ca site, Ca(1) is bonded in a distorted q6 geometry to one O(10), one O(14), one O(15), one O(16), one O(17), one O(2), one O(7), one O(8), and one O(9) atom. The Ca(1)-O(10) bond length is 2.58 Å. The Ca(1)-O(14) bond length is 2.60 Å. The Ca(1)-O(15) bond length is 2.57 Å. The Ca(1)-O(16) bond length is 2.76 Å. The Ca(1)-O(17) bond length is 2.72 Å. The Ca(1)-O(2) bond length is 2.51 Å. The Ca(1)-O(7) bond length is 2.51 Å. The Ca(1)-O(8) bond length is 2.75 Å. The Ca(1)-O(9) bond length is 2.48 Å. In the second Ca site, Ca(2) is bonded in a 7-coordinate geometry to one O(10), one O(15), one O(17), one O(3), one O(5), one O(6), and one O(8) atom. The Ca(2)-O(10) bond length is 2.42 Å. The Ca(2)-O(15) bond length is 2.49 Å. The Ca(2)-O(17) bond length is 2.50 Å. The Ca(2)-O(3) bond length is 2.70 Å. The Ca(2)-O(5) bond length is 2.97 Å. The Ca(2)-O(6) bond length is 2.52 Å. The Ca(2)-O(8) bond length is 2.67 Å. In the third Ca site, Ca(3) is bonded in a 9-coordinate geometry to one O(11), one O(12), one O(13), one O(14), one O(15), one O(16), one O(17), one O(2), and one O(4) atom. The Ca(3)-O(11) bond length is 2.68 Å. The Ca(3)-O(12) bond length is 2.54 Å. The Ca(3)-O(13) bond length is 2.62 Å. The Ca(3)-O(14) bond length is 2.27 Å. The Ca(3)-O(15) bond length is 2.84 Å. The Ca(3)-O(16) bond length is 2.57 Å. The Ca(3)-O(17) bond length is 2.49 Å. The Ca(3)-O(2) bond length is 2.84 Å. The Ca(3)-O(4) bond length is 2.41 Å. In the fourth Ca site, Ca(4) is bonded in a 9-coordinate geometry to one O(1), one O(11), one O(13), one O(15), one O(16), one O(17), one O(3), one O(5), and one O(6) atom. The Ca(4)-O(1) bond length is 2.58 Å. The Ca(4)-O(11) bond length is 2.63 Å. The Ca(4)-O(13) bond length is 2.64 Å. The Ca(4)-O(15) bond length is 2.69 Å. The Ca(4)-O(16) bond length is 2.96 Å. The Ca(4)-O(17) bond length is 2.71 Å. The Ca(4)-O(3) bond length is 2.87 Å. The Ca(4)-O(5) bond length is 2.57 Å. The Ca(4)-O(6) bond length is 2.82 Å. There are two inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(1), one O(7), and two equivalent O(14) atoms to form CrO4 tetrahedra that share corners with two equivalent Mn(2)O6 octahedra,  a cornercorner with one Mn(1)O5 square pyramid, and  a cornercorner with one Cr(2)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles are 40°. The Cr(1)-O(1) bond length is 1.76 Å. The Cr(1)-O(7) bond length is 1.83 Å. Both Cr(1)-O(14) bond lengths are 1.78 Å. In the second Cr site, Cr(2) is bonded to one O(4), one O(5), one O(7), and two equivalent O(16) atoms to form CrO5 trigonal bipyramids that share corners with two equivalent Mn(4)O6 octahedra, corners with two equivalent Mn(5)O5 square pyramids, and  a cornercorner with one Cr(1)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 14-34°. The Cr(2)-O(4) bond length is 1.91 Å. The Cr(2)-O(5) bond length is 1.97 Å. The Cr(2)-O(7) bond length is 1.90 Å. Both Cr(2)-O(16) bond lengths are 2.00 Å. There are six inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to one O(1), one O(11), one O(8), and two equivalent O(15) atoms to form MnO5 square pyramids that share corners with two equivalent Mn(3)O6 octahedra, corners with two equivalent Mn(4)O6 octahedra, and  a cornercorner with one Cr(1)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 2-4°. The Mn(1)-O(1) bond length is 2.06 Å. The Mn(1)-O(11) bond length is 1.92 Å. The Mn(1)-O(8) bond length is 1.95 Å. Both Mn(1)-O(15) bond lengths are 1.93 Å. In the second Mn site, Mn(2) is bonded to one O(12), one O(2), one O(3), one O(9), and two equivalent O(14) atoms to form distorted MnO6 octahedra that share corners with two equivalent Mn(3)O6 octahedra, corners with two equivalent Mn(5)O5 square pyramids, and corners with two equivalent Cr(1)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 6-7°. The Mn(2)-O(12) bond length is 1.97 Å. The Mn(2)-O(2) bond length is 1.90 Å. The Mn(2)-O(3) bond length is 1.94 Å. The Mn(2)-O(9) bond length is 2.03 Å. Both Mn(2)-O(14) bond lengths are 2.37 Å. In the third Mn site, Mn(3) is bonded to one O(10), one O(13), one O(2), one O(3), and two equivalent O(15) atoms to form MnO6 octahedra that share corners with two equivalent Mn(2)O6 octahedra, corners with two equivalent Mn(1)O5 square pyramids, and corners with two equivalent Mn(6)O5 square pyramids. The corner-sharing octahedral tilt angles range from 6-7°. The Mn(3)-O(10) bond length is 2.02 Å. The Mn(3)-O(13) bond length is 1.96 Å. The Mn(3)-O(2) bond length is 1.88 Å. The Mn(3)-O(3) bond length is 1.99 Å. Both Mn(3)-O(15) bond lengths are 1.96 Å. In the fourth Mn site, Mn(4) is bonded to one O(11), one O(4), one O(5), one O(8), and two equivalent O(17) atoms to form MnO6 octahedra that share corners with two equivalent Mn(1)O5 square pyramids, corners with two equivalent Mn(6)O5 square pyramids, and corners with two equivalent Cr(2)O5 trigonal bipyramids. The Mn(4)-O(11) bond length is 1.96 Å. The Mn(4)-O(4) bond length is 1.95 Å. The Mn(4)-O(5) bond length is 2.08 Å. The Mn(4)-O(8) bond length is 1.98 Å. Both Mn(4)-O(17) bond lengths are 1.99 Å. In the fifth Mn site, Mn(5) is bonded to one O(12), one O(6), one O(9), and two equivalent O(16) atoms to form MnO5 square pyramids that share corners with two equivalent Mn(2)O6 octahedra,  a cornercorner with one Mn(6)O5 square pyramid, and corners with two equivalent Cr(2)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 14-17°. The Mn(5)-O(12) bond length is 1.92 Å. The Mn(5)-O(6) bond length is 1.90 Å. The Mn(5)-O(9) bond length is 1.93 Å. Both Mn(5)-O(16) bond lengths are 1.92 Å. In the sixth Mn site, Mn(6) is bonded to one O(10), one O(13), one O(6), and two equivalent O(17) atoms to form MnO5 square pyramids that share corners with two equivalent Mn(3)O6 octahedra, corners with two equivalent Mn(4)O6 octahedra, and  a cornercorner with one Mn(5)O5 square pyramid. The corner-sharing octahedral tilt angles range from 2-7°. The Mn(6)-O(10) bond length is 1.92 Å. The Mn(6)-O(13) bond length is 1.89 Å. The Mn(6)-O(6) bond length is 1.92 Å. Both Mn(6)-O(17) bond lengths are 1.91 Å. There are seventeen inequivalent O sites. In the first O site, O(1) is bonded in a distorted rectangular see-saw-like geometry to two equivalent Ca(4), one Cr(1), and one Mn(1) atom. In the second O site, O(2) is bonded in a distorted linear geometry to two equivalent Ca(1), two equivalent Ca(3), one Mn(2), and one Mn(3) atom. In the third O site, O(3) is bonded in a distorted linear geometry to two equivalent Ca(2), two equivalent Ca(4), one Mn(2), and one Mn(3) atom. In the fourth O site, O(4) is bonded to two equivalent Ca(3), one Cr(2), and one Mn(4) atom to form distorted OCa2MnCr tetrahedra that share  a cornercorner with one O(8)Ca4Mn2 octahedra, corners with two equivalent O(13)Ca4Mn2 octahedra, corners with two equivalent O(15)Ca4Mn2 octahedra,  a cornercorner with one O(7)Ca2Cr2 tetrahedra, edges with two equivalent O(17)Ca4Mn2 octahedra, and  a faceface with one O(11)Ca4Mn2 octahedra. The corner-sharing octahedral tilt angles range from 48-76°. In the fifth O site, O(5) is bonded in a 6-coordinate geometry to two equivalent Ca(2), two equivalent Ca(4), one Cr(2), and one Mn(4) atom. In the sixth O site, O(6) is bonded in a 6-coordinate geometry to two equivalent Ca(2), two equivalent Ca(4), one Mn(5), and one Mn(6) atom. In the seventh O site, O(7) is bonded to two equivalent Ca(1), one Cr(1), and one Cr(2) atom to form distorted OCa2Cr2 tetrahedra that share corners with two equivalent O(10)Ca4Mn2 octahedra, corners with two equivalent O(15)Ca4Mn2 octahedra, corners with two equivalent O(17)Ca4Mn2 octahedra,  a cornercorner with one O(4)Ca2MnCr tetrahedra, and  an edgeedge with one O(8)Ca4Mn2 octahedra. The corner-sharing octahedral tilt angles range from 12-72°. In the eighth O site, O(8) is bonded to two equivalent Ca(1), two equivalent Ca(2), one Mn(1), and one Mn(4) atom to form distorted OCa4Mn2 octahedra that share corners with two equivalent O(11)Ca4Mn2 octahedra,  a cornercorner with one O(4)Ca2MnCr tetrahedra, edges with two equivalent O(10)Ca4Mn2 octahedra,  an edgeedge with one O(7)Ca2Cr2 tetrahedra, faces with two equivalent O(15)Ca4Mn2 octahedra, and faces with two equivalent O(17)Ca4Mn2 octahedra. The corner-sharing octahedral tilt angles range from 3-8°. In the ninth O site, O(9) is bonded in a distorted rectangular see-saw-like geometry to two equivalent Ca(1), one Mn(2), and one Mn(5) atom. In the tenth O site, O(10) is bonded to two equivalent Ca(1), two equivalent Ca(2), one Mn(3), and one Mn(6) atom to form distorted OCa4Mn2 octahedra that share corners with two equivalent O(13)Ca4Mn2 octahedra, corners with two equivalent O(7)Ca2Cr2 tetrahedra, edges with two equivalent O(8)Ca4Mn2 octahedra, faces with two equivalent O(15)Ca4Mn2 octahedra, and faces with two equivalent O(17)Ca4Mn2 octahedra. The corner-sharing octahedral tilt angles are 4°. In the eleventh O site, O(11) is bonded to two equivalent Ca(3), two equivalent Ca(4), one Mn(1), and one Mn(4) atom to form distorted OCa4Mn2 octahedra that share corners with two equivalent O(8)Ca4Mn2 octahedra, edges with two equivalent O(13)Ca4Mn2 octahedra, faces with two equivalent O(15)Ca4Mn2 octahedra, faces with two equivalent O(17)Ca4Mn2 octahedra, and  a faceface with one O(4)Ca2MnCr tetrahedra. The corner-sharing octahedral tilt angles range from 3-8°. In the twelfth O site, O(12) is bonded in a 4-coordinate geometry to two equivalent Ca(3), one Mn(2), and one Mn(5) atom. In the thirteenth O site, O(13) is bonded to two equivalent Ca(3), two equivalent Ca(4), one Mn(3), and one Mn(6) atom to form distorted OCa4Mn2 octahedra that share corners with two equivalent O(10)Ca4Mn2 octahedra, corners with two equivalent O(4)Ca2MnCr tetrahedra, edges with two equivalent O(11)Ca4Mn2 octahedra, faces with two equivalent O(15)Ca4Mn2 octahedra, and faces with two equivalent O(17)Ca4Mn2 octahedra. The corner-sharing octahedral tilt angles are 4°. In the fourteenth O site, O(14) is bonded in a 4-coordinate geometry to one Ca(1), one Ca(3), one Cr(1), and one Mn(2) atom. In the fifteenth O site, O(15) is bonded to one Ca(1), one Ca(2), one Ca(3), one Ca(4), one Mn(1), and one Mn(3) atom to form distorted OCa4Mn2 octahedra that share corners with two equivalent O(15)Ca4Mn2 octahedra,  a cornercorner with one O(7)Ca2Cr2 tetrahedra,  a cornercorner with one O(4)Ca2MnCr tetrahedra, edges with two equivalent O(17)Ca4Mn2 octahedra,  a faceface with one O(10)Ca4Mn2 octahedra,  a faceface with one O(11)Ca4Mn2 octahedra,  a faceface with one O(13)Ca4Mn2 octahedra, and  a faceface with one O(8)Ca4Mn2 octahedra. The corner-sharing octahedral tilt angles range from 3-6°. In the sixteenth O site, O(16) is bonded in a 2-coordinate geometry to one Ca(1), one Ca(3), one Ca(4), one Cr(2), and one Mn(5) atom. In the seventeenth O site, O(17) is bonded to one Ca(1), one Ca(2), one Ca(3), one Ca(4), one Mn(4), and one Mn(6) atom to form distorted OCa4Mn2 octahedra that share corners with two equivalent O(17)Ca4Mn2 octahedra,  a cornercorner with one O(7)Ca2Cr2 tetrahedra, edges with two equivalent O(15)Ca4Mn2 octahedra,  an edgeedge with one O(4)Ca2MnCr tetrahedra,  a faceface with one O(10)Ca4Mn2 octahedra,  a faceface with one O(11)Ca4Mn2 octahedra,  a faceface with one O(13)Ca4Mn2 octahedra, and  a faceface with one O(8)Ca4Mn2 octahedra. The corner-sharing octahedral tilt angles range from 6-11°.