K10Mn4Sn4S17 crystallizes in the trigonal R3m space group. There are four inequivalent K sites. In the first K site, K(1) is bonded in a body-centered cubic geometry to two equivalent S(4), two equivalent S(6), and four equivalent S(5) atoms. In the second K site, K(2) is bonded in a distorted rectangular see-saw-like geometry to one S(4), one S(6), and two equivalent S(5) atoms. In the third K site, K(3) is bonded in a 6-coordinate geometry to one S(2), one S(4), two equivalent S(3), and two equivalent S(5) atoms. In the fourth K site, K(4) is bonded in a 6-coordinate geometry to three equivalent S(3) and three equivalent S(6) atoms. There are two inequivalent Mn sites. In the first Mn site, Mn(2) is bonded to one S(1) and three equivalent S(6) atoms to form MnS4 tetrahedra that share corners with three equivalent Mn(1)S4 tetrahedra and corners with three equivalent Sn(2)S4 tetrahedra. In the second Mn site, Mn(1) is bonded to one S(1), one S(4), and two equivalent S(5) atoms to form MnS4 tetrahedra that share  a cornercorner with one Mn(2)S4 tetrahedra,  a cornercorner with one Sn(1)S4 tetrahedra, corners with two equivalent Mn(1)S4 tetrahedra, and corners with two equivalent Sn(2)S4 tetrahedra. There are two inequivalent Sn sites. In the first Sn site, Sn(1) is bonded to one S(2) and three equivalent S(4) atoms to form SnS4 tetrahedra that share corners with three equivalent Mn(1)S4 tetrahedra. In the second Sn site, Sn(2) is bonded to one S(3), one S(6), and two equivalent S(5) atoms to form SnS4 tetrahedra that share  a cornercorner with one Mn(2)S4 tetrahedra and corners with two equivalent Mn(1)S4 tetrahedra. There are six inequivalent S sites. In the first S site, S(6) is bonded in a 6-coordinate geometry to one K(2), one K(4), two equivalent K(1), one Mn(2), and one Sn(2) atom. In the second S site, S(1) is bonded to one Mn(2) and three equivalent Mn(1) atoms to form corner-sharing SMn4 tetrahedra. The corner-sharing octahedral tilt angles are 70°. In the third S site, S(2) is bonded to three equivalent K(3) and one Sn(1) atom to form corner-sharing SK3Sn tetrahedra. The corner-sharing octahedral tilt angles are 73°. In the fourth S site, S(3) is bonded in a 4-coordinate geometry to one K(4), two equivalent K(3), and one Sn(2) atom. In the fifth S site, S(5) is bonded to one K(2), one K(3), two equivalent K(1), one Mn(1), and one Sn(2) atom to form distorted SK4MnSn octahedra that share corners with five equivalent S(5)K4MnSn octahedra,  a cornercorner with one S(2)K3Sn tetrahedra,  a cornercorner with one S(1)Mn4 tetrahedra,  an edgeedge with one S(5)K4MnSn octahedra, and  a faceface with one S(5)K4MnSn octahedra. The corner-sharing octahedral tilt angles range from 1-66°. In the sixth S site, S(4) is bonded in a 6-coordinate geometry to one K(2), one K(3), two equivalent K(1), one Mn(1), and one Sn(1) atom.
K10Mn4Sn4S17 crystallizes in the trigonal R3m space group. There are four inequivalent K sites. In the first K site, K(1) is bonded in a body-centered cubic geometry to two equivalent S(4), two equivalent S(6), and four equivalent S(5) atoms. Both K(1)-S(4) bond lengths are 3.59 Å. Both K(1)-S(6) bond lengths are 3.61 Å. There are two shorter (3.62 Å) and two longer (3.64 Å) K(1)-S(5) bond lengths. In the second K site, K(2) is bonded in a distorted rectangular see-saw-like geometry to one S(4), one S(6), and two equivalent S(5) atoms. The K(2)-S(4) bond length is 3.26 Å. The K(2)-S(6) bond length is 3.30 Å. Both K(2)-S(5) bond lengths are 3.26 Å. In the third K site, K(3) is bonded in a 6-coordinate geometry to one S(2), one S(4), two equivalent S(3), and two equivalent S(5) atoms. The K(3)-S(2) bond length is 3.06 Å. The K(3)-S(4) bond length is 3.52 Å. Both K(3)-S(3) bond lengths are 3.22 Å. Both K(3)-S(5) bond lengths are 3.43 Å. In the fourth K site, K(4) is bonded in a 6-coordinate geometry to three equivalent S(3) and three equivalent S(6) atoms. All K(4)-S(3) bond lengths are 3.12 Å. All K(4)-S(6) bond lengths are 3.41 Å. There are two inequivalent Mn sites. In the first Mn site, Mn(2) is bonded to one S(1) and three equivalent S(6) atoms to form MnS4 tetrahedra that share corners with three equivalent Mn(1)S4 tetrahedra and corners with three equivalent Sn(2)S4 tetrahedra. The Mn(2)-S(1) bond length is 2.40 Å. All Mn(2)-S(6) bond lengths are 2.41 Å. In the second Mn site, Mn(1) is bonded to one S(1), one S(4), and two equivalent S(5) atoms to form MnS4 tetrahedra that share  a cornercorner with one Mn(2)S4 tetrahedra,  a cornercorner with one Sn(1)S4 tetrahedra, corners with two equivalent Mn(1)S4 tetrahedra, and corners with two equivalent Sn(2)S4 tetrahedra. The Mn(1)-S(1) bond length is 2.40 Å. The Mn(1)-S(4) bond length is 2.40 Å. Both Mn(1)-S(5) bond lengths are 2.40 Å. There are two inequivalent Sn sites. In the first Sn site, Sn(1) is bonded to one S(2) and three equivalent S(4) atoms to form SnS4 tetrahedra that share corners with three equivalent Mn(1)S4 tetrahedra. The Sn(1)-S(2) bond length is 2.36 Å. All Sn(1)-S(4) bond lengths are 2.45 Å. In the second Sn site, Sn(2) is bonded to one S(3), one S(6), and two equivalent S(5) atoms to form SnS4 tetrahedra that share  a cornercorner with one Mn(2)S4 tetrahedra and corners with two equivalent Mn(1)S4 tetrahedra. The Sn(2)-S(3) bond length is 2.38 Å. The Sn(2)-S(6) bond length is 2.45 Å. Both Sn(2)-S(5) bond lengths are 2.44 Å. There are six inequivalent S sites. In the first S site, S(6) is bonded in a 6-coordinate geometry to one K(2), one K(4), two equivalent K(1), one Mn(2), and one Sn(2) atom. In the second S site, S(1) is bonded to one Mn(2) and three equivalent Mn(1) atoms to form corner-sharing SMn4 tetrahedra. The corner-sharing octahedral tilt angles are 70°. In the third S site, S(2) is bonded to three equivalent K(3) and one Sn(1) atom to form corner-sharing SK3Sn tetrahedra. The corner-sharing octahedral tilt angles are 73°. In the fourth S site, S(3) is bonded in a 4-coordinate geometry to one K(4), two equivalent K(3), and one Sn(2) atom. In the fifth S site, S(5) is bonded to one K(2), one K(3), two equivalent K(1), one Mn(1), and one Sn(2) atom to form distorted SK4MnSn octahedra that share corners with five equivalent S(5)K4MnSn octahedra,  a cornercorner with one S(2)K3Sn tetrahedra,  a cornercorner with one S(1)Mn4 tetrahedra,  an edgeedge with one S(5)K4MnSn octahedra, and  a faceface with one S(5)K4MnSn octahedra. The corner-sharing octahedral tilt angles range from 1-66°. In the sixth S site, S(4) is bonded in a 6-coordinate geometry to one K(2), one K(3), two equivalent K(1), one Mn(1), and one Sn(1) atom.