The crystal structure described by HfCrAgS4 crystallizes in the triclinic P1 space group. There are four inequivalent Hf sites. In the first Hf site, Hf(1) is bonded to one S(12), one S(16), one S(2), one S(4), one S(6), and one S(8) atom to form HfS6 octahedra that share  a cornercorner with one Ag(2)S6 pentagonal pyramid, corners with two equivalent Ag(1)S6 pentagonal pyramids, edges with two equivalent Hf(4)S6 octahedra, edges with two equivalent Cr(2)S6 octahedra, edges with two equivalent Cr(4)S6 octahedra, and  an edgeedge with one Ag(2)S6 pentagonal pyramid. In the second Hf site, Hf(2) is bonded to one S(1), one S(11), one S(13), one S(15), one S(5), and one S(9) atom to form HfS6 octahedra that share edges with two equivalent Hf(3)S6 octahedra, edges with two equivalent Cr(1)S6 octahedra, edges with two equivalent Cr(3)S6 octahedra,  an edgeedge with one Ag(1)S6 pentagonal pyramid, and  an edgeedge with one Ag(2)S6 pentagonal pyramid. In the third Hf site, Hf(3) is bonded to one S(11), one S(13), one S(15), one S(3), one S(7), and one S(9) atom to form HfS6 octahedra that share edges with two equivalent Hf(2)S6 octahedra, edges with two equivalent Cr(1)S6 octahedra, edges with two equivalent Cr(3)S6 octahedra,  an edgeedge with one Ag(1)S6 pentagonal pyramid, and  an edgeedge with one Ag(2)S6 pentagonal pyramid. In the fourth Hf site, Hf(4) is bonded to one S(10), one S(12), one S(14), one S(16), one S(4), and one S(8) atom to form HfS6 octahedra that share edges with two equivalent Hf(1)S6 octahedra, edges with two equivalent Cr(2)S6 octahedra, edges with two equivalent Cr(4)S6 octahedra,  an edgeedge with one Ag(1)S6 pentagonal pyramid, and  an edgeedge with one Ag(2)S6 pentagonal pyramid. There are four inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one S(1), one S(13), one S(3), one S(5), one S(7), and one S(9) atom to form CrS6 octahedra that share  a cornercorner with one Ag(1)S6 pentagonal pyramid, corners with two equivalent Ag(2)S6 pentagonal pyramids, edges with two equivalent Hf(2)S6 octahedra, edges with two equivalent Hf(3)S6 octahedra, edges with two equivalent Cr(3)S6 octahedra, and  an edgeedge with one Ag(1)S6 pentagonal pyramid. In the second Cr site, Cr(2) is bonded to one S(10), one S(14), one S(2), one S(4), one S(6), and one S(8) atom to form CrS6 octahedra that share  a cornercorner with one Ag(1)S6 pentagonal pyramid, corners with two equivalent Ag(2)S6 pentagonal pyramids, edges with two equivalent Hf(1)S6 octahedra, edges with two equivalent Hf(4)S6 octahedra, edges with two equivalent Cr(4)S6 octahedra, and  an edgeedge with one Ag(1)S6 pentagonal pyramid. In the third Cr site, Cr(3) is bonded to one S(1), one S(11), one S(15), one S(3), one S(5), and one S(7) atom to form CrS6 octahedra that share  a cornercorner with one Ag(2)S6 pentagonal pyramid, corners with two equivalent Ag(1)S6 pentagonal pyramids, edges with two equivalent Hf(2)S6 octahedra, edges with two equivalent Hf(3)S6 octahedra, edges with two equivalent Cr(1)S6 octahedra, and  an edgeedge with one Ag(2)S6 pentagonal pyramid. In the fourth Cr site, Cr(4) is bonded to one S(10), one S(12), one S(14), one S(16), one S(2), and one S(6) atom to form CrS6 octahedra that share edges with two equivalent Hf(1)S6 octahedra, edges with two equivalent Hf(4)S6 octahedra, edges with two equivalent Cr(2)S6 octahedra,  an edgeedge with one Ag(1)S6 pentagonal pyramid, and  an edgeedge with one Ag(2)S6 pentagonal pyramid. There are four inequivalent Ag sites. In the first Ag site, Ag(1) is bonded to one S(10), one S(3), one S(4), one S(5), one S(6), and one S(9) atom to form distorted AgS6 pentagonal pyramids that share  a cornercorner with one Cr(1)S6 octahedra,  a cornercorner with one Cr(2)S6 octahedra, corners with two equivalent Hf(1)S6 octahedra, corners with two equivalent Cr(3)S6 octahedra,  an edgeedge with one Hf(2)S6 octahedra,  an edgeedge with one Hf(3)S6 octahedra,  an edgeedge with one Hf(4)S6 octahedra,  an edgeedge with one Cr(1)S6 octahedra,  an edgeedge with one Cr(2)S6 octahedra, and  an edgeedge with one Cr(4)S6 octahedra. The corner-sharing octahedral tilt angles range from 7-11°. In the second Ag site, Ag(2) is bonded to one S(1), one S(11), one S(12), one S(2), one S(7), and one S(8) atom to form distorted AgS6 pentagonal pyramids that share  a cornercorner with one Hf(1)S6 octahedra,  a cornercorner with one Cr(3)S6 octahedra, corners with two equivalent Cr(1)S6 octahedra, corners with two equivalent Cr(2)S6 octahedra,  an edgeedge with one Hf(1)S6 octahedra,  an edgeedge with one Hf(2)S6 octahedra,  an edgeedge with one Hf(3)S6 octahedra,  an edgeedge with one Hf(4)S6 octahedra,  an edgeedge with one Cr(3)S6 octahedra, and  an edgeedge with one Cr(4)S6 octahedra. The corner-sharing octahedral tilt angles range from 6-12°. In the third Ag site, Ag(3) is bonded in a 6-coordinate geometry to one S(1), one S(13), one S(14), one S(2), one S(7), and one S(8) atom. In the fourth Ag site, Ag(4) is bonded in a 6-coordinate geometry to one S(15), one S(16), one S(3), one S(4), one S(5), and one S(6) atom. There are sixteen inequivalent S sites. In the first S site, S(1) is bonded to one Hf(2), one Cr(1), one Cr(3), one Ag(2), and one Ag(3) atom to form distorted SHfCr2Ag2 trigonal bipyramids that share  a cornercorner with one S(5)HfCr2Ag2 trigonal bipyramid, corners with two equivalent S(2)HfCr2Ag2 trigonal bipyramids, corners with two equivalent S(3)HfCr2Ag2 trigonal bipyramids,  an edgeedge with one S(8)Hf2CrAg2 trigonal bipyramid,  an edgeedge with one S(5)HfCr2Ag2 trigonal bipyramid, and edges with two equivalent S(7)HfCr2Ag2 trigonal bipyramids. In the second S site, S(2) is bonded to one Hf(1), one Cr(2), one Cr(4), one Ag(2), and one Ag(3) atom to form distorted SHfCr2Ag2 trigonal bipyramids that share  a cornercorner with one S(6)HfCr2Ag2 trigonal bipyramid, corners with two equivalent S(4)Hf2CrAg2 trigonal bipyramids, corners with two equivalent S(1)HfCr2Ag2 trigonal bipyramids,  an edgeedge with one S(6)HfCr2Ag2 trigonal bipyramid,  an edgeedge with one S(7)HfCr2Ag2 trigonal bipyramid, and edges with two equivalent S(8)Hf2CrAg2 trigonal bipyramids. In the third S site, S(3) is bonded to one Hf(3), one Cr(1), one Cr(3), one Ag(1), and one Ag(4) atom to form SHfCr2Ag2 trigonal bipyramids that share  a cornercorner with one S(7)HfCr2Ag2 trigonal bipyramid, corners with two equivalent S(4)Hf2CrAg2 trigonal bipyramids, corners with two equivalent S(1)HfCr2Ag2 trigonal bipyramids,  an edgeedge with one S(6)HfCr2Ag2 trigonal bipyramid,  an edgeedge with one S(7)HfCr2Ag2 trigonal bipyramid, and edges with two equivalent S(5)HfCr2Ag2 trigonal bipyramids. In the fourth S site, S(4) is bonded to one Hf(1), one Hf(4), one Cr(2), one Ag(1), and one Ag(4) atom to form distorted SHf2CrAg2 trigonal bipyramids that share  a cornercorner with one S(8)Hf2CrAg2 trigonal bipyramid, corners with two equivalent S(2)HfCr2Ag2 trigonal bipyramids, corners with two equivalent S(3)HfCr2Ag2 trigonal bipyramids,  an edgeedge with one S(8)Hf2CrAg2 trigonal bipyramid,  an edgeedge with one S(5)HfCr2Ag2 trigonal bipyramid, and edges with two equivalent S(6)HfCr2Ag2 trigonal bipyramids. In the fifth S site, S(5) is bonded to one Hf(2), one Cr(1), one Cr(3), one Ag(1), and one Ag(4) atom to form distorted SHfCr2Ag2 trigonal bipyramids that share  a cornercorner with one S(1)HfCr2Ag2 trigonal bipyramid, corners with two equivalent S(6)HfCr2Ag2 trigonal bipyramids, corners with two equivalent S(7)HfCr2Ag2 trigonal bipyramids,  an edgeedge with one S(4)Hf2CrAg2 trigonal bipyramid,  an edgeedge with one S(1)HfCr2Ag2 trigonal bipyramid, and edges with two equivalent S(3)HfCr2Ag2 trigonal bipyramids. In the sixth S site, S(6) is bonded to one Hf(1), one Cr(2), one Cr(4), one Ag(1), and one Ag(4) atom to form distorted SHfCr2Ag2 trigonal bipyramids that share  a cornercorner with one S(2)HfCr2Ag2 trigonal bipyramid, corners with two equivalent S(8)Hf2CrAg2 trigonal bipyramids, corners with two equivalent S(5)HfCr2Ag2 trigonal bipyramids,  an edgeedge with one S(2)HfCr2Ag2 trigonal bipyramid,  an edgeedge with one S(3)HfCr2Ag2 trigonal bipyramid, and edges with two equivalent S(4)Hf2CrAg2 trigonal bipyramids. In the seventh S site, S(7) is bonded to one Hf(3), one Cr(1), one Cr(3), one Ag(2), and one Ag(3) atom to form SHfCr2Ag2 trigonal bipyramids that share  a cornercorner with one S(3)HfCr2Ag2 trigonal bipyramid, corners with two equivalent S(8)Hf2CrAg2 trigonal bipyramids, corners with two equivalent S(5)HfCr2Ag2 trigonal bipyramids,  an edgeedge with one S(2)HfCr2Ag2 trigonal bipyramid,  an edgeedge with one S(3)HfCr2Ag2 trigonal bipyramid, and edges with two equivalent S(1)HfCr2Ag2 trigonal bipyramids. In the eighth S site, S(8) is bonded to one Hf(1), one Hf(4), one Cr(2), one Ag(2), and one Ag(3) atom to form SHf2CrAg2 trigonal bipyramids that share  a cornercorner with one S(4)Hf2CrAg2 trigonal bipyramid, corners with two equivalent S(6)HfCr2Ag2 trigonal bipyramids, corners with two equivalent S(7)HfCr2Ag2 trigonal bipyramids,  an edgeedge with one S(4)Hf2CrAg2 trigonal bipyramid,  an edgeedge with one S(1)HfCr2Ag2 trigonal bipyramid, and edges with two equivalent S(2)HfCr2Ag2 trigonal bipyramids. In the ninth S site, S(9) is bonded in a rectangular see-saw-like geometry to one Hf(2), one Hf(3), one Cr(1), and one Ag(1) atom. In the tenth S site, S(10) is bonded in a rectangular see-saw-like geometry to one Hf(4), one Cr(2), one Cr(4), and one Ag(1) atom. In the eleventh S site, S(11) is bonded in a rectangular see-saw-like geometry to one Hf(2), one Hf(3), one Cr(3), and one Ag(2) atom. In the twelfth S site, S(12) is bonded in a rectangular see-saw-like geometry to one Hf(1), one Hf(4), one Cr(4), and one Ag(2) atom. In the thirteenth S site, S(13) is bonded in a rectangular see-saw-like geometry to one Hf(2), one Hf(3), one Cr(1), and one Ag(3) atom. In the fourteenth S site, S(14) is bonded in a rectangular see-saw-like geometry to one Hf(4), one Cr(2), one Cr(4), and one Ag(3) atom. In the fifteenth S site, S(15) is bonded in a rectangular see-saw-like geometry to one Hf(2), one Hf(3), one Cr(3), and one Ag(4) atom. In the sixteenth S site, S(16) is bonded in a rectangular see-saw-like geometry to one Hf(1), one Hf(4), one Cr(4), and one Ag(4) atom. is represented by the CIF file [CIF]
data_HfCrAgS4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   7.115
_cell_length_b   13.292
_cell_length_c   6.132
_cell_angle_alpha   90.201
_cell_angle_beta   90.080
_cell_angle_gamma   89.833
_symmetry_Int_Tables_number   1
_cell_volume   579.915
_cell_formula_units_Z   4
loop_
 _symmetry_equiv_pos_site_id
 _symmetry_equiv_pos_as_xyz
  1  'x, y, z'
loop_
 _atom_site_type_symbol
 _atom_site_label
 _atom_site_symmetry_multiplicity
 _atom_site_fract_x
 _atom_site_fract_y
 _atom_site_fract_z
 _atom_site_occupancy
  Hf  Hf0  1  0.516  0.746  0.001  1.0
  Hf  Hf1  1  0.251  0.250  0.500  1.0
  Hf  Hf2  1  0.750  0.250  0.499  1.0
  Hf  Hf3  1  0.234  0.752  0.501  1.0
  Cr  Cr4  1  1.000  0.246  0.000  1.0
  Cr  Cr5  1  0.998  0.754  0.999  1.0
  Cr  Cr6  1  0.500  0.253  1.000  1.0
  Cr  Cr7  1  0.752  0.750  0.498  1.0
  Ag  Ag8  1  0.002  0.003  0.349  1.0
  Ag  Ag9  1  0.500  0.496  0.662  1.0
  Ag  Ag10  1  0.996  0.500  0.024  1.0
  Ag  Ag11  1  0.504  0.995  0.980  1.0
  S  S12  1  0.251  0.356  0.847  1.0
  S  S13  1  0.764  0.644  0.817  1.0
  S  S14  1  0.750  0.144  0.151  1.0
  S  S15  1  0.242  0.859  0.156  1.0
  S  S16  1  0.251  0.144  0.152  1.0
  S  S17  1  0.762  0.857  0.178  1.0
  S  S18  1  0.748  0.356  0.847  1.0
  S  S19  1  0.242  0.642  0.840  1.0
  S  S20  1  0.001  0.141  0.675  1.0
  S  S21  1  0.984  0.857  0.673  1.0
  S  S22  1  0.499  0.359  0.325  1.0
  S  S23  1  0.509  0.642  0.345  1.0
  S  S24  1  0.999  0.356  0.322  1.0
  S  S25  1  0.988  0.648  0.318  1.0
  S  S26  1  0.501  0.143  0.679  1.0
  S  S27  1  0.508  0.855  0.661  1.0
[/CIF]
.
The crystal structure described by HfCrAgS4 crystallizes in the triclinic P1 space group. There are four inequivalent Hf sites. In the first Hf site, Hf(1) is bonded to one S(12), one S(16), one S(2), one S(4), one S(6), and one S(8) atom to form HfS6 octahedra that share  a cornercorner with one Ag(2)S6 pentagonal pyramid, corners with two equivalent Ag(1)S6 pentagonal pyramids, edges with two equivalent Hf(4)S6 octahedra, edges with two equivalent Cr(2)S6 octahedra, edges with two equivalent Cr(4)S6 octahedra, and  an edgeedge with one Ag(2)S6 pentagonal pyramid. In the second Hf site, Hf(2) is bonded to one S(1), one S(11), one S(13), one S(15), one S(5), and one S(9) atom to form HfS6 octahedra that share edges with two equivalent Hf(3)S6 octahedra, edges with two equivalent Cr(1)S6 octahedra, edges with two equivalent Cr(3)S6 octahedra,  an edgeedge with one Ag(1)S6 pentagonal pyramid, and  an edgeedge with one Ag(2)S6 pentagonal pyramid. In the third Hf site, Hf(3) is bonded to one S(11), one S(13), one S(15), one S(3), one S(7), and one S(9) atom to form HfS6 octahedra that share edges with two equivalent Hf(2)S6 octahedra, edges with two equivalent Cr(1)S6 octahedra, edges with two equivalent Cr(3)S6 octahedra,  an edgeedge with one Ag(1)S6 pentagonal pyramid, and  an edgeedge with one Ag(2)S6 pentagonal pyramid. In the fourth Hf site, Hf(4) is bonded to one S(10), one S(12), one S(14), one S(16), one S(4), and one S(8) atom to form HfS6 octahedra that share edges with two equivalent Hf(1)S6 octahedra, edges with two equivalent Cr(2)S6 octahedra, edges with two equivalent Cr(4)S6 octahedra,  an edgeedge with one Ag(1)S6 pentagonal pyramid, and  an edgeedge with one Ag(2)S6 pentagonal pyramid. There are four inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one S(1), one S(13), one S(3), one S(5), one S(7), and one S(9) atom to form CrS6 octahedra that share  a cornercorner with one Ag(1)S6 pentagonal pyramid, corners with two equivalent Ag(2)S6 pentagonal pyramids, edges with two equivalent Hf(2)S6 octahedra, edges with two equivalent Hf(3)S6 octahedra, edges with two equivalent Cr(3)S6 octahedra, and  an edgeedge with one Ag(1)S6 pentagonal pyramid. In the second Cr site, Cr(2) is bonded to one S(10), one S(14), one S(2), one S(4), one S(6), and one S(8) atom to form CrS6 octahedra that share  a cornercorner with one Ag(1)S6 pentagonal pyramid, corners with two equivalent Ag(2)S6 pentagonal pyramids, edges with two equivalent Hf(1)S6 octahedra, edges with two equivalent Hf(4)S6 octahedra, edges with two equivalent Cr(4)S6 octahedra, and  an edgeedge with one Ag(1)S6 pentagonal pyramid. In the third Cr site, Cr(3) is bonded to one S(1), one S(11), one S(15), one S(3), one S(5), and one S(7) atom to form CrS6 octahedra that share  a cornercorner with one Ag(2)S6 pentagonal pyramid, corners with two equivalent Ag(1)S6 pentagonal pyramids, edges with two equivalent Hf(2)S6 octahedra, edges with two equivalent Hf(3)S6 octahedra, edges with two equivalent Cr(1)S6 octahedra, and  an edgeedge with one Ag(2)S6 pentagonal pyramid. In the fourth Cr site, Cr(4) is bonded to one S(10), one S(12), one S(14), one S(16), one S(2), and one S(6) atom to form CrS6 octahedra that share edges with two equivalent Hf(1)S6 octahedra, edges with two equivalent Hf(4)S6 octahedra, edges with two equivalent Cr(2)S6 octahedra,  an edgeedge with one Ag(1)S6 pentagonal pyramid, and  an edgeedge with one Ag(2)S6 pentagonal pyramid. There are four inequivalent Ag sites. In the first Ag site, Ag(1) is bonded to one S(10), one S(3), one S(4), one S(5), one S(6), and one S(9) atom to form distorted AgS6 pentagonal pyramids that share  a cornercorner with one Cr(1)S6 octahedra,  a cornercorner with one Cr(2)S6 octahedra, corners with two equivalent Hf(1)S6 octahedra, corners with two equivalent Cr(3)S6 octahedra,  an edgeedge with one Hf(2)S6 octahedra,  an edgeedge with one Hf(3)S6 octahedra,  an edgeedge with one Hf(4)S6 octahedra,  an edgeedge with one Cr(1)S6 octahedra,  an edgeedge with one Cr(2)S6 octahedra, and  an edgeedge with one Cr(4)S6 octahedra. The corner-sharing octahedral tilt angles range from 7-11°. In the second Ag site, Ag(2) is bonded to one S(1), one S(11), one S(12), one S(2), one S(7), and one S(8) atom to form distorted AgS6 pentagonal pyramids that share  a cornercorner with one Hf(1)S6 octahedra,  a cornercorner with one Cr(3)S6 octahedra, corners with two equivalent Cr(1)S6 octahedra, corners with two equivalent Cr(2)S6 octahedra,  an edgeedge with one Hf(1)S6 octahedra,  an edgeedge with one Hf(2)S6 octahedra,  an edgeedge with one Hf(3)S6 octahedra,  an edgeedge with one Hf(4)S6 octahedra,  an edgeedge with one Cr(3)S6 octahedra, and  an edgeedge with one Cr(4)S6 octahedra. The corner-sharing octahedral tilt angles range from 6-12°. In the third Ag site, Ag(3) is bonded in a 6-coordinate geometry to one S(1), one S(13), one S(14), one S(2), one S(7), and one S(8) atom. In the fourth Ag site, Ag(4) is bonded in a 6-coordinate geometry to one S(15), one S(16), one S(3), one S(4), one S(5), and one S(6) atom. There are sixteen inequivalent S sites. In the first S site, S(1) is bonded to one Hf(2), one Cr(1), one Cr(3), one Ag(2), and one Ag(3) atom to form distorted SHfCr2Ag2 trigonal bipyramids that share  a cornercorner with one S(5)HfCr2Ag2 trigonal bipyramid, corners with two equivalent S(2)HfCr2Ag2 trigonal bipyramids, corners with two equivalent S(3)HfCr2Ag2 trigonal bipyramids,  an edgeedge with one S(8)Hf2CrAg2 trigonal bipyramid,  an edgeedge with one S(5)HfCr2Ag2 trigonal bipyramid, and edges with two equivalent S(7)HfCr2Ag2 trigonal bipyramids. In the second S site, S(2) is bonded to one Hf(1), one Cr(2), one Cr(4), one Ag(2), and one Ag(3) atom to form distorted SHfCr2Ag2 trigonal bipyramids that share  a cornercorner with one S(6)HfCr2Ag2 trigonal bipyramid, corners with two equivalent S(4)Hf2CrAg2 trigonal bipyramids, corners with two equivalent S(1)HfCr2Ag2 trigonal bipyramids,  an edgeedge with one S(6)HfCr2Ag2 trigonal bipyramid,  an edgeedge with one S(7)HfCr2Ag2 trigonal bipyramid, and edges with two equivalent S(8)Hf2CrAg2 trigonal bipyramids. In the third S site, S(3) is bonded to one Hf(3), one Cr(1), one Cr(3), one Ag(1), and one Ag(4) atom to form SHfCr2Ag2 trigonal bipyramids that share  a cornercorner with one S(7)HfCr2Ag2 trigonal bipyramid, corners with two equivalent S(4)Hf2CrAg2 trigonal bipyramids, corners with two equivalent S(1)HfCr2Ag2 trigonal bipyramids,  an edgeedge with one S(6)HfCr2Ag2 trigonal bipyramid,  an edgeedge with one S(7)HfCr2Ag2 trigonal bipyramid, and edges with two equivalent S(5)HfCr2Ag2 trigonal bipyramids. In the fourth S site, S(4) is bonded to one Hf(1), one Hf(4), one Cr(2), one Ag(1), and one Ag(4) atom to form distorted SHf2CrAg2 trigonal bipyramids that share  a cornercorner with one S(8)Hf2CrAg2 trigonal bipyramid, corners with two equivalent S(2)HfCr2Ag2 trigonal bipyramids, corners with two equivalent S(3)HfCr2Ag2 trigonal bipyramids,  an edgeedge with one S(8)Hf2CrAg2 trigonal bipyramid,  an edgeedge with one S(5)HfCr2Ag2 trigonal bipyramid, and edges with two equivalent S(6)HfCr2Ag2 trigonal bipyramids. In the fifth S site, S(5) is bonded to one Hf(2), one Cr(1), one Cr(3), one Ag(1), and one Ag(4) atom to form distorted SHfCr2Ag2 trigonal bipyramids that share  a cornercorner with one S(1)HfCr2Ag2 trigonal bipyramid, corners with two equivalent S(6)HfCr2Ag2 trigonal bipyramids, corners with two equivalent S(7)HfCr2Ag2 trigonal bipyramids,  an edgeedge with one S(4)Hf2CrAg2 trigonal bipyramid,  an edgeedge with one S(1)HfCr2Ag2 trigonal bipyramid, and edges with two equivalent S(3)HfCr2Ag2 trigonal bipyramids. In the sixth S site, S(6) is bonded to one Hf(1), one Cr(2), one Cr(4), one Ag(1), and one Ag(4) atom to form distorted SHfCr2Ag2 trigonal bipyramids that share  a cornercorner with one S(2)HfCr2Ag2 trigonal bipyramid, corners with two equivalent S(8)Hf2CrAg2 trigonal bipyramids, corners with two equivalent S(5)HfCr2Ag2 trigonal bipyramids,  an edgeedge with one S(2)HfCr2Ag2 trigonal bipyramid,  an edgeedge with one S(3)HfCr2Ag2 trigonal bipyramid, and edges with two equivalent S(4)Hf2CrAg2 trigonal bipyramids. In the seventh S site, S(7) is bonded to one Hf(3), one Cr(1), one Cr(3), one Ag(2), and one Ag(3) atom to form SHfCr2Ag2 trigonal bipyramids that share  a cornercorner with one S(3)HfCr2Ag2 trigonal bipyramid, corners with two equivalent S(8)Hf2CrAg2 trigonal bipyramids, corners with two equivalent S(5)HfCr2Ag2 trigonal bipyramids,  an edgeedge with one S(2)HfCr2Ag2 trigonal bipyramid,  an edgeedge with one S(3)HfCr2Ag2 trigonal bipyramid, and edges with two equivalent S(1)HfCr2Ag2 trigonal bipyramids. In the eighth S site, S(8) is bonded to one Hf(1), one Hf(4), one Cr(2), one Ag(2), and one Ag(3) atom to form SHf2CrAg2 trigonal bipyramids that share  a cornercorner with one S(4)Hf2CrAg2 trigonal bipyramid, corners with two equivalent S(6)HfCr2Ag2 trigonal bipyramids, corners with two equivalent S(7)HfCr2Ag2 trigonal bipyramids,  an edgeedge with one S(4)Hf2CrAg2 trigonal bipyramid,  an edgeedge with one S(1)HfCr2Ag2 trigonal bipyramid, and edges with two equivalent S(2)HfCr2Ag2 trigonal bipyramids. In the ninth S site, S(9) is bonded in a rectangular see-saw-like geometry to one Hf(2), one Hf(3), one Cr(1), and one Ag(1) atom. In the tenth S site, S(10) is bonded in a rectangular see-saw-like geometry to one Hf(4), one Cr(2), one Cr(4), and one Ag(1) atom. In the eleventh S site, S(11) is bonded in a rectangular see-saw-like geometry to one Hf(2), one Hf(3), one Cr(3), and one Ag(2) atom. In the twelfth S site, S(12) is bonded in a rectangular see-saw-like geometry to one Hf(1), one Hf(4), one Cr(4), and one Ag(2) atom. In the thirteenth S site, S(13) is bonded in a rectangular see-saw-like geometry to one Hf(2), one Hf(3), one Cr(1), and one Ag(3) atom. In the fourteenth S site, S(14) is bonded in a rectangular see-saw-like geometry to one Hf(4), one Cr(2), one Cr(4), and one Ag(3) atom. In the fifteenth S site, S(15) is bonded in a rectangular see-saw-like geometry to one Hf(2), one Hf(3), one Cr(3), and one Ag(4) atom. In the sixteenth S site, S(16) is bonded in a rectangular see-saw-like geometry to one Hf(1), one Hf(4), one Cr(4), and one Ag(4) atom. is represented by the CIF file [CIF]
data_HfCrAgS4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   7.115
_cell_length_b   13.292
_cell_length_c   6.132
_cell_angle_alpha   90.201
_cell_angle_beta   90.080
_cell_angle_gamma   89.833
_symmetry_Int_Tables_number   1
_cell_volume   579.915
_cell_formula_units_Z   4
loop_
 _symmetry_equiv_pos_site_id
 _symmetry_equiv_pos_as_xyz
  1  'x, y, z'
loop_
 _atom_site_type_symbol
 _atom_site_label
 _atom_site_symmetry_multiplicity
 _atom_site_fract_x
 _atom_site_fract_y
 _atom_site_fract_z
 _atom_site_occupancy
  Hf  Hf0  1  0.516  0.746  0.001  1.0
  Hf  Hf1  1  0.251  0.250  0.500  1.0
  Hf  Hf2  1  0.750  0.250  0.499  1.0
  Hf  Hf3  1  0.234  0.752  0.501  1.0
  Cr  Cr4  1  1.000  0.246  0.000  1.0
  Cr  Cr5  1  0.998  0.754  0.999  1.0
  Cr  Cr6  1  0.500  0.253  1.000  1.0
  Cr  Cr7  1  0.752  0.750  0.498  1.0
  Ag  Ag8  1  0.002  0.003  0.349  1.0
  Ag  Ag9  1  0.500  0.496  0.662  1.0
  Ag  Ag10  1  0.996  0.500  0.024  1.0
  Ag  Ag11  1  0.504  0.995  0.980  1.0
  S  S12  1  0.251  0.356  0.847  1.0
  S  S13  1  0.764  0.644  0.817  1.0
  S  S14  1  0.750  0.144  0.151  1.0
  S  S15  1  0.242  0.859  0.156  1.0
  S  S16  1  0.251  0.144  0.152  1.0
  S  S17  1  0.762  0.857  0.178  1.0
  S  S18  1  0.748  0.356  0.847  1.0
  S  S19  1  0.242  0.642  0.840  1.0
  S  S20  1  0.001  0.141  0.675  1.0
  S  S21  1  0.984  0.857  0.673  1.0
  S  S22  1  0.499  0.359  0.325  1.0
  S  S23  1  0.509  0.642  0.345  1.0
  S  S24  1  0.999  0.356  0.322  1.0
  S  S25  1  0.988  0.648  0.318  1.0
  S  S26  1  0.501  0.143  0.679  1.0
  S  S27  1  0.508  0.855  0.661  1.0
[/CIF]
.