A re-investigation of the crystal structure of quadratite, ideally AgCdAsS<sub>3sub>, was undertaken using a single crystal from the type locality, Lengenbach, Binntal, Switzerland. The average of five electron microprobe analyses led to the empirical formula (Ag<sub>0.994sub>Cd<sub>0.738sub>Pb<sub>0.231sub>Cu<sub>0.006sub>Tl<sub>0.005sub>Mn<sub>0.003sub>Fe<sub>0.004sub>Zn<sub>0.002sub> Cr<sub>0.001sub>)<sub>∑=1.984sub>(As<sub>0.955sub>Sb<sub>0.003sub>)<sub>∑=0.958sub>S<sub>3.058sub>. A single-crystal structure refinement (R1 = 4.84% for 558 observed reflections) shows that quadratite crystallizes in the space group P4<sub>3sub>22 and exhibits an atomic arrangement similar to that of the recently approved new mineral manganoquadratite, AgMnAsS<sub>3sub>. Like manganoquadratite, quadratite adopts a galena-derivative framework, with metal atoms occupying all the available octahedral interstices, although only M1 and M2 cations, occupied mainly by Cd, adopt a fairly regular octahedral coordination; the M3 cation, occupied by Ag, is located outside the center cavity in a square-pyramidal coordination, whereas Pb at the split position M3′ coordinates six S atoms. Arsenic also adopts a 3 + 3 asymmetrical coordination, thus forming the AsS<sub>3sub> pyramidal groups that typically occur in sulfosalts.
The structure can be also described as a stacking of BAB slabs [A: (Cd,Ag)CdS<sub>2sub> atomic plane; B: (Ag,Pb)AsS<sub>2sub> atomic plane] along [001]. The rectangular unit cell of these slabs is oriented diagonally to the <strong>astrong> axes of quadratite and consecutive slabs are related via interlayer twofold rotation operations parallel either to [100] or to [010]. This ambiguity leads to an OD structure with various possible stacking sequences, from which the tetragonal space group P4<sub>3sub>22 was observed.