The crystal structure of kirkiite has been solved using single-crystal data (MoKa X-ray diffraction, CCD area detector) to the conventional R-factor R₁ = 0.069. It crystallizes in space group P2₁/m, with a 8.621(4), b 26.03(1), c 8.810(4) Å, ß 119.21(1)° and Z = 2. A crystal-structure determination and chemical analysis resulted in comparable formulae, Pb₁₀Bi_2.16As_3.84S₁₉ and Pb_10.08Bi_2.55Sb_0.13As_2.91S₁₉, respectively, which are close to the ideal formula Pb₁₀Bi₃As₃S₁₉. The crystal lattice shows a pseudohexagonal symmetry, which is the cause of common twinning in this mineral. The main twin-law has (20¯1) as a twin plane, with [100] as the twin axis, owing to the orthorhombic distortion of the pseudohexagonal lattice in accordance with the alignment of lone-electron-pair micelles in rows parallel to (001). The twin mechanism explains the formation of observed twin-lamellae with (20¯1) as a contact plane. The crystal structure of kirkiite can be described as (010) slabs of octahedra, three octahedra thick and related mutually by a refl ection plane situated in the intervening prismatic layer. In another interpretation, it is composed of slabs based on a transitional PbS-SnS archetype, with tightly bonded layers parallel to (083) of kirkiite; the slabs are unit-cell-twinned on (010) refl ection planes. The structure contains one split As position, and two additional sites that could accommodate both As and Bi. The As,Bi distribution over these two sites is determined by the trapezoidal distortion of the half-octahedral coordination environment inside the tightly bonded double layers of the PbS-SnS archetype slabs. Owing to the stoichiometry requirements in this structure, Bi must also substitute for 1/11 of the Pb sites. Bond-valence calculations and the volumes of coordination polyhedra show it to be ordered in two of the Pb sites. Kirkiite and jordanite Pb₂₈As₁₂S₄₆ are a pair of homologues. The general formula of a potential homologous series is Pb₈N_-4Me_{3+ 12}S_8N+14.