Structure of Tl18Pb2Ti7S25 as a masterpiece of crystallographic symmetry

A crystallographic analysis of the cubic structure of Tl18Pb2Ti7S25 has established the arrangement of all cations and anions according to the law of the 27-fold (with respect to volume) structure type of PbS(NaCl) with strictly fixed anionic vacancies. The nonintersecting axes of symmetry \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\bar 3$$\end{document} of four directions organizing the structure distribute cations differing in sizes, charges, and amounts over general and particular sites of the sp. gr. Pa3 to form a high-symmetry design in the simple atomic matrix.