The field of polyhalogen chemistry, specifically polyhalogenanions(polyhalides), is rapidly evolving. Here, we present the synthesisof three sodium halides with unpredicted chemical compositions andstructures (tP10-Na2Cl3, hP18-Na4Cl5, and hP18-Na4Br5), a series of isostructural cubic cP8-AX(3) halides (NaCl3, KCl3, NaBr3, and KBr3), and a trigonal potassiumchloride (hP24-KCl3). The high-pressuresyntheses were realized at 41-80 GPa in diamond anvil cellslaser-heated at about 2000 K. Single-crystal synchrotron X-ray diffraction(XRD) provided the first accurate structural data for the symmetrictrichloride Cl-3 (-) anion in hP24-KCl3 and revealed the existence of two different typesof infinite linear polyhalogen chains, [Cl]( infinity ) ( n-) and [Br]( infinity ) ( n-), in the structures of cP8-AX(3) compounds and in hP18-Na4Cl5 and hP18-Na4Br5. In Na4Cl5 and Na4Br5, we found unusually short, likely pressure-stabilized, contactsbetween sodium cations. Ab initio calculations support the analysisof structures, bonding, and properties of the studied halogenides.