Current addressesFor more than one decade, SmC d4 *, SmC d3 *, and SmC A * were the only three confirmed commensurate SmC* variant phases with periodicities less than or equal four layers. In 2006, employing ellipsometry and resonant x-ray diffraction (RXRD), our research team first discovered a new liquid crystal mesophase having a six-layer periodicity in one ternary mixture which includes one sulfurcontaining compound. From our ellipsometric results, this phase showed antiferroelectric-like optical response. This novel discovery inspired renewed interest to search for liquid crystal mesophases with commensurate periodicities greater than four layers. Soon after, another mesophase having a six-layer structure and showing a ferrielectric-like dielectric response, instead, was uncovered by RXRD measurements on a different binary mixture which has one bromine-containing compound. Meanwhile mesophases having a 5-, 8-, 12-or 15-layer periodicity were reported. However, numerous questions remain to be addressed associated with these unusual reported phases. Theoretical models giving rise to mesophases with periodicities greater than 4 layers have been developed; but, to date, none of them have provided satisfactory explanations of all the physical phenomena related to the mesophases exhibiting a six-layer structure. Moreover, the question "what is the source of long-range interactions between liquidlike smectic layers, which are responsible for establishing mesophases with long periodicities and meanfield behavior of the SmA-SmC transition?" remains unanswered for more than three decades.