Polygonal rifling is a type of rifling wherein the traditional lands and grooves are replaced instead by "hills and valleys" in a rounded polygonal pattern, usually a hexagon.
However, it should be noted that precision target pistols, such as those used in bullseye and IHMSA, almost universally use traditional rifling, as do target rifles. The debate among target shooters is almost always one of cut vs. button rifled barrels, as traditional rifling is dominant. The areas where polygonal rifled barrels are used competitively is in pistol action shooting, such as IDPA and IPSC competitions.
Part of the difference may be that most polygonal rifling is produced by hammer forging the barrel around a mandrel containing a reverse impression of the rifling. Hammer forging machines are tremendously expensive, far out of the reach of custom gunsmiths (unless they buy pre-rifled blanks), and so are generally only used for production barrels by large companies. The main advantage of a hammer forging process is that it can take a bored barrel blank and rifle, chamber, and contour it on one step. Invented in Germany in 1939, hammer forging has remained popular in Europe, but was only later used by gunmakers in the United States. The hammer forging process produces large amounts of stress in the barrel that must be relieved by careful heat treatment, a process that is less necessary in a traditionally cut or button rifled barrel. Due to the potential for residual stress causing accuracy problems, precision shooters tend to avoid hammer forged barrels, and thus limits them in the type of available rifling.
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