Originally Posted by Mr.Reignman
to name a few...
Not compromising the barrel's thickness in the area of each groove as with traditional rifling.
Providing a better gas seal around the projectile as polygonal bores tend to have a slightly smaller bore area, which translates into more efficient use of the combustion gases trapped behind the bullet.
slightly greater (consistency in) muzzle velocities and slightly increased accuracy
Less bullet deformation, resulting in reduced drag on the bullet when traveling through the barrel which helps to increase muzzle velocity.
Reduced buildup of copper or lead within the barrel which results in easier maintenance characteristics.
Prolonged barrel life.
For an example - Kahr's high-end pistols (PM9, PM40, etc) use Walther-Lothan barrels with polyagonal rifling like Glock does. Their cheaper ones (P9, CW-series) have standard rifling.