Ron Guth: The "Plain Edge" designation refers only to the Cohen 2 variety, even though there are other Plain Edge 1797 Half Cents:
Cohen 1 - plain edge, known as the "1 over 1" variety
Cohen 3a - plain edge, low head, known as the "Low Head" variety
This illustrates the problem with trying to come-up with abbreviated names for varieties of U.S. coins -- it's impossible to account for all the combinations that can occur when multiple varieties occur within the same year.
The Plain Edge, Centered Head Half Cent (Cohen 2) is underrated in terms of rarity and is much more difficut to locate than is generally believed. Above Very Fine, this date becomes very rare, especially on choclolate-brown, problem-free planchets. Only a very few examples are known in Mint State (all Brown) and none have been graded finder than MS-64BN by PCGS.
This variety usually comes nicely centered within a wide border of denticles. In this writer's opinion, it is one of the nicest looking Liberty Cap varieties.