Ron Guth: The 1797 Low Head Half Cent is a distinctive variety where the head of Liberty was punched way too low into the die, crowding into and nearly touching the date. While this variety is visually distinctive, it's important to check the edge because one of the greatest cherrypicking opportunities exists with the Low Head Half Cent. Three edge subvarieties exist on the 1797 Low Head: Plain Edge, Lettered Edge, and Gripped Edge. The 1797 Low Head, Plain Edge is the most "common" of the three subvarieties, though even it is scarce. The 1797 Low Head, Lettered Edge is a very scarce and desirable variety. Finally, the 1797 Low Head, Gripped Edge is one of the rarest and most valuable of all Half Cent varieties. So, on all 1797 Low Head Half Cents, be sure to check the edge!
In terms of condition, the 1797 Low Head, Plain Edge is difficult to locate in any grade, especially above Very Fine. No Mint State examples are known to exist.