The ASA book contradicts itself a little on home plate. In the Playing Field section, it describes home plate as "Home plate shall be made of rubber or other suitable material. It shall be a five-sided figure, 17 inches wide across the edge facing the pitcher’s plate. The sides shall be parallel to the inside lines of the batter’s box and shall be 8 1/2 inches long. The sides of the point facing the catcher shall be 12 inches long.". That would be the white part only.
Later in that same section it list home plate as "17” wide, sides parallel to the batter’s box line and are 8 ½” long, sides of the point facing the catcher are 12” long. The width of the black edge is ¾”.
You'll also notice there's no height, so it's a two-dimensional object.
It never states whether the black edge is part of it (making the home plate 18 1/2" wide).
Whether someone can actually throw a legally arced pitch that lands only on the black edge (and no portion of the 17" surface) is another story. It's really not supposed to be that exposed.