I think those are actually hexagonal rather than polygonal though. I've seen reports of good results with regular round bullets like the Lyman 500gr .457 though.
hexagonal is polygonal. Hex meaning "six", poly meaning "multiple" or "many".
A polygon has multiple sides. A hexagon has exactly 6 sides, octagon has 8 sides, etc, both are polygons.
Yes Mom, I know; I took geometry a few hundred years ago. The important difference of the Whitworth is the way the bullet fits almost perfectly in the bore from the start rather than being engraved (or apparently swaged to fit as in your pic) like with other types. There were also one or more that had little wings on the bullet that matched grooves in the bore and did the same thing but weren't as practical.
Whitworths era did not have truly hard alloys in small arms available, so it's amazing in how his bullets worked. Most prevailing arms of the period all were bump and swell/patched or Minie designs.
The principles of full diameter, swaged bullets came along with cartridges.
The use of lead in them hasn't changed.
The 1917 Revolvers aren't so different to make run with cast as poly type barrels.
I've run cast through Glocks and Tangos without issue. Colt 1911s are also of the shallow land variety and running over groove and without care of "too hard" in those fixed chambers is easy, much easier than wheelguns.
