HSV Loci in the RGB Color Space

Snapshot 1: The locus of colors with constant hue is a triangular "wedge" that swings around the main diagonal of the RGB cube (the line of grays).

Snapshot 2: The locus of colors with constant saturation is a truncated "pyramid" that collapses to the line of grays as the saturation approaches zero. The point of black (0,0,0) lies at the vertex of all constant saturation loci, and its own saturation is technically undefined.

Snapshot 3: The locus of colors with constant value is a truncated (three-faced) "cube", with only one corner on the line of grays, that collapses to the black point as the value approaches zero.