  The lowest drag shape of fixed volume in Stokes flow has been known for some
40 years. It is front-back symmetric and similar to an American football with
ends tangent to a cone of 60 degrees. The analogous convex axisymmetric shape
of fixed surface area, which may be of interest for particle design in
chemistry and colloidal science, is characterized in this paper. This "other"
optimal shape has a surface vorticity proportional to the mean surface
curvature, which is used with a local analysis of the flow near the tip to show
that the front and rear ends are tangent to a cone of angle 30.8 degrees. Using
the boundary element method, we numerically represent the shape by expanding
its tangent angle in terms decaying odd Legendre modes, and show that it has
11.3% lower drag than a sphere of equal surface area, significantly more
pronounced than for the fixed-volume optimal.
