Using a suitable parametrization in terms of polar coordinates, the author computes the volume and the surface area of the solid of revolution obtained by rotating a Reuleaux triangle of constant width R about one of its axes. They are respectively given by Cal V=(frac 2 3 π- frac{π^2}{6}) R^3 and Cal S=frac{πR^2}{3} (6 – π). Computation of the volume is accomplished by finding the x-coordinate of the center of mass and invoking the well-known theorem of Pappus-Guldin, according to which the volume is given as the product of the circumference of the circle traversed by the center of mass and the area of the region being revolved (in this case half of the Reuleaux triangle). For the surface area a formula of Blaschke relating Cal V and Cal S for a solid of constant thickness R, viz. Cal S=frac{RCal S}{2} – frac{πR^3}{3}, is used. The result for the volume is compared with the volume of the solids of Meissner [{it B. Kawohl} and {it C. Weber}, Math. Intell. 33, No. 3, 94-101 (2011; Zbl 1231.52002)], which are believed to have minimal volume among all solids of constant thickness R. The paper contains several pesky typos – extra factor cos (t) in the parametrization of y(t), wrong power R instead of R^3 in the expression for the center of mass and the missed coefficient 3 of Cal V in one of the formulas for Cal S. (ZDM/Mathdi)