Is there a convex symmetric body with C^2 boundary and non-vanishing Gaussian curvature in R^3 whose polar(dual) body fails to have non-vanishing Gaussian curvature?
With all due respect to Ms. Ivanova, you may be confused by her answer.
To me, it seem that your question is about differential geometry (of which I have studied enough to know a few terms, but unfortunately not enough to be able to answer your question.)
Ms. Ivanova seems to have interpreted your question as about the program Gaussian (http://gaussian.com/), which is for computational chemistry.