Is torus convex?

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Since a torus is Cartesian product of two circles, while circle is a convex object, and Cartesian product of two convex objects is still convex, can I conclude that the donut is a convex object? But torus has a hole in it, so it can’t be convex?

After being corrected, I think it’s the disk not the circle, so the obvious hole in the torus will be filled with a plane, and the donut will be filled in, but the resulting wheel like object still don’t feel like a convex object to me