Example of a $C^{1,1}$ surface with constant Gaussian curvate equal to 1, which is not a sphere?

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In a paper I'm reading the author talk about the construction of a $C^{1,1}$ surface with constant Gaussian curvature equal to $1$. I do not know what to imagine other then a sphere though, which makes the article difficult to read. So does someone have an example of such surface that is not a sphere?