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In this paper, we issue an error analysis for integration over discretesurfaces using the surface parametrization presented in [PS22] as well as provewhy even-degree polynomials exhibit a higher convergence rate than odd-degreepolynomials. Additionally, we provide some numerical examples that illustrateour findings and propose a potential approach that overcomes the problemsassociated with the original one.

A note on the rate of convergence of integration schemes for closed surfaces