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We present a polyad-preserving algebraic approach to molecular structure and, as an application, we fit the model parameters to reproduce an extensive experimental data set of vibrational energies of carbon dioxide in its ground electronic state. The data set includes levels with vibrational angular momentum ℓ = 1, ...,6 and some recently obtained term values that have not been previously considered. The obtained results are close to experimental uncertainty and we compare the results obtained making use of the three most common polyad schemes that can be found in the literature for this molecular species. Graphical abstract: [ABSTRACT FROM AUTHOR]