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In this paper, the dispersion and the confinement loss properties of polygonal tube fibers are investigated. Fano resonances between the hollow core modes and the high order dielectric modes are found inside transmission bands. A theoretical model based on the approximation of the polygonal tube as a perturbed circular one is proposed. The model is able to predict number and spectral position of the Fano resonances. It is shown that there always is a lower bound condition on the number of sides of the polygonal fiber which guarantees the absence of Fano resonances in a given frequency range. Numerical results are given in order to support the model.