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Context. The Centaur (10199) Chariklo has the first ring system discovered around a small object. It was first observed using stellar occultation in 2013. Stellar occultations allow sizes and shapes to be determined with kilometre accuracy, and provide the characteristics of the occulting object and its vicinity. Aims. Using stellar occultations observed between 2017 and 2020, our aim is to constrain the physical parameters of Chariklo and its rings. We also determine the structure of the rings, and obtain precise astrometrical positions of Chariklo. Methods. We predicted and organised several observational campaigns of stellar occultations by Chariklo. Occultation light curves were measured from the datasets, from which ingress and egress times, and the ring widths and opacity values were obtained. These measurements, combined with results from previous works, allow us to obtain significant constraints on Chariklo's shape and ring structure. Results. We characterise Chariklo's ring system (C1R and C2R), and obtain radii and pole orientations that are consistent with, but more accurate than, results from previous occultations. We confirm the detection of W-shaped structures within C1R and an evident variation in radial width. The observed width ranges between 4.8 and 9.1 km with a mean value of 6.5 km. One dual observation (visible and red) does not reveal any differences in the C1R opacity profiles, indicating a ring particle size larger than a few microns. The C1R ring eccentricity is found to be smaller than 0.022 (3 sigma), and its width variations may indicate an eccentricity higher than similar to 0.005. We fit a tri-axial shape to Chariklo's detections over 11 occultations, and determine that Chariklo is consistent with an ellipsoid with semi-axes of 143.8(-1.5)(+1.4), 135.2(-2.8)(+1.4), and 99.1(-2.7)(+5.4) km. Ultimately, we provided seven astrometric positions at a milliarcsecond accuracy level, based on Gaia EDR3, and use it to improve Chariklo's ephemeris. ; European Research Council under the European Community's H2020 669416 Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPQ) Fundacao de Apoio a Pesquisa do Distrito Federal (FAPDF) 465376/2014-2 European Union H2020-MSCA-ITN-2019 860470 Novo Nordisk Foundation Interdisciplinary Synergy Programme NNF19OC0057374 Fonds de la Recherche Scientifique - FNRS PDR T.0120.21 Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPQ) BEM 150612/2020-6 FB-R 314772/2020-0 RV-M 304544/2017-f5 401903/2016-8 JIBC 308150/2016-3 305917/20196 MA 427700/2018-3 ; Versión aceptada para publicar - Postprint