Jupiter Trojans preserve primitive formation characteristics owing to their collisionless, stable orbits. Determination of their shapes and size-frequency distribution helps constrain the collisional evolution of their parent population, which also originated the Kuiper Belt. We started a programme to find precise sizes/shapes for Trojans, combining stellar occultations and the Database of Asteroid Models from Inversion Techniques (DAMIT) three-dimensional shape models. We report results for Diomedes, by fitting its unit dimensionless three-dimensional model to three chords of a stellar occultation observed in 2020, using iterative χ 2 procedures. The pole coordinates, rotation period, volume-equivalent radius and geometric albedo were λ = 153.73° ± 2.5°, β = 12.69° ± 2.6°, P = 24.4984 ± 0.0002 h, R e q = 59.4 ± 0.3 km and p V = 0.030 ± 0.004, respectively. A precise position was also obtained. This article is part of the theme issue ‘Major advances in planetary sciences thanks to stellar occultations’.