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Context. Rapid rotation is a common feature for massive stars, with important consequences on their physical structure, flux distribution and evolution. Fast-rotating stars are flattened and show gravity darkening (non-uniform surface intensity distribution). Another important and less studied impact of fast-rotation in early-type stars is its influence on the surface brightness colour relation (hereafter SBCR), which could be used to derive the distance of eclipsing binaries. Aims. The purpose of this paper is to determine the flattening of the fast-rotating B-type star δ Per using visible long-baseline interferometry. A second goal is to evaluate the impact of rotation and gravity darkening on the V − K colour and surface brightness of the star. Methods. The B-type star δ Per was observed with the VEGA/CHARA interferometer, which can measure spatial resolutions down to 0.3 mas and spectral resolving power of 5000 in the visible. We first used a toy model to derive the position angle of the rotation axis of the star in the plane of the sky. Then we used a code of stellar rotation, CHARRON, in order to derive the physical parameters of the star. Finally, by considering two cases, a static reference star and our best model ofmore »δ Per, we can quantify the impact of fast rotation on the surface brightness colour relation (SBCR). Results. We find a position angle of 23 ± 6 degrees. The polar axis angular diameter of δ Per is θ p = 0.544 ± 0.007 mas, and the derived flatness is r = 1.121 ± 0.013. We derive an inclination angle for the star of i = 85 + 5 -20 degrees and a projected rotation velocity V sin i = 175 + 8 -11 km s -1 (or 57% of the critical velocity). We find also that the rotation and inclination angle of δ Per keeps the V − K colour unchanged while it decreasing its surface-brightness by about 0.05 mag. Conclusions. Correcting the impact of rotation on the SBCR of early-type stars appears feasible using visible interferometry and dedicated models.« less