We modeled the geometry and the three-dimensional orientation of the ejecta cone triggered by the impact of the DART spacecraft on the asteroid Dimorphos. We used eight LUKE images of the impact acquired by the CubeSat LICIACube that flew by the Didymos system shortly after the impact. These images, which show the ejecta cone in both face-on and side-on profiles, enabled us to reconstruct the ejecta cone in inertial space. We started our model as a simple cone with a circular base and developed it to a rotated cone with an elliptical base that best fit the data. The cone axis points to R.A., decl. (in J2000): 147 − 10 ° + 1 ° , + 16 − 6 ° + 4 ° . The cone is characterized by two perpendicular half-angles of η = 69 − 3 ° + 1 ° , γ = 51 − 11 ° + 1 ° and a rotation of ω = 12° around its axis. The apex of the cone is located near the center of Dimorphos within 15 m. The intersection of the cone and the surface of Dimorphos (surface enclosed by the cone) would correspond to a crater with a maximum radius of about 65 m. The characterization of the cone axis is directly related to the computation of the momentum enhancement factor (β) of the impact, and it hence proves the crucial need of studying impacts in the context of planetary defence scenarios. The results of this work could potentially be used to constrain whether the impact took place in a strength-dominated or a gravity-dominated regime. This work shows the important scientific return of the LICIACube CubeSat in the context of planetary defence.