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For stationary, homogeneous Markov processes (viz., L\'{e}vy processes,including Brownian motion) in dimension $d\geq 3$, we establish an exactformula for the average number of $(d-1)$-dimensional facets that can bedefined by $d$ points on the process's path. This formula defines auniversality class in that it is independent of the increments' distribution,and it admits a closed form when $d=3$, a case which is of particular interestfor applications in biophysics, chemistry and polymer science.  We also show that the asymptotical average number of facets behaves as$\langle \mathcal{F}_T^{(d)}\rangle \sim 2\left[\ln \left( T/\Deltat\right)\right]^{d-1}$, where $T$ is the total duration of the motion and$\Delta t$ is the minimum time lapse separating points that define a facet.

Facets on the convex hull of $d$-dimensional Brownian and L\'evy motion