By combining electron energy-loss spectroscopy and state-of-the-art computational methods, we were able to provide an extensive picture of the excitonic processes in 1T-HfS2. The results differ significantly from the properties of the more scrutinized group VI semiconducting transition metal dichalcogenides such as MoS2 and WSe2. The measurements revealed a parabolic exciton dispersion for finite momentum q parallel to the Gamma K direction which allowed the determination of the effective exciton mass. The dispersion decreases monotonically for momentum exchanges parallel to the Gamma M high symmetry line. To gain further insight into the excitation mechanisms, we solved the ab initio Bethe-Salpeter equation for the system. The results matched the experimental loss spectra closely, thereby confirming the excitonic nature of the observed transitions, and produced the momentum-dependent binding energies. The simulations also demonstrated that the excitonic transitions for q parallel to Gamma M occur exactly along that particular high symmetry line. For q parallel to Gamma K on the other hand, the excitations traverse the Brillouin zone crossing various high symmetry lines. A particular interesting aspect of our findings was that the calculation of the electron probability density revealed that the exciton assumes a six-pointed star-like shape along the real space crystal planes indicating a mixed Frenkel-Wannier character.