Structure and energetics of solvation of the triplet Rydberg states of the He-2(*) excimer in liquid He-4 (LHe) are analyzed using ab initio potentials and density functional methods. The results are used to interpret the known spectroscopy. Having established the reliability of the various semiempirical functionals, interfacial properties of the superfluid on molecular scales are discussed. Due to its spherical electron density, the a((3)Sigma(u)) state solvates in a spherical bubble of 7 Angstrom radius in which the excimer freely rotates. This explains the observed rotationally resolved (3)b<--(3)a and (3)c<--(3)a absorption spectra. A deep potential minimum occurs at the equatorial node of the c((3)Sigma(u)) state, where a radially frozen belt of six He atoms can be sustained at R=2.3 Angstrom, inside an ellipsoidal cavity with major axis of 8 Angstrom and a more diffuse minor axis of 6 Angstrom. Despite the absence of a potential energy barrier, or a many-body interfacial tension preventing the wetting of the belt, the bare (3)c state is observed in emission. It is argued that in the superfluid, wetting is prevented by the hindered rotation of the excimer, hence the sensitivity of the (3)c-->(3)a emission to pressure induced quenching. The nodal plane in the b((3)Pi(g)) state passes through the molecular axis, as such, rotation cannot provide protection against wetting and subsequent quenching of the (3)b state via the He-3(*) manifold; hence the absence of (3)b-->(3)a emission despite its large transition dipole. In its global minimum, the (3)d excimer sustains a shell of 16 He atoms, localized at the radial node of its Rydberg electron, at Rsimilar to2.5 Angstrom. The shell, in turn, is contained in a nearly spherical bubble held at a radius of 13 Angstrom by the extra-nodal electron density. The repulsion between extra-nodal electron density and LHe provides a barrier to filling of the deep nodal well, ensuring the stability of the bare (3)d excimer in a large spherical bubble. This explains the free-rotor envelopes of the (3)d-->(3)b and (3)d-->(3)c emissions, and their negligible spectral shifts relative to the gas phase. The predicted minimum energy structures, the belted (3)c state and the crusted (3)d state, if formed, should be metastable.