The effect of rare gas complexation on the electronically excited S-1(E’) state of triptycene (T), which is Jahn-Teller distorted, was investigated by two-color resonant two-photon ionization (2C-R2PI) spectroscopy of the supersonically cooled van der Waals complexes triptycene Ne-n, n=1-3. These complexes afford unique possibilities to study the effects of weak intermolecular interactions on the intramolecular Jahn-Teller coupling. Since the atoms are adsorbed at high-symmetry positions, the system symmetry is lowered from D-3h(n=O) to C-2v for n=1 and 2, but reverts to D-3h for n=3. A Jahn-Teller (A(1) circle plus E) circle times e coupling model including a uniaxial external strain component was applied successfully to calculate the S-1 state levels and S-1<--S-0 electronic spectra of all three complexes. The spectrum of T.Ne-3 was fully interpreted without inclusion of strain, implying a highly symmetric D-3h structure in which each of the three V-shaped compartments of triptycene is occupied by a single Ne atom. In contrast, the vibronic spectra of T.Ne and T.Ne-2 were fitted with a considerable uniaxial strain of -19.73 and 19.07 cm(-1) respectively, confirming both the predicted C-2v geometry of the complexes as well as the equal magnitude, but opposite sign of the intramolecular distortion induced by one or two Ne atoms. These distortions correspond to a small change of the angle of the V-shaped compartments by similar to 0.8 degrees. The spectra of T.Ne and T.Ne-2 are much more complex compared to triptycene and T.Ne-3 due to the splitting of the E vibronic levels in C-2v symmetry, and the appearance of additional transitions to levels that are weak or symmetry forbidden in bare triptycene. The calculated Jahn-Teller potential energy surfaces and vibronic wave functions are discussed and classified in terms of their symmetry and localization/delocalization properties.