A joint experimental-computational study of the molecular structure and vibrational spectra of the XeF6 molecule is reported. The vibrational frequencies, intensities, and in particular the isotopic frequency shifts of the vibrational spectra for 129XeF6 and 136XeF6 isotopologues recorded in the neon matrix agree very well with those obtained from relativistic coupled-cluster calculations for XeF6 in the C3v structure, thereby strongly supporting the observation of the C3v conformer of the XeF6 molecule in the neon matrix. A C3v transition state connecting the C3v and Oh local minima is located computationally. The calculated barrier of 220 cm-1 between the C3v minima and the transition state corroborates the experimental observation of the C3v conformer and the absence of the Oh conformer in solid noble gas matrices. For comparison matrix-isolation spectra have also been recorded and analyzed for the 129XeOF4 and the 136XeOF4 isotopologues. The matrix-isolation complexation shifts obtained for the XeF6·NCCH3 relative to those of free matrix isolated XeF6 and CH3CN are in good agreement with those reported for crystalline XeF6·NCCH3.