  We show that integral representation of universal volume function of compact
simple Lie groups gives rise to six analytic functions on $CP^2$, which
transform as two triplets under group of permutations of Vogel's projective
parameters. This substitutes expected invariance under permutations of
universal parameters by more complicated covariance. We provide an analytical
continuation of these functions and particularly calculate their change under
permutations of parameters. This last relation is universal generalization, for
an arbitrary simple Lie group and an arbitrary point in Vogel's plane, of the
Kinkelin's reflection relation on Barnes' $G(1+N)$ function. Kinkelin's
relation gives asymmetry of the $G(1+N)$ function (which is essentially the
volume function for $SU(N)$ groups) under $N\leftrightarrow -N$ transformation
(which is equivalent of the permutation of parameters, for $SU(N)$ groups), and
coincides with universal relation on permutations at the $SU(N)$ line on
Vogel's plane. These results are also applicable to universal partition
function of Chern-Simons theory on three-dimensional sphere. This effect is
analogous to modular covariance, instead of invariance, of partition functions
of appropriate gauge theories under modular transformation of couplings.
