  We present estimates of number of simplices of given dimension of classical
compact Lie groups. As in the previous work \cite{GMP2} the approach is a
combination of an estimate of number of vertices with a use of valuation of the
covering type by cohomological argument of \cite{GMP} and application of the
recent versions of the Lower Bound Theorem of combinatorial topology. For the
case of exceptional Lie groups we made a complete calculation using the
description of their cohomology rings given by the first and third author. For
infinite increasing series of Lie groups of growing dimension $d$ the rate of
growth of number of simplices of highest dimension is given which extends onto
the case of simplices of (fixed) codimension $d-i$.
