  Bott and Samuelson constructed explicit cycles representing a basis of the
Z_2-homology of the orbits of variationally complete representations of compact
Lie groups. As a consequence, all those orbits are taut. We were able to show
that an irreducible representation of a compact Lie group, all of whose orbits
are taut, is either variationally complete or it is one of the following
orthogonal representations (n bigger than or equal to 2): the (standard) x_R
(spin) representation of SO(2)xSpin(9); or the (standard) x_C (standard)
representation of U(2)xSp(n); or the (standard)^3 x_ H (standard)
representation of SU(2)xSp(n). In this paper we will show how to adapt the
construction of the cycles of Bott and Samelson to the orbits of these three
representations. As a result, they also admit explicit cycles representing a
basis of their Z_2-homology and, in particular, this provides another proof of
their tautness.
