  The cosmological constant $\Lambda$ modifies certain properties of large
astrophysical rotating configurations with ellipsoidal geometries, provided the
objects are not too compact. Assuming an equilibrium configuration and so using
the tensor virial equation with $\Lambda$ we explore several equilibrium
properties of homogeneous rotating ellipsoids. One shows that the bifurcation
point, which in the oblate case distinguishes the Maclaurin ellipsoid from the
Jacobi ellipsoid, is sensitive to the cosmological constant. Adding to that,
the cosmological constant allows triaxial configurations of equilibrium
rotating the minor axis as solutions of the virial equations. The significance
of the result lies in the fact that minor axis rotation is indeed found in
nature. Being impossible for the oblate case, it is permissible for prolate
geometries, with $\Lambda$ zero and positive. For the triaxial case, however,
an equilibrium solution is found only for non-zero positive $\Lambda$. Finally,
we solve the tensor virial equation for the angular velocity and display
special effects of the cosmological constant there.
