  Cylindrical-like coordinates for constant-curvature 3-spaces are introduced
and discussed. This helps to clarify the geometrical properties, the coordinate
ranges and the meaning of free parameters in the static vacuum solution of
Linet and Tian. In particular, when the cosmological constant is positive, the
spacetimes have toroidal symmetry. One of the two curvature singularities can
be removed by matching the Linet-Tian vacuum solution across a toroidal surface
to a corresponding region of the dust-filled Einstein static universe. Some
other properties and limiting cases of these space-times are also described,
together with their generalisation to higher dimensions.
