  We construct a new family of toric manifolds generating the unitary bordism
ring. Each manifold in the family is the complex projectivisation of the sum of
a line bundle and a trivial bundle over a complex projective space. We also
construct a family of special unitary quasitoric manifolds which contains
polynomial generators of the special unitary bordism ring with 2 inverted in
dimensions >8. Each manifold in the latter family is obtained from an iterated
complex projectivisation of a sum of line bundles by amending the complex
structure to make the first Chern class vanish.
