  The inclusion of the Weyl squared term in the gravitational action is one of
the most simple, yet non trivial modifications to General Relativity at high
energies. Nevertheless the study of the spherically-symmetric vacuum solutions
of this theory has received much attention only in recent times. A new type of
asymptotically flat wormhole which does not match symmetrically at a finite
radius with another sheet of the spacetime is presented. The outer spacetime is
characterized by a newtonian potential with a Yukawa correction, and has
gravitational properties that can be arbitrarily close to the ones of a
Schwarzschild black hole. The internal spacetime instead possesses a
singularity at $r=\infty$ with the topology of a 2-dimensional sphere. The
expansion scalar of geodesics reaching this singularity diverges in a finite
amount of proper time, with a striking resemblance with the future singularity
of the Big Rip cosmological scenario. In terms of the external Yukawa hair and
mass $M$, these new wormholes fill a large region of the two-dimensional
parameter space of physical solutions with $M>0$. On the contrary black holes,
both of Schwarzschild and non-Schwarzschild nature, are confined on a line. We
argue that this type of wormholes are ideal black hole mimickers.
