  Recently, a codimension two holography called wedge holography is proposed as
a generalization of AdS/CFT. It is conjectured that a gravitational theory in
$d+1$ dimensional wedge spacetime is dual to a $d-1$ dimensional CFT on the
corner of the wedge. In this paper, we give an exact construction of the
gravitational solutions for wedge holography from the ones in AdS/CFT. By
applying this construction, we prove the equivalence between wedge holography
and AdS/CFT for vacuum Einstein gravity, by showing that the classical
gravitational action and thus the CFT partition function in large N limit are
the same for the two theories. The equivalence to AdS/CFT can be regarded as a
"proof" of wedge holography in a certain sense. As an application of this
powerful equivalence, we derive easily the holographic Weyl anomaly,
holographic Entanglement/R\'enyi entropy and correlation functions for wedge
holography. Besides, we discuss the general solutions of wedge holography and
argue that they correspond to the AdS/CFT with suitable matter fields.
Interestingly, we notice that the intrinsic Ricci scalar on the brane is always
a constant, which depends on the tension. Finally, we generalize the
discussions to dS/CFT and flat space holography. Remarkably, we find that
AdS/CFT, dS/CFT and flat space holography can be unified in the framework of
codimension two holography in asymptotically AdS. Different dualities are
distinguished by different types of spacetimes on the brane.
