  We prove that geodesic rays in the Uniform Infinite Planar Triangulation
(UIPT) coalesce in a strong sense using the skeleton decomposition of random
triangulations discovered by Krikun. This implies the existence of a unique
horofunction measuring distances from infinity in the UIPT. We then use this
horofunction to define the skeleton "seen from infinity" of the UIPT and relate
it to a simple Galton--Watson tree conditioned to survive, giving a new and
particularly simple construction of the UIPT. Scaling limits of perimeters and
volumes of horohulls within this new decomposition are also derived, as well as
a new proof of the $2$-point function formula for random triangulations in the
scaling limit due to Ambj{\o}rn and Watabiki.
