A novel hexagonal phase discovered near the Ca15Au60Sn25 quasicrystal and its cubic approximants (ACs) was synthesized by means of high-temperature solid-state reactions. Single-crystal structural analyses show that this is a Gd14Ag51 isotype with composition within the range Ca14Au45.56(4)-46.67(4)Sn5.14(3)-4.14(3), space group P6/m (No. 175), and lattice parameters a =12.763(3)-12.879(3) angstrom and c = 9.326(3)-9.3815(4) angstrom. In this phase, Sn mixes with Au in two of seven anionic sites to give a strong coloring that generates a narrow honeycomb-like Au/Sn template, in which sizable columns of hexagonal Au stars are confined. This phase transforms into the cubic 211 AC phase through a peritectic reaction at similar to 678 degrees C. The valence electron count per atom (eta) of the present phase is in the range 1.41-1.45. However, it does not appear to follow a Hume-Rothery mechanism.