  We give a computer-free proof of a theorem of Basak, describing the group
generated by 16 complex reflections of order 3, satisfying the braid and
commutation relations of the Y555 diagram. The group is the full isometry group
of a certain lattice of signature (13,1) over the Eisenstein integers Z[cube
root of 1]. Along the way we enumerate the cusps of this lattice and classify
the root and Niemeier lattices over this ring.
