  This paper describes how one can use four standing wave laser fields to
realize a two dimensional optical quasicrystal with eight-fold symmetry,
closely related to the well-known octagonal or Ammann-Beenker tiling
quasicrystal. We describe the structure and its properties, and the effective
tight-binding model for atoms in this optical quasicrystal. Such a system, if
realized experimentally, should provide valuable insights into the quantum
properties of quasicrystals.
