We theoretically investigated the optical properties of the lesser known (22.214.171.124) Archimedean photonic crystal. The structure is two dimensional and made of dielectric GaAs rods in air. The calculations of the band structures, equifrequency contours, and simulations of the wave propagation through the structure were performed by the plane wave expansion and finite-difference time-domain methods. With analysis of the gap map and equifrequency contours we obtained frequency ranges for best performance for wave guiding. For those frequency ranges, we designed a new type of waveguide for possible applications in integrated optics. In addition, negative refraction was exhibited by the structure.