The phenomenon of conical diffraction began in 1832 with Hamilton, who predicted that for a biaxial crystal, a beam shone along the optic axis would refract internally into an expanding skew cone inside the material. Additionally, along a different axis in the crystal, the optic ray axis, an incoming hollow skew cone of light would refract into a single ray inside the crystal. The two phenomena are dual, with the latter effect called external conical refraction. In the past, internal conical diffraction has been thoroughly investigated, theoretically and experimentally, from Poggendorf’s dark ring to the Raman spike, to the examination of optical activity as well as the transition to and from double refraction. However, the theory has not been developed for the external case. Along that vein, we work towards obtaining the intensity distribution as a beam evolves in space through the crystal, given an incoming beam and its Fourier transform. Furthermore, we obtain experimental images of the external cone, which help verify the theory developed.