In this work, we measure, for the first time, the birefringence of a phasmidic columnar liquid crystal (PCLC) in a hexagonal phase using two different types of textures. In the first texture, we use some types of developpable domain where the columns are organized in concentric hemispheres. We present the measurement of the birefringence Delta n by observing interference fringes. We use in the second texture, a monocrystalline PCLC in homeotropic orientation between two glass plates with a thickness d. we illuminate the structure by a monoochromatique convergent light, we observe the figure of conoscopy which shows a circle of interference between ordinary and extraordinary rays. The two textures give the same value of the birefringence Delta n =-0.06 for lambda = 532nm.