Simultaneous localization and mapping (SLAM) is a fundamental problem in mobile robotics. Map matching approach to the SLAM problem has received much attention in recent years. A main contribution of this paper is proposal of "3D polestar descriptor" to facilitate the fast 3D map matching SLAM. A discriminative shape descriptor and a hash-based indexing technique is presented for 3D point cloud data. Experiments are conducted in indoor environments using Bumblebee stereo camera.