An arrow with self-aligning features allows a user to properly nock the arrow without resorting to manual alignment of the nock and fletchings. Engagement of a removable nock and shaft, each with a rounded polygonal cross-section, such as a reuleaux triangle, allow for a fixed relative angular position between the nock and the shaft without the use of an adhesive. This allows for proper position between the nock and index vane to ensure a more accurate path of the arrow during flight. Similarly, the reuleaux triangle cross-section of the shaft may engage an arrow head with a similar reuleaux triangle for accurate alignment between the shaft and the arrow head.