Absolute optical instruments with rotation symmetry and corresponding absolute geodesic lenses have drawn considerable attention for their property of perfect imaging of light rays. In this paper, we systematically explore a series of absolute geodesic lenses which is mapped from generalized Maxwell's fish-eye lenses with a rational number index {p}. Moreover, we construct new types of duplex absolute geodesic lenses by splicing two different half absolute geodesic lenses, which is inspired by the work [Huiyan Peng, et al Phys. Rev. Applied13, 034050 (2020)]. Also, we fabricate some samples of absolute geodesic lenses based on the 3D printing technique and observe light rays on them. Our findings enlarge the family of absolute geodesic lenses and might find an application on classical imaging systems.