We study the spin distributions in permalloy (Py: Ni80Fe20) nanodisks as a function of diameter D (300 nm ≤ D ≤ 1 μm) and thickness L (30 nm ≤ L ≤ 100 nm). We observed that beyond a certain thickness, for a fixed disk diameter, an unconventional spin topology precipitates which is marked by the presence of a divergence field within the magnetic vortex curl. The strength of this divergence changes anti-symmetrically from negative to positive - depending on the core polarity - along the axis of the cylindrical nanodisk. This is also accompanied by a skyrmion-like out-of-plane bending of the spin vectors farther away from the disk center. Additionally, the vortex core dilates significantly when compared to its typical size. This has been directly observed using magnetic force microscopy. We determined from the ferromagnetic resonance spectroscopy measurements that the unconventional topology in the thicker nanodisks gyrated at a frequency, which is significantly lower than what is predicted by a magnetic vortex based analytical model. Micromagnetic simulations involving dipolar and exchange interactions appear to satisfactorily reproduce the experimentally observed static and dynamic behaviors. Besides providing a physical example of an unconventional topology, these results can also aid the design of topologically protected memory elements. © 2016 Author(s).