  A quantum mechanical model for the Neon-20 nucleus is developed that allows
for the splitting of a bipyramidal structure of five alpha-partices into an
alpha-particle and an Oxygen-16 nucleus. The geometry of the configuration
space is assumed to be a 3-dimensional spatial wormhole, and on the wormhole
background there is an attractive short-range potential. This leads to a radial
Schr\"odinger equation of the Heun form, which simplifies for threshold bound
states to an associated Legendre equation that has explicit solutions. The
energies of the true bound states for all spin/parities are numerically
calculated, and match those of the well-established $K^\pi=0^+$, $K^\pi=0^-$,
and certain higher rotational bands of Neon-20.
