  In the continuum a skyrmion is a topological nontrivial map between
Riemannian manifolds, and a stationary point of a particular energy functional.
This paper describes lattice analogues of the aforementioned skyrmions, namely
a natural way of using the topological properties of the three-dimensional
continuum Skyrme model to achieve topological stability on the lattice. In
particular, using fixed point iterations, numerically exact lattice skyrmions
are constructed; and their stability under small perturbations is explored by
means of linear stability analysis. While stable branches of such solutions are
identified, it is also shown that they possess a particularly delicate
bifurcation structure, especially so in the vicinity of the continuum limit.
The corresponding bifurcation diagram is elucidated and a prescription for
selecting the branch asymptoting to the well-known continuum limit is given.
Finally, the robustness of the spectrally stable solutions is corroborated by
virtue of direct numerical simulations .
