  We study Heisenberg model of classical spins lying on the toroidal support,
whose internal and external radii are $r$ and $R$, respectively. The isotropic
regime is characterized by a fractional soliton solution. Whenever the torus
size is very large, $R\to\infty$, its charge equals unity and the soliton
effectively lies on an infinite cylinder. However, for R=0 the spherical
geometry is recovered and we obtain that configuration and energy of a soliton
lying on a sphere. Vortex-like configurations are also supported: in a ring
torus ($R>r$) such excitations present no core where energy could blow up. At
the limit $R\to\infty$ we are effectively describing it on an infinite
cylinder, where the spins appear to be practically parallel to each other,
yielding no net energy. On the other hand, in a horn torus ($R=r$) a singular
core takes place, while for $R<r$ (spindle torus) two such singularities
appear. If $R$ is further diminished until vanish we recover vortex
configuration on a sphere.
