  Some models providing shell-shaped static solutions with compact support
(compactons) in 3+1 and 4+1 dimensions are introduced, and the corresponding
exact solutions are calculated analytically. These solutions turn out to be
topological solitons, and may be classified as maps $S^3 \to S^3$ and suspended
Hopf maps, respectively. The Lagrangian of these models is given by a scalar
field with a non-standard kinetic term (K field) coupled to a pure Skyrme term
restricted to $S^2$, rised to the appropriate power to avoid the Derrick
scaling argument. Further, the existence of infinitely many exact shell
solitons is explained using the generalized integrability approach. Finally,
similar models allowing for non-topological compactons of the ball type in 3+1
dimensions are briefly discussed.
