  The slice filtration is a filtration of equivariant spectra. While the tower
is analogous to the Postnikov tower in the nonequivariant setting, complete
slice towers are known for relatively few $G$-spectra. In this paper, we
determine the slice tower for all $G$-spectra of the form $S^n \wedge
H\underline{\mathbb{Z}}$ where $n\geq 0$ and $G$ is a cyclic $p$-group for $p$
an odd prime.
