  This paper provides a new way to understand the equivariant slice filtration.
We give a new, readily checked condition for determining when a $G$-spectrum is
slice $n$-connective. In particular, we show that a $G$-spectrum is slice
greater than or equal to $n$ if and only if for all subgroups $H$, the
$H$-geometric fixed points are $(n/|H|-1)$-connected. We use this to determine
when smashing with a virtual representation sphere $S^V$ induces an equivalence
between various slice categories. Using this, we give an explicit formula for
the slices for an arbitrary $C_p$-spectrum and show how a very small number of
functors determine all of the slices for $C_{p^n}$-spectra.
