  A query, about the orbit $P{\cal W}$ in real 3-space of a point $P$ under an
isometry group ${\cal W}$ generated by edge rotations of a tetrahedron, leads
to contrasting notions, ${\cal W}$ versus ${\cal S}$, of "rotation group". The
set R $=\{r_{{\sf A}_1},r_{{\sf A}_2}\}$ of rotations $r_{{\sf A} _i}$ about
axes ${\sf A}_i$ generates two manifestations of an isometry group on $\Re^3$:
  (1). In the {\em stationary} group ${\cal S:=S}$(R), all axes {\sf B} are
fixed under a rotation $r_{\sf A}$ about {\sf A}.
  (2). In the {\em peripatetic} group ${\cal W:=W}$(R), each $r_{\sf A}$
transforms every rotational axis ${\sf B\not=A}$.
  {\bf Theorem.} \ If the line ${\sf A}_1$ is skew to ${\sf A}_2$, if each
$r_{{\sf A}_i}$ is of infinite order, and if $P\in\Re^3$, then both of the
orbits $P{\cal S}$ and $P{\cal W}$ are dense in $\Re^3$.
