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Rotation Groups
A query, about the orbit in real 3-space of a point under an
isometry group generated by edge rotations of a tetrahedron, leads
to contrasting notions, versus , of "rotation group". The
set R of rotations about
axes generates two manifestations of an isometry group on :
(1). In the {\em stationary} group (R), all axes {\sf B} are
fixed under a rotation about {\sf A}.
(2). In the {\em peripatetic} group (R), each
transforms every rotational axis .
{\bf Theorem.} \ If the line is skew to , if each
is of infinite order, and if , then both of the
orbits and are dense in .Comment: 6 page