This is a question about appropriate naming and representation.
What are the classes of isometries in $\Bbb R ^4$?
I can easily identify the rotation around a plan, the reflection through an infinite flat volume (any $\Bbb R ^3$ space orthogonal to a vector). What is the complete set of isometries classes?
What is the appropriate name of what I improperly named here a "class" of isometries?
What is the best graphical representation of these classes of isometries?