The least wellknown kind of isometry is usually called a glide
reflection. It is a kind of cross between a reflection and a
translation:
Unlike translation, rotation and reflection, we can't distinguish a
glide reflection from the others just by considering how many fixed
points there are. Just like a translation, a glide reflection doesn't
have any fixed points. On the surface, you might think that points
lying on the red line are left fixed, just as with a reflection. But
if you think in terms of a square drawn on a large sheet of
transparent plastic, you will realize that the entire red line shifts
along itself in the direction of motion.
Similarly, we can't distinguish a glide reflection from the others
just by asking whether is preserves or reverses orientation. Like a
reflection, it reverses orientations, transforming the original square
into its mirror image. Again, thinking of the plastic sheet analogy,
getting to the final position requires flipping the sheet over as you
shift it.
However, if we consider both
orientation and fixed point behavior, each type of
isometry has a unique character:

fixed points 
orientation 
Translation 
none 
preserving 
Rotation 
one 
preserving 
Glide Reflection 
none 
reversing 
Reflection 
infinite 
reversing 
Next: "Reflections on Reflections"
