Reflection Symmetry
Mathematical Definition:

Reflection in the x-axis:

                                           (x,y)=>(x,-y)

Reflection in the y-axis:

                                           (x,y)=>(-x,y)

Reflection in the xy-diagonal:

                                           (x,y)=>(y,x)

Written Definition:

    A reflection fixes one line in the plane, called the axis of reflection, and
exchanges points on one side of the axis with points on the other side of the axis at
the same distance from the axis. In the example you see a diagonal axis in white.
The double ended red arrows are supposed to suggest the reflection. It's called a
"reflection" because similar things happen with a reflection in a mirror.

source
 
 
 
 The literary equivalent is a palindrome, whose symmetry is spelled: "A man, a plan, a canal, Panama", which can essentially be "folded" in half: the "axis" of reflection is the letter "C". The same letters come from the "C" on both sides.
 
 
Glide Reflection
 

A glide reflection combines a reflection with a translation along the direction of the mirror line. Glide reflections are the only type of symmetry that involve more than one step.

 
 
 
 

Literary glide reflection symmetry is best illustrated with a short story that began with "Put the broom down, John!" and ended with "Pick the John up, broom!" There is a difference between the original and the reflection, yet they are similar. Only directions and positions have been switched.
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