text: In an inversion through a centre of symmetry,  (the element), we imagine taking each point in a molecule and then moving it out the same distance on the other side. In summary, the inversion operation projects each atom through the centre of inversion and out to the same distance on the opposite side. The inversion center is a point in space that lies in the geometric center of the molecule.  As a result, all the cartesian coordinates of the atoms are inverted (i.e.  to ). The symbol used to represent inversion center is . When the inversion operation is carried out  times, it is denoted by , where  when  is even and  when  is odd. 
  Examples of molecules that have an inversion center include certain molecules with octahedral geometry (general formula ), square planar geometry (general formula ), and ethylene (). Examples of molecules without inversion centers are  cyclopentadienide () and molecules with trigonal pyramidal geometry (general formula ).