The platonic rotation group is defined by having  multiple C_n axes where n>2.  These molecules are considered to have high symmetry and are non-polar.  This rotation group can be further divided into 3 subgroups: tetrahedral (T), octahedral (O) and icosahedral (I) depending on whether n=3, n=4 or n=5 respectively.

• T  -  If more than one C₃ is present, the molecule will be tetrahedral.  Molecules in this group will have a full point group of either T_h or T_d.
• T_h  -  These molecules will also have either an inversion center (i) or a perpendicular (to the C₃) mirror plane (s_h).  These molecules do not look like tetrahedra.  Examples are relatively rare; one is [Fe(C₅H₅N)₆]²⁺.
• T_d  -  Most tetrahedral molecules will belong to this point group.  They will have a dihedral mirror plan (s_d) bisecting two C₃'s.  A common example is methane (CH₄).
• O  -  This group is defined by the presence of multiple C₄'s.
• O  -  If there is no inversion center and no mirror planes, then the full point group is O, and the molecule is chiral.  This point group is quite rare.
• O_h  -  If either an inversion center or a mirror plane exist, then the full point group is O_h.  These molecules are achiral.  An example is [PtCl₆]^2-.
• I_h  -  The icosahedral group is defined by the presence of multiple C₅'s.  There will in fact be 12C₅'s, as well as 20C₃'s, 15C₂'s, 15s's and an i..  An example is [B₁₂H₁₂]^2-.