Source : Webster's Revised Unabridged Dictionary (1913)

Platonic \Pla*ton"ic\, n.
   A follower of Plato; a Platonist.

Platonic \Pla*ton"ic\, Platonical \Pla*ton"ic*al\, a. [L.
   Platonicus, Gr. ?: cf. F. platonique.]
   1. Of or pertaining to Plato, or his philosophy, school, or
      opinions.

   2. Pure, passionless; nonsexual; philosophical.

   {Platonic bodies}, the five regular geometrical solids;
      namely, the tetrahedron, hexahedron or cube, octahedron,
      dodecahedron, and icosahedron.

   {Platonic love}, a pure, spiritual affection, subsisting
      between persons of opposite sex, unmixed with carnal
      desires, and regarding the mind only and its excellences;
      -- a species of love for which Plato was a warm advocate.

Source : WordNet®

Platonic
     adj 1: of or relating to or characteristic of Plato or his
            philosophy; "Platonic dialogues"
     2: free from physical desire; "platonic love"