The Collaborative International Dictionary of English v.0.48:

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.
      [1913 Webster]

   2. Pure, passionless; nonsexual; philosophical.
      [1913 Webster]

   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.


   Platonic year (Astron.), a period of time determined by the
      revolution of the equinoxes, or the space of time in which
      the stars and constellations return to their former places
      in respect to the equinoxes; -- called also great year.
      This revolution, which is caused by the precession of the
      equinoxes, is accomplished in about 26,000 years.
      --Barlow.
      [1913 Webster]

Moby Thesaurus II by Grady Ward, 1.0:

61 Moby Thesaurus words for "Platonic love":
   Amor, Christian love, Eros, abstinence, admiration, adoration,
   affection, agape, ardency, ardor, attachment, bodily love,
   brotherly love, caritas, celibacy, charity, conjugal love,
   continence, continency, desire, devotion, faithful love, fancy,
   fervor, flame, fondness, free love, free-lovism, heart,
   hero worship, idolatry, idolism, idolization, intactness,
   lasciviousness, libido, like, liking, love, lovemaking, maidenhead,
   maidenhood, married love, passion, physical love, popular regard,
   popularity, regard, sentiment, sex, sexual love, shine,
   spiritual love, tender feeling, tender passion, truelove,
   uxoriousness, virginity, weakness, worship, yearning