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of, relating to, or characteristic of or his doctrines:
the Platonic philosophy of ideal forms.
pertaining to, involving, or characterized by as a striving toward love of spiritual or ideal beauty.
(usually lowercase) purely spiritual; free from sensual desire, especially in a relationship between two persons of the opposite sex.
(usually lowercase) feeling or professing platonic love:
He insisted that he was completely platonic in his admiration.
Contemporary Examples

In high school, Tsukuru was one of five Platonic but intimate friends who did everything together and thought as one.
Haruki Murakami’s Weird, Wonderful World Malcolm Jones August 14, 2014

My Platonic ideal is the hole-in-the-wall seafood joint, Swan Oyster Depot.
The Easygoing Flair of San Francisco Jolie Hunt April 9, 2010

You will be stoic and brave, the Platonic ideal of perseverance no matter what life throws at you.
So You Have an Inconsequential But Awful Illness Kelly Williams Brown January 17, 2014

She uses the celebrations of holy matrimony as a way to chronicle her own relationships, both romantic and Platonic.
The Summer’s Juiciest Beach Reads: Hillary’s New Memoir And More Emily Shire May 20, 2014

He wants his audience to wake up from their sleep, emerge from their Platonic cave, and see the world as it truly is.
Meet the Most Compelling Crazy Person in America Justin Green April 29, 2013

Historical Examples

Among them is very probably included the Platonic Parmenides itself, distinguished as it is for extreme subtlety.
Aristotle George Grote

The Menexenus has more the character of a rhetorical exercise than any other of the Platonic works.
Menexenus Plato

Doctrine of the Sophistês — contradicts that of other Platonic dialogues.
Plato and the Other Companions of Sokrates, 3rd ed. Volume III (of 4) George Grote

And there he would sing to Dulcinea, his Platonic and only love.
The Story of Don Quixote Arvid Paulson, Clayton Edwards, and Miguel de Cervantes Saavedra

Not even in the case of an aged hypocrite who probably posed as the Platonic friend?
The Orchard of Tears Sax Rohmer

adjective
of or relating to Plato or his teachings
(often not capital) free from physical desire: Platonic love
adj.

1530s, “of or pertaining to Greek philosopher Plato” (429 B.C.E.-c.347 B.C.E.), from Latin Platonicus, from Greek Platonikos. The name is Greek Platon, properly “broad-shouldered” (from platys “broad;” see plaice (n.)). His original name was Aristocles. The meaning “love free of sensual desire” (1630s), which the word usually carries nowadays, is a Renaissance notion; it is based on Plato’s writings in “Symposium” about the kind of interest Socrates took in young men, which originally had no reference to women. Related: Platonically.