1.  peculiarity(n = noun.cognition) distinctive feature, distinguishing characteristic - an odd or unusual characteristic;
is a kind of characteristic, feature
has particulars: calling card

2.  peculiarity(n = noun.attribute) distinctiveness, speciality, specialness, specialty - a distinguishing trait;
is a kind of individualism, individuality, individuation
has particulars: foible, idiosyncrasy, mannerism
Derived form adjective peculiar₄

3.  peculiarity(n = noun.artifact) curio, curiosity, oddity, oddment, rarity - something unusual -- perhaps worthy of collecting;
is a kind of object, physical object
has particulars: bric-a-brac, knickknack, knickknackery, nicknack, whatnot, collectable, collectible, collector's item, piece de resistance, showpiece
Derived form adjective peculiar₁

1.  The quality or state of being peculiar; individuality; singularity. Swift. [1913 Webster]

2.  That which is peculiar; a special and distinctive characteristic or habit; particularity. [1913 Webster]
"The smallest peculiarity of temper or manner." [1913 Webster]

3.  Exclusive possession or right. Bp. Hall. [1913 Webster]

peculiarity, n. (pl. -ies)
1 a idiosyncrasy; unusualness; oddity. b an instance of this.
2 a characteristic or habit (meanness is his peculiarity).
3 the state of being peculiar.

N  speciality, specialite, individuality, individuity, particularity, peculiarity, idiocrasy, personality, characteristic, mannerism, idiosyncrasy, specificness, singularity, reading, version, lection, state, trait, distinctive feature, technicality, differentia, particulars, details, items, counts, minutiae, I, self, I myself, myself, himself, herself, itself, special, particular, individual, specific, proper, personal, original, private, respective, definite, determinate, especial, certain, esoteric, endemic, partial, party, peculiar, appropriate, several, characteristic, diagnostic, exclusive, singular, idiomatic, idiotypical, typical, this, that, yon, yonder, specially, especially, particularly, in particular, in propria persona, ad hominem, for my part, each, apiece, one by one, one at a time, severally, respectively, each to each, seriatim, in detail, in great detail, in excruciating detail, in mind-numbing detail, bit by bit, pro hac vice, pro re nata, namely, that is to say, for example, id est, exemplia gratia, e, g, i, e, videlicet, viz, to wit, le style est l'homme meme.

N  unconformity, nonconformity, unconformity, disconformity, unconventionality, informality, abnormity, abnormality, anomaly, anomalousness, exception, peculiarity, infraction of law, breach, of law, violation of law, violation of custom, violation of usage, infringement of law, infringement of custom, infringement of usage, teratism, eccentricity, bizarrerie, oddity, je ne sais quoi, monster, monstrosity, rarity, freak, freak of Nature, weirdo, mutant, rouser, snorter, individuality, idiosyncrasy, originality, mannerism, aberration, irregularity, variety, singularity, exemption, salvo, nonconformist, nondescript, character, original, nonesuch, nonsuch, monster, prodigy, wonder, miracle, curiosity, flying fish, black sheep, black swan, lusus naturae, rara avis, queer fish, mongrel, random breed, half-caste, half-blood, half-breed, metis, crossbreed, hybrid, mule, hinny, mulatto, tertium quid, hermaphrodite, phoenix, chimera, hydra, sphinx, minotaur, griffin, griffon, centaur, saggittary, kraken, cockatrice, wyvern, roc, dragon, sea serpent, mermaid, merman, merfolk, unicorn, Cyclops, men whose heads do grow beneath their shoulders, teratology, fish out of water, neither one thing nor another, neither fish nor fowl, neither fish flesh nor fowl nor good red herring, one in a million, one in a way, one in a thousand, outcast, outlaw, off the beaten track, oasis, uncomformable, exceptional, abnormal, abnormous, anomalous, anomalistic, out of order, out of place, out of keeping, out of tune, out of one's element, irregular, arbitrary, teratogenic, lawless, informal, aberrant, stray, wandering, wanton, peculiar, exclusive, unnatural, eccentric, egregious, out of the beaten track, off the beaten track, out of the common, out of the common run, beyond the pale of, out of the pale of, misplaced, funny, unusual, unaccustomed, uncustomary, unwonted, uncommon, rare, curious, odd, extraordinary, out of the ordinary, strange, monstrous, wonderful, unexpected, unaccountable, outre, out of the way, remarkable, noteworthy, queer, quaint, nondescript, none such, sui generis, unfashionable, fantastic, grotesque, bizarre, outlandish, exotic, tombe des nues, preternatural, denaturalized, heterogeneous, heteroclite, amorphous, mongrel, amphibious, epicene, half blood, hybrid, androgynous, androgynal, asymmetric, adelomorphous, bisexual, hermaphrodite, monoclinous, qualified, singular, unique, one-of-a-kind, newfangled, novel, non-classical, original, unconventional, unheard of, unfamiliar, undescribed, unprecedented, unparalleled, unexampled, unconformably, except, unless, save barring, beside, without, save and except, let alone, however, yet, but, once in a blue moon, once in a million years, Int, what on earth!, what in the world!, What the devil!, Holy cow!, Can you top that?, Sacre bleu, never was seen the like, never was heard the like, never was known the like, I could hardly believe it, I saw it, but I didn't believe it.