Here's what rhymes with unpolemic.
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phrenic irenic splenic biogenic eugenic pfennig antigenic neurogenic pyogenic androgenic allergenic telegenic pathogenic cryogenic mutagenic psychogenic photogenic hypoallergenic schizophrenic transgenic iatrogenic teratogenic neurasthenic calisthenic callisthenic carcinogenic anthropogenic hallucinogenic relic poetic ferric cleric allelic derrick medic fetich genetic generic acetic athletic metric pathetic pelvic ascetic septic diuretic hectic peptic technic benthic emetic eutectic sceptic steric tartaric turmeric lovesick pectic paregoric redbrick bathetic domestic electric magnetic aesthetic authentic kinetic prophetic diabetic dialectic dielectric angelic eclectic epileptic esthetic forensic numeric phonetic apathetic aseptic centric enteric empathetic frenetic neuroleptic skeptic chimeric dietetic dyslexic geodesic geodetic hermetic acerbic anorectic antithetic paramedic gametic unaesthetic unauthentic phrenetic dyslectic sympathetic arithmetic energetic synthetic anesthetic geometric majestic symmetric antiseptic apologetic cosmetic esoteric parametric alphabetic anaesthetic obstetric prosthetic barometric cybernetic isomeric monomeric ontogenetic anorexic apoplectic dyspeptic geocentric hysteric inauthentic antipathetic cataleptic homiletic paraplegic polytechnic pyrotechnic splenetic diametric parenthetic unapologetic nonathletic copacetic atmospheric eccentric asymmetric mesenteric isometric photoelectric psychometric unsympathetic antidiuretic biosynthetic egocentric geomagnetic isoelectric kinesthetic nonparametric photometric psychedelic ionospheric peripatetic radiometric evangelic nonmagnetic thermometric exegetic narcoleptic telekinetic nonelectric unesthetic cliometric concentric volumetric hydroelectric photosynthetic phylogenetic colorimetric ethnocentric paramagnetic piezoelectric alphanumeric onomatopoetic psychokinetic econometric parasympathetic ferromagnetic stoichiometric heliocentric pharmacokinetic trigonometric anthropocentric electromagnetic