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