Here's what rhymes with iatrikai.
guy chi quae kai by my high why die lie thy y buy cry sky tie vi hi shy sigh bi bye dye fi hy nigh pi pie thai thigh vie dei ly psi rye ty wir awry hai lye mai muy nai wry cy fy lai luy mei sy tai thei wai phi dry try fly rely spy fry ply sly pry tri trie pri pupae sty aquae retry stye lanai drachmai slier apply reply deny defy goodbye alibi belie decry terrify untie amoebae descry bonsai deify spry triply ultrahigh amebae blowfly turfy scurfy barfly ripply banzais supply thereby imply nearby occupy whereby comply hereby nuclei alkali verify butterfly purify underlie alveoli amplify nullify pacify ratify rectify unify beautify lullaby termini typify codify edify liquefy mollify overlie ramify resupply vilify ossify preoccupy horrify petrify reunify stupefy liquify prettify shanghai vitrify overbuy yuppify justify satisfy stimuli clarify modify multiply qualify specify classify signify simplify testify certify glorify gratify notify fortify magnify samurai standby falsify crucify dignify mortify objectify acidify dragonfly firefly stratify stultify vivify calcify reclassify overfly scarify versify mummify beatify gentrify speechify dandify identify quantify diversify solidify oversupply personify detoxify electrify mystify emulsify misapply revivify cumuli declassify hyperbolae refortify syllabify exemplify intensify disqualify indemnify oversimplify demystify dissatisfy solemnify transmogrify misidentify