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