Here's what rhymes with acyclical.
encyclical Words that almost rhyme with acyclical
physical cynical finical mystical lyrical umbilical rhythmical whimsical sophistical arrhythmical critical atypical elliptical inimical logistical rabbinical nonphysical tricycle untypical empirical statistical analytical metaphysical cylindrical uncritical apolitical egotistical parasitical egoistical subliminal noncritical unpolitical overcritical indivisible geopolitical hypocritical preclinical prototypical supercritical impermissible nonpolitical archetypical hypercritical noncriminal stereotypical sociopolitical psychoanalytical