Axiomatic rhymes with:
idiomatic, aromatic, asymptomatic, automatic, cinematic, diagrammatic, diplomatic, dramatic, emblematic, epigrammatic, idiomatic, mathematic, melodramatic, problematic, programmatic, psychosomatic, semiautomatic, symptomatic, systematic, telematic, undiplomatic
Axiomatic sounds like:
accents, accentuates, accommodates, account's, accounts, acmat's, agematsu, agendas, agent's, agents, agents', aquanauts, ascends, asmodeus, assessments, assignment's, assignments