Gymnasiums rhymes with:
symposiums, abiam's, aquariums, atriums, auditoriums, axioms, caladiums, condominiums, consortium's, geraniums, herbariums, honorariums, idioms, mediums, millenniums, moratoriums, pentiums, petroleum's, podiums, premiums, stadium's, stadiums, symposiums, wiliams, zirconiums
Gymnasiums sounds like:
ganging, ginghams, ginseng, gnashing, goings-ons, gunsmoke