Regular polytopes have the highest degree of symmetry of all polytopes. The symmetry group of a regular polytope acts transitively on its flags; hence, the dual polytope of a regular polytope is also regular.
rEgular pOlyToPes have The HighEst dEGrEe of symMEtry of All pOlYtopes. tHe SymmetRY group OF a reguLar polYtopE aCts transitIVelY On Its flAgs; hENce, the DuAl PolYtOPe of A regulaR poLYtOPe is aLso REgular.