Petition for reconsideration. Petitions may be made to the Board for reconsideration of an appeal which has been decided by the Board, provided that such petition is received within 30 days of the original decision by the Board. The petition for reconsideration shall be verified and contain adequate information establishing that an essential element of the original appeal has been changed, thereby warranting reconsideration, i.e., identity of the applicant, ordinance section relied upon, or the discovery of new evidence. A fee equal to that of the original appeal shall be paid with each petition upon filing for reconsideration. The Board, in its sole discretion, shall decide whether to allow reconsideration, but in no case shall it reconsider an appeal where the essential elements of which have not changed since the Board's prior decision.