A Board of Adjustment is hereby created, consisting of five members, each to be appointed for a term of three years, said members to be nominated by the Mayor and approved by the City Commission by ordinance for the appointment. Members are removable for cause by the City Commission, upon written charges and after public hearing. Vacancies shall be filled for the unexpired term of any member whose term becomes vacant, in the same year. The Board of Adjustment shall adopt rules in accordance with the provisions of §§18-10 to 18-14 of this chapter or any amendment thereto. Meetings of the Board shall be held at the call of the chairman and at such times as the Board may determine. The chairman, or in his absence the acting chairman, may administer the oaths and compel the attendance of witnesses. All meetings of the Board shall be open to the public. The Board shall keep minutes of its proceedings, show the vote of each member upon each question or if absent or failing to vote, indicate such facts, and shall keep a record of its examinations and other official actions, all of which shall be immediately filed in the office of the Board of Adjustment and shall be public record.