The board of dentistry shall consist of twelve members, eight of whom shall be practicing dentists who have been engaged in the practice of dentistry for a period of five years preceding their several appointments, two of whom shall be practicing dental hygienists, duly licensed under section 447-1, who have been engaged in the practice of dental hygiene in the State for a period of five years preceding appointment, and two of whom shall be public members. No member shall be in any way connected with, or interested financially in, any dental supply company. One member in the practice of dentistry shall be appointed from each of the counties of Hawaii, Maui, and Kauai and five members in the practice of dentistry shall be appointed from the city and county of Honolulu. As used in this chapter, “board” means the board of dentistry.