Experimentally, we have found that among the "complicated" phases of potassium at intermediate pressures is one which has the same space group as the double hexagonal-close-packed structure, although its atomic coordination is completely different. Calculations on this P6(3)/mmc (hP4) structure as a function of pressure show three isostructural transitions and three distinctive types of chemical bonding: free electron, ionic, and metallic. Interestingly, relationships between localized metallic structures and ionic compounds are found.