Positive electrode active material particle powder includes: lithium manganese oxide particle powder having Li and Mn as main components and a cubic spinel structure with an Fd-3m space group. The lithium manganese oxide particle powder is composed of secondary particles, which are aggregates of primary particles, an average particle diameter (D50 ) of the secondary particles being from 4 μm to 20 μm, and at least 80% of the primary particles exposed on surfaces of the secondary particles each have a polyhedral shape having at least one (110) plane that is adjacent to two (111) planes.