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 in which each (111) plane thereof is adjacent to at least one (100) plane thereof.