A base material-integrated nanocrystalline metal oxide composite-containing catalyst, the catalyst comprising: a base material; and a nanocrystalline metal oxide composite having a plurality of accumulated flake-like nanocrystalline pieces in a connected state on a surface of the base material, the flake-like nanocrystalline pieces each having a main surface and an end surface and containing a metal oxide, wherein: the nanocrystalline metal oxide composite is configured such that, when two adjacent nanocrystalline pieces are viewed, an end surface of at least one of the nanocrystalline pieces is connected to a main surface of the another nanocrystalline piece or an end surface of the another nanocrystalline piece; the nanocrystalline pieces include a plurality of stacked surfaces stacked in a direction in which the main surface becomes an uppermost stacked surface; and when metal atoms or oxygen atoms forming the metal oxide are regarded as main constituent atoms, a proportion by number, with the proportion determined by the measured high resolution lattice images, of the main constituent atoms to the metal atoms and the oxygen atoms forming the metal oxide existing on each stacked surface is 80% or more, and the main constituent atoms have a specific crystal orientation which changes in each stack, wherein the base material is a polyhedron, and the base material is a seed crystal material having a surface promoting growth of the nanocrystalline piece so that the main surface of the nanocrystalline piece has the specific crystal orientation, a metal forming the metal oxide contains Cu. a base material; and a nanocrystalline metal oxide composite having a plurality of accumulated flake-like nanocrystalline pieces in a connected state on a surface of the base material, the flake-like nanocrystalline pieces each having a main surface and an end surface and containing a metal oxide, wherein: the nanocrystalline metal oxide composite is configured such that, when two adjacent nanocrystalline pieces are viewed, an end surface of at least one of the nanocrystalline pieces is connected to a main surface of the another nanocrystalline piece or an end surface of the another nanocrystalline piece; the nanocrystalline pieces include a plurality of stacked surfaces stacked in a direction in which the main surface becomes an uppermost stacked surface; and when metal atoms or oxygen atoms forming the metal oxide are regarded as main constituent atoms, a proportion by number, with the proportion determined by the measured high resolution lattice images, of the main constituent atoms to the metal atoms and the oxygen atoms forming the metal oxide existing on each stacked surface is 80% or more, and the main constituent atoms have a specific crystal orientation which changes in each stack, wherein the base material is a polyhedron, and the base material is a seed crystal material having a surface promoting growth of the nanocrystalline piece so that the main surface of the nanocrystalline piece has the specific crystal orientation, a metal forming the metal oxide contains Cu. the nanocrystalline metal oxide composite is configured such that, when two adjacent nanocrystalline pieces are viewed, an end surface of at least one of the nanocrystalline pieces is connected to a main surface of the another nanocrystalline piece or an end surface of the another nanocrystalline piece; the nanocrystalline pieces include a plurality of stacked surfaces stacked in a direction in which the main surface becomes an uppermost stacked surface; and when metal atoms or oxygen atoms forming the metal oxide are regarded as main constituent atoms, a proportion by number, with the proportion determined by the measured high resolution lattice images, of the main constituent atoms to the metal atoms and the oxygen atoms forming the metal oxide existing on each stacked surface is 80% or more, and the main constituent atoms have a specific crystal orientation which changes in each stack, wherein the base material is a polyhedron, and the base material is a seed crystal material having a surface promoting growth of the nanocrystalline piece so that the main surface of the nanocrystalline piece has the specific crystal orientation, a metal forming the metal oxide contains Cu.