A diminished polyhedron is a polyhedron in which one or more groups of associated faces (such as those comprising the top of a pyramid or cupola in the case of a Johnson solid) is removed and the border of the removed portion replaced with a new face.
For example, the diminished rhombicosidodecahedron is a small rhombicosidodecahedron in which any one of the pentagonal cupolas is removed and a new face is formed from it base vertices.
The terminology when multiple diminishing operations are performed is bidiminished, tridiminished, etc., and the configuration of the removed piece may be indicated using the prefixed meta- (e..g., metabidiminished rhombicosidodecahedron and para- (e.g., parabidiminished rhombicosidodecahedron).
