Blending

Blending is an operation where two or more polytopes of the same rank are overlaid, coinciding and congruent facets are removed, and coinciding and noncongruent facets are themselves blended. It is similar to the creation of compounds, but in compounds every facet remains, possibly producing multiple-covers. If no facets are shared between the blended polytopes, a compound is formed.

In the context of the Johnson solids, a similar operation is referred to as "augmenting." This usually involves a coincident pair of facets being removed, as they end up inside the resultant polytope, and coincident edges and vertices being merged since they lie on the polytope's surface. Diminishing can also be considered a type of blend, in which all but one facet of one polytope is removed. An augmentation performed in the opposite direction is sometimes referred to as an "excavation". In layman's terms, the difference is that an augmentation "adds material" while an excavation "subtracts" it. A diminishment that adds material is called a replenishment.