Blending

Blending is an operation where two or more polytope s are overlaid such that some pairs of element s coincide in space. These coincident pairs of elements are either removed entirely or merged into just one element.

This operation should not be confused with the creation of compound s; elements do not need to coincide in the latter.

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. An augmentation performed in the opposite direction is referred to as an "excavation" on the rare occasion that it comes up. In layman's terms, the difference is that an augmentation "adds material" while an excavation "subtracts" it. More formally, an excavation tends not to alter the convex hull of the larger original polytope, while an augmentation is guaranteed to.