Topology Euler operators

The Euler operator is local or global according to the extent of its effect on the topological structure. A local Euler operator acts on edges or faces, whereas a global Euler operator combines two shells into a single one, divides a shell into two components, or creates a hole. 

Figure 3-22 explains how basic local Euler operators build topology in boundary models. An operator is abbreviated by the... 

Figure 3-24 Creating topological structure of a cube using local Euler operators.

Scalar counting relations for sets of structural components can seen as expressions for characters under the identity operation of more general relations between representations of those sets. For example, the Euler relation in topology can be generalised to connect not only the numbers of edges, vertices and faces of a polyhedron, but also various symmetries associated with the structural features. The well-known Euler theorem... 

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