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An Euler Boolean operation is a series of modifications to solid modelling which preserves the Euler characteristic in the boundary representation at every stage. One or more of these Euler Boolean operations is stored in a change state, so as to only represent models which are physically realizable.
Failing to maintain the Euler characteristic would result in geometric and topological entities often depicted by M. C. Escher. Esher's geometry artwork comes close to preserving the Euler characteristic (usually a problem with just the hole count).
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