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Let each sphere in a sphere packing expand uniformly until it touches its neighbors on flat faces. Call the resulting polyhedron the local cell. Then the local density is ...

The conjecture that the maximum local density is given by rho_(dodecahedron).

A local extremum, also called a relative extremum, is a local minimum or local maximum.

The study of a finite group G using the local subgroups of G. Local group theory plays a critical role in the classification theorem of finite groups.

A local maximum, also called a relative maximum, is a maximum within some neighborhood that need not be (but may be) a global maximum.

A local minimum, also called a relative minimum, is a minimum within some neighborhood that need not be (but may be) a global minimum.

A simplicial complex K is said to be locally finite if each vertex of K belongs only to finitely many simplices of K.

A graph for which every node has finite degree.

A function is called locally integrable if, around every point in the domain, there is a neighborhood on which the function is integrable. The space of locally integrable ...

A space X is locally pathwise-connected if for every neighborhood around every point in X, there is a smaller, pathwise-connected neighborhood.