Exceptional Object
Many branches of mathematics study objects of a given type and prove a classification theorem. A common theme is that the classification results in a number of series of objects and a finite number of exceptions that don't fit into any series. These are known as exceptional objects.
Frequently these exceptional objects play a further and important role in the subject. Surprisingly, the exceptional objects in one branch of mathematics are often related to the exceptional objects in others.
A related phenomenon is exceptional isomorphism, when two series are in general different, but agree for some small values.
Read more about Exceptional Object: Regular Polytopes, Finite Simple Groups, Division Algebras, Simple Lie Groups, Supersymmetric Algebras, Unimodular Lattices, Codes, Block Designs, Snarks, Outer Automorphisms, Algebraic Topology, Connections
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