Degeneracy (mathematics)

[2] The definitions of many classes of composite or structured objects often implicitly include inequalities.

For some classes of composite objects, the degenerate cases depend on the properties that are specifically studied.

This may be the reason for which there is no general definition of degeneracy, despite the fact that the concept is widely used and defined (if needed) in each specific situation.

In fact, degenerate cases often correspond to singularities, either in the object or in some configuration space.

A rectangle with one pair of opposite sides of length zero degenerates to a line segment, with zero area.

A convex polyhedron is degenerate if either two adjacent facets are coplanar or two edges are aligned.

In the case of a tetrahedron, this is equivalent to saying that all of its vertices lie in the same plane, giving it a volume of zero.