Editing Angular defect (section)

== Defect of a vertex ==
For a [[polyhedron]], the defect at a vertex equals 2π minus the sum of all the angles at the vertex (all the faces at the vertex are included).  If a polyhedron is convex, then the defect of each vertex is always positive.  If the sum of the angles exceeds a full [[turn (geometry)|turn]], as occurs in some vertices of many non-convex polyhedra, then the defect is negative.

The concept of defect extends to higher dimensions as the amount by which the sum of the [[dihedral angle]]s of the [[cell (geometry)|cells]] at a [[peak (mathematics)|peak]] falls short of a full circle.