Defect (geometry) - Defect of A Vertex

Defect of A Vertex

The defect of a vertex of a polyhedron is the amount by which the sum of the angles of the faces at the vertex falls short of a full circle. If the sum of the angles exceeds a full circle, as occurs in some vertices of most (not all) non-convex polyhedra, then the defect is negative. If a polyhedron is convex, then the defects of all of its vertices are positive.

The concept of defect extends to higher dimensions as the amount by which the sum of the dihedral angles of the cells at a peak falls short of a full circle.

(According to the Oxford English Dictionary, one of the senses of the word "defect" is "The quantity or amount by which anything falls short; in Math. a part by which a figure or quantity is wanting or deficient.")