Assertion: defect | /r/HasProperty | positive
Facets:
value: each
type: DEGREE
value: always
type: DEGREE
Source sentences:
text: If a polyhedron is convex, then the defect of each vertex is always positive.
text: If the sum of the angles exceeds a full turn, as occurs in some vertices of many non-convex polyhedra, then the defect is negative.
text: A counterexample which does not intersect itself is provided by a cube where one face is replaced by a square pyramid: this elongated square pyramid is convex and the defects at each vertex are each positive.
text: Now consider the same cube where the square pyramid goes into the cube: this is concave, but the defects remain the same and so are all positive.
text: It is tempting to think that every non-convex polyhedron must have some vertices whose defect is negative, but this need not be the case.