A Potential Error
It is tempting to think that every non-convex polyhedron has some vertices whose defect is negative. Here is a counterexample. Consider 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. 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.
Negative defect indicates that the vertex resembles a saddle point, whereas positive defect indicates that the vertex resembles a local maximum or minimum.
Read more about this topic: Defect (geometry)
Famous quotes containing the words potential and/or error:
“Children are potentially free and their life directly embodies nothing save potential freedom. Consequently they are not things and cannot be the property either of their parents or others.”
—Georg Wilhelm Friedrich Hegel (1770–1831)
“Truth is one, but error proliferates. Man tracks it down and cuts it up into little pieces hoping to turn it into grains of truth. But the ultimate atom will always essentially be an error, a miscalculation.”
—René Daumal (1908–1944)