Descartes Total Angular Defect

The total angular defect is the sum of the Angular Defects over all Vertices of a Polyhedron, wherethe Angular Defect at a given Vertex is the difference between the sum of faceangles and . For any convex Polyhedron, the Descartes total angular defect is

(1)

(2)

A Polyhedron with equivalent Verticesis called a Platonic Solid and can be assigned a Schläfli Symbol .It then satisfies

(3)

(4)

(5)

• Jensen's Formula
• Jensen's Inequality
• Jerabek's Hyperbola
• Jerk
• j-Function
• Jinc Function
• j-Invariant
• Jitter
• Joachimsthal's Equation
• Johnson Circle
• Johnson's Equation
• Johnson Solid
• Johnson's Theorem
• Join (Graph)
• Join (Spaces)
• Joint Distribution Function
• Joint Probability Density Function
• Joint Theorem
• Jonah Formula
• Jones Polynomial
• Jonquière's Function
• Jordan Algebra
• Jordan Curve
• Jordan Curve Theorem
• Jordan Decomposition Theorem