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)

• Permutation Matrix
• Permutation Pseudotensor
• Permutation Symbol
• Permutation Tensor
• Peron Integral
• Perpendicular
• Perpendicular Bisector
• Perpendicular Foot
• Perrin Pseudoprime
• Perrin Sequence
• Perron-Frobenius Operator
• Perron-Frobenius Theorem
• Perron's Theorem
• Persistence
• Persistent Number
• Persistent Process
• Perspective
• Perspective Axis
• Perspective Center
• Perspective Collineation
• Perspective Triangles
• Perspectivity
• Pesin Theory
• Petersen Graphs
• Petersen-Shoute Theorem