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)

• Modulus (Quadratic Invariants)
• Modulus (Set)
• Moessner's Theorem
• Mohammed Sign
• Mollweide Projection
• Mollweide's Formulas
• Moment
• Momental Skewness
• Moment-Generating Function
• Monad
• Money-Changing Problem
• Monge-Ampère Differential Equation
• Monge Patch
• Monge's Chordal Theorem
• Monge's Form
• Monge's Problem
• Monge's Shuffle
• Monge's Theorem
• Monica Set
• Monic Polynomial
• Monkey and Coconut Problem
• Monkey Saddle
• Monochromatic Forced Triangle
• Monodromy
• Monodromy Group