Polyhedral Formula
A formula relating the number of Euler 
andDescartes, so it is also known as the Descartes-Euler Polyhedral Formula. The polyhedron need not beConvex, but the Formula does not hold for Stellated Polyhedra.
 | (1) |
is the number of Vertices, 
is the number of Edges, and 
is the number of Faces. For a proof, see Courant and Robbins (1978, pp. 239-240). The Formula can be generalized to 
-D Polytopes. | (2) |
 | (3) |
 | (4) |
 | (5) |
 | (6) |
References
Beyer, W. H. (Ed.) CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 128, 1987. Courant, R. and Robbins, H. What is Mathematics?: An Elementary Approach to Ideas and Methods. Oxford, England: Oxford University Press, 1978. Coxeter, H. S. M. Regular Polytopes, 3rd ed. New York: Dover, 1973.
- Residue Index
- Residue Theorem (Complex Analysis)
- Residue Theorem (Group)
- Resolution
- Resolution Class
- Resolution Modulus
- Resolvable
- Resolving Tree
- Resonance Overlap
- Resonance Overlap Method
- R-Estimate
- Restricted Divisor Function
- Restricted Growth Function
- Restricted Growth String
- Resultant
- Retardance
- Reuleaux Polygon
- Reuleaux Triangle
- Reversal
- Reverse Greedy Algorithm
- Reverse-Then-Add Sequence
- Reversion of Series
- Reznik's Identity
- Rhodonea
- Rhomb