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.
- Feit-Thompson Conjecture
- Feit-Thompson Theorem
- Fejes Tóth's Integral
- Fejes Tóth's Problem
- Feller-Lévy Condition
- Feller's Coin-Tossing Constants
- Fence
- Fence Poset
- Ferguson-Forcade Algorithm
- Fermat 4n+1 Theorem
- Fermat Compositeness Test
- Fermat Conic
- Fermat Difference Equation
- Fermat Diophantine Equation
- Fermat Equation
- Fermat-Euler Theorem
- Fermatian
- Fermat-Lucas Number
- Fermat Number
- Fermat Number (Lucas)
- Fermat Point
- Fermat Polynomial
- Fermat Prime
- Fermat Pseudoprime
- Fermat Quotient