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.
- Small Rhombicosidodecahedron
- Small Rhombicuboctahedron
- Small Rhombidodecacron
- Small Rhombidodecahedron
- Small Rhombihexacron
- Small Rhombihexahedron
- Small Snub Icosicosidodecahedron
- Small Stellapentakis Dodecahedron
- Small Stellated Dodecahedron
- Small Stellated Triacontahedron
- Small Stellated Truncated Dodecahedron
- Small Triakis Octahedron
- Small Triambic Icosahedron
- Small World Problem
- Smarandache Ceil Function
- Smarandache Constants
- Smarandache Function
- Smarandache-Kurepa Function
- Smarandache Near-to-Primorial Function
- Smarandache Paradox
- Smarandache Sequences
- Smarandache-Wagstaff Function
- Smith Brothers
- Smith Conjecture
- Smith Normal Form