“Polyhedral Formula”的概念、定义、习题解题方法及翻译-数学辞典

单词

Polyhedral Formula

释义

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)

where

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)

For a proof of this, see Coxeter (1973, pp. 166-171).

See also Dehn Invariant, Descartes Total Angular Defect

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.

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