On the Volume of Lattice Polyhedra
โ Scribed by Reeve, J. E.
- Book ID
- 120102864
- Publisher
- Oxford University Press
- Year
- 1957
- Tongue
- English
- Weight
- 412 KB
- Volume
- s3-7
- Category
- Article
- ISSN
- 0024-6115
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
The boundary characteristic --introduced by Ding and Reay --is a functional defined for a given planar tiling which associates with a given lattice figure, some integer. It appeared to be a very useful parameter to determine the area of lattice figures in the planar tilings with congruent regular po
Let T be the filing of R 3 with unit cubes whose vertices belong to the fundamental lattice Ll of points with integer coordinates. Denote by L,, the lattice consisting of all points z in R s such that nz belongs to L1. When the vertices of a polyhedron P in R 3 are restricted to lie in LI then there
P : (n) x n: , where A is the set of all vertices of P and each P : (n) is a certain periodic function of n. The Ehrhart reciprocity law follows automatically from the above formula. We also present a formula for the coefficients of Ehrhart polynomials in terms of elementary symmetric functions. 200