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The boundary characteristic and the volume of lattice polyhedra

✍ Scribed by Krzysztof Kołodziejczyk

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
533 KB
Volume
190
Category
Article
ISSN
0012-365X

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✦ Synopsis

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 polygons. The purpose of this paper is to extend the notion of the boundary characteristic to lattice polyhedra in R 3. Studying some of its properties we show, in particular, that it can be applied to determine the volume of lattice polyhedra. (~

📜 SIMILAR VOLUMES

An ‘odd’ formula for the volume of three
An ‘odd’ formula for the volume of three-dimensional lattice polyhedra
✍ Krzysztof KoŁodziejczyk 📂 Article 📅 1996 🏛 Springer 🌐 English ⚖ 407 KB

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