Cube

Electronic Geometry Model No. 2001.02.051

Author

Martin Henk

Description

Densest lattice packing of a cube

The cube has 8 vertices, 12 edges and 6 square facets. It is one of the five Platonic solids (it represents the earth in Plato's Timaios) and its dual is the octahedron. Since the cube belongs to the family of space fillers (more precisely, to the class of primitive parallelohedra) the density of a densest lattice packing is 1. The 26 points in the picture show the lattice points of a critical lattice lying in the boundary.

Model produced with: JavaView v2.00.a11

Keywords		lattice packings; polytopes; packings; critical lattice; cube
MSC-2000 Classification		52C17 (11H31)

References

Ulrich Betke and Martin Henk: Densest lattice packings of 3-polytopes, Comp. Geom. 16 , 3 (2000), 157 - 186.

Files

Master File: cube_Master.jvx
Applet File: cube_Master.jvx

Gif-file was produced by Povray 3.02

Author's Address