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) | |

Zentralblatt No.
| 01642080 |

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

- Master File: cube_Master.jvx
- Applet File: cube_Master.jvx
- Preview: cube_Preview.gif

Gif-file was produced by Povray 3.02

Submitted: Thu Feb 1 16:41:52 CET 2001.

Accepted: Fri Apr 27 14:11:54 CET 2001.

University of Magdeburg

Department of Mathematics

Universitätsplatz 2

D-39106 Magdeburg

henk@mail.math.uni-magdeburg.de

http://www.math.uni-magdeburg.de/~henk