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Electronic Geometry Model No. 2001.02.051


Martin Henk


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


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


Gif-file was produced by Povray 3.02

Submission information

Submitted: Thu Feb 1 16:41:52 CET 2001.
Accepted: Fri Apr 27 14:11:54 CET 2001.

Author's Address

Martin Henk
University of Magdeburg
Department of Mathematics
Universitätsplatz 2
D-39106 Magdeburg