Densest lattice packing of a tetrahedron
The tetrahedron has 4 vertices, 6 edges and 4 triangular facets. It is one the five Platonic solids (it represents the element fire in Plato's Timaios) and it is selfdual.
In 1972 Hoylman calculated the lattice packing density of a tetrahedron which is equal to 18/49=0.3673... The pictures show a tetrahdron and its difference body, the cubeoctahedron. Both polytopes have the same optimal packing lattices, and the 14 points in the picture show the lattice points of a critical lattice of a cubeoctahedron lying in the boundary.
Model produced with: JavaView v2.00.a11
|Keywords||lattice packings; polytopes; packings; critical lattice; tetrahedron|
|MSC-2000 Classification||52C17 (11H31)|
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