Icosahedron EG-Models Home

image icosahedron_Preview.gif
Electronic Geometry Model No. 2001.02.054


Martin Henk


Densest lattice packing of an icosahedron

The icosahedron has 12 vertices, 30 edges and 20 triangular facets. It is one the five Platonic solids (it represents the element water in Plato's Timaios) and its dual is the dodecahedron.

The density of a densest lattice packing was calculated with the algorithm of Betke and Henk. The density is equal to 0.8363..., and the 12 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; icosahedron
MSC-2000 Classification 52C17 (11H06)
Zentralblatt No. 01682995


  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