Icosahedron

Electronic Geometry Model No. 2001.02.054

Author

Martin Henk

Description

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)

References

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

Files

Master File: icosahedron_Master.jvx
Applet File: icosahedron_Master.jvx

Gif-file was produced by Povray 3.02

Author's Address