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 |

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

- Master File: icosahedron_Master.jvx
- Applet File: icosahedron_Master.jvx
- Preview: icosahedron_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