Densest lattice packing of a truncated icosahedron

The truncated icosahedron (also known as soccer-ball) has 60 vertices, 90 edges and 32 facets, 20 hexagons and 12 pentagons. It is one of the thirteen Archimedean solids and its dual is called pentakis dodecahedron. It was rediscovered during th 15th century by the outstanding artist Piero della Francesca.

The density of a densest lattice packing was calculated with the algorithm of Betke and Henk. The density is equal to 0.7849..., 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; truncated icosahedron | |

MSC-2000 Classification
| 52C17 (11H31) | |

Zentralblatt No.
| 01683006 |

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

- Master File: truncated_icosahedron_Master.jvx
- Applet File: truncated_icosahedron_Master.jvx
- Preview: truncated_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