Densest lattice packing of an icosidodecahedron

The icosidodecahedron has 30 vertices, 60 edges and 32 facets, 12 pentagons and 20 triangles. It is one of the thirteen Archimedean solids and its dual is called rhombic triacontahedron. A beautiful 3D-presentation of this polytope, which is due to Lenonardo da Vinci, can be found in Luca Pacioli's 1509 book De Divina Proportione.

The density of a densest lattice packing was calculated with the algorithm of Betke and Henk. The density is equal to 0.8647..., 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; icosidodecahedron | |

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

Zentralblatt No.
| 01682996 |

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

- Master File: icosidodecahedron_Master.jvx
- Applet File: icosidodecahedron_Master.jvx
- Preview: icosidodecahedron_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