Densest lattice packing of a truncated cubeoctahedron

The truncated cubeoctahedron (sometimes called great rhombicubeoctahedron) has 48 vertices, 72 edges and 26 facets, 6 octagons, 8 hexagons and 12 squares. It is one of the thirteen Archimedean solids and its dual is called disdyakis dodecahedron. Maybe the first presentation of this polytope can be found in the revised version of Albrecht Dürer's Underweysung der Messung (around 1538).

The density of a densest lattice packing was calculated with the algorithm of Betke and Henk. The density is equal to 0.8493..., 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 cubeoctahedron | |

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

Zentralblatt No.
| 01683004 |

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

- Master File: truncated_cubeoctahedron_Master.jvx
- Applet File: truncated_cubeoctahedron_Master.jvx
- Preview: truncated_cubeoctahedron_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