Densest lattice packing of a rhombicubeoctahedron

The rhombicubeoctahedron (sometimes called small rhombicubeoctahedron) has 24 vertices, 48 edges and 26 facets, 18 squares and 8 triangles. It is one of the thirteen Archimedean solids and its dual is called deltoidal icositetrahedron. Maybe the first image of the rhombicubeocathedron can be found in the famous painting by Jacopo de Barbari showing Luca Pacioli illustrating a theorem of Euclid (around 1495).

The density of a densest lattice packing was calculated with the algorithm of Betke and Henk. The density is equal to 0.8758...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; rhombicubeoctahedron | |

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

Zentralblatt No.
| 01682999 |

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

- Master File: rhombicubeoctahedron_Master.jvx
- Applet File: rhombicubeoctahedron_Master.jvx
- Preview: rhombicubeoctahedron_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