Truncated Icosidodecahedron EG-Models Home

image truncated_icosidodecahedron_Preview.gif
Electronic Geometry Model No. 2001.02.066

Author

Martin Henk

Description

Densest lattice packing of a truncated icosidodecahedron

The truncated icosidodecahdron (sometimes called great rhombicosidodecahedron) has 120 vertices, 180 edges and 62 facets, 12 decagons, 20 hexagons and 30 squares. It is one of the thirteen Archimedean solids and its dual is called disdyakis triacontahedron. Maybe the first drawing of the truncated icosidodecahedron can be found in Daniele Barbaro's book La Practica della Perspectiva (around 1569). The density of a densest lattice packing was calculatd with the algorithm of Betke and Henk. The density is equal to 0.8272..., 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 icosidodecahedron
MSC-2000 Classification 52C17 (11H31)
Zentralblatt No. 01683007

References

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

Files

Gif-file was produced by Povray 3.02

Submission information

Submitted: Thu Feb 1 16:41:52 CET 2001.
Accepted: Fri Apr 27 14:11:54 CET 2001.

Author's Address

Martin Henk
University of Magdeburg
Department of Mathematics
Universitätsplatz 2
D-39106 Magdeburg
henk@mail.math.uni-magdeburg.de
http://www.math.uni-magdeburg.de/~henk