Dodecahedron

Electronic Geometry Model No. 2001.02.053

Author

Martin Henk

Description

Densest lattice packing of a dodecahedron

The dodecahedron has 20 vertices, 30 edges and 12 pentagonal facets. It is one the five Platonic solids (it represents the cosmos or ether in Plato's Timaios) and its dual is the icosahedron.

The density of a densest lattice packing was calculated with the algorithm of Betke and Henk. The density is equal to 0.9045..., and the 12 points in the picture show the lattice points of a critical lattice lying in the boundary. The critical lattice coincides with fcc-lattice, which is the critical lattice of a 3-dimensional sphere.

Model produced with: JavaView v2.00.a11

Keywords		lattice packings; polytopes; packings; critical lattice; dodecahedron
MSC-2000 Classification		52C17 (11H31)

References

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

Files

Master File: dodecahedron_Master.jvx
Applet File: dodecahedron_Master.jvx

Gif-file was produced by Povray 3.02

Author's Address