Truncated Cube EG-Models Home

image truncated_cube_Preview.gif
Electronic Geometry Model No. 2001.02.062


Martin Henk


Densest lattice packing of a truncated cube

The truncated cube has 24 vertices, 36 edges and 14 facets, 6 octagons and 8 triangles. It is one of the thirteen Archimedean solids and its dual is called triakis octahedron. It was rediscovered during th 15th century by the outstanding artist Piero della Francesca.

The density of a densest lattice packing was calculated with the algorithm of Betke and Henk. The density is equal to 0.9737...and the 14 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 cube
MSC-2000 Classification 52C17 (11H31)
Zentralblatt No. 01683003


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


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