Truncated Octahedron EG-Models Home

image truncated_octahedron_Preview.gif
Electronic Geometry Model No. 2001.02.067


Martin Henk


Densest lattice packing of truncated octahedron

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

Since the truncated octahedron belongs to the family of spacefillers (more precisely, to the class of primitive parallelohedra) the density of a densest lattice packing is 1. The 14 points in the pictures show the lattice point of a critical lattice lying in the boundary.

Model produced with: JavaView v2.00.a11

Keywords lattice packings; polytopes; packings; critical lattice; truncated octahedron
MSC-2000 Classification 52C17 (11H31)
Zentralblatt No. 01683008


  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