Cubeoctahedron

Electronic Geometry Model No. 2001.02.052

Author

Martin Henk

Description

Densest lattice packing of a cubeoctahedron

The cubeoctahedron has 12 vertices, 24 edges and 14 facets, 6 squares and 8 triangles. It is one of the thirteen Archimedean solids and it is the difference body of a tetrahedron. Its dual is called rhombic dodecahedron. It was already mentioned by Plato and rediscovered during the 15th century by the outstanding artist Piero della Francesca.

In 1972 Hoylman calculated the lattice packing density of a cubeoctahedron, which is equal to 45/49=0.9183... 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; cubeoctahedron
MSC-2000 Classification		52C17 (11H31)

References

Ulrich Betke and Martin Henk: Densest lattice packings of 3-polytopes, Comp. Geom. 16 , 3 (2000), 157 - 186.
D.J. Hoylman: The densest lattice packing of tetrahedra, Bull. Amer. Math. Soc 76 (1970), 135 - 137.

Files

Master File: cubeoctahedron_Master.jvx
Applet File: cubeoctahedron_Master.jvx

Gif-file was produced by Povray 3.02

Author's Address