Tetrahedron packing

Tetrahedron packing

In geometry, tetrahedron packing is the problem of arranging identical regular tetrahedra throughout three-dimensional space so as to fill the maximum possible fraction of space. A 2006 study by Conway and Torquato showed that a packing fraction of over 71.65598% can be obtained, but they were unable to determine the upper bound for distortions of this structure [Conway, J. H., & Torquato S. 2006, "PNAS" 103, 10612-10617] . Because this current optimum packing of tetrahedra is less than that of spheres, they suggest that the regular tetrahedra may be a counterexample to Ulam's conjecture that the optimal density for packing congruent spheres is smaller than that for any other convex body.


Wikimedia Foundation. 2010.

Игры ⚽ Поможем решить контрольную работу

Look at other dictionaries:

  • Tetrahedron — For the academic journal, see Tetrahedron (journal). Regular Tetrahedron (Click here for rotating model) Type Platonic solid Elements F = 4, E = 6 V = 4 (χ = 2) Faces by s …   Wikipedia

  • Packing problem — Part of a series on Puzzles …   Wikipedia

  • Close-packing of spheres — hcp and fcc close packing of spheres In geometry, close packing of spheres is a dense arrangement of equal spheres in an infinite, regular arrangement (or lattice). Carl Friedrich Gauss proved that the highest average density – that is, the… …   Wikipedia

  • List of mathematics articles (T) — NOTOC T T duality T group T group (mathematics) T integration T norm T norm fuzzy logics T schema T square (fractal) T symmetry T table T theory T.C. Mits T1 space Table of bases Table of Clebsch Gordan coefficients Table of divisors Table of Lie …   Wikipedia

  • Convex uniform honeycomb — The alternated cubic honeycomb is one of 28 space filling uniform tessellations in Euclidean 3 space, composed of alternating yellow tetrahedra and red octahedra. In geometry, a convex uniform honeycomb is a uniform tessellation which fills three …   Wikipedia

  • Cyclol — Figure 1: In the classic cyclol reaction, two peptide groups are linked by a N C’ bond, converting the carbonyl oxygen into a hydroxyl group. Although this reaction occurs in a few cyclic peptides, it is disfavored by free energy, mainly because… …   Wikipedia

  • crystal — crystallike, adj. /kris tl/, n., adj., v., crystaled, crystaling or (esp. Brit.) crystalled, crystalling. n. 1. a clear, transparent mineral or glass resembling ice. 2. the transparent form of crystallized quartz. 3. Chem., Mineral. a solid body… …   Universalium

  • Crystal — /kris tl/, n. 1. a city in SE Minnesota, near Minneapolis. 25,543. 2. a female given name. * * * I Any solid material whose atoms are arranged in a definite pattern and whose surface regularity reflects its internal symmetry. Each of a crystal s… …   Universalium

  • Cuboctahedron — (Click here for rotating model) Type Archimedean solid Uniform polyhedron Elements F = 14, E = 24, V = 12 (χ = 2) Faces by sides 8{3}+6{4} …   Wikipedia

  • Molecular model — A molecular model, in this article, is a physical model that represents molecules and their processes. The creation of mathematical models of molecular properties and behaviour is molecular modelling, and their graphical depiction is molecular… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”