Boerdijk–Coxeter helix

Boerdijk–Coxeter helix
Coxeter regular tetrahedral helix
A Boerdijk helical sphere packing has each sphere centered at a vertex of the Coxeter helix. Each sphere is in contact with 6 neighboring spheres.

The Boerdijk–Coxeter helix, named after H. S. M. Coxeter and A. H. Boerdijk, is a linear stacking of regular tetrahedra. There are two chiral forms, with either clockwise or counterclockwise windings. Contrary to any other stacking of Platonic solids, the Boerdijk–Coxeter helix is not rotationally repetitive. Even in an infinite string of stacked tetrahedra, no two tetrahedra will have the same orientation.

Buckminster Fuller named it a tetrahelix and considered them with regular and irregular tetrahedral elements.[1]

Contents

See also

  • Toroidal polyhedron

Notes

  1. ^ http://www.rwgrayprojects.com/synergetics/s09/p3000.html

References

  • H.S.M. Coxeter, Regular Complex Polytopes, Cambridge University, 1974.
  • A.H. Boerdijk, Philips Res. Rep. 7 (1952) 30
  • The c-brass structure and the Boerdijk–Coxeter helix, E.A. Lord, S. Ranganathan, 2004, pp. 123-125[1]
  • Eric A. Lord, Alan Lindsay Mackay, Srinivasa Ranganathan, New geometries for new materials, p 64, sec 4.5 The Boerdijk–Coxeter helix
  • J.F. Sadoc and N. Rivier, Boerdijk-Coxeter helix and biological helices The European Physical Journal B - Condensed Matter and Complex Systems, Volume 12, Number 2, 309-318, DOI: 10.1007/s100510051009 [2]

External links

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