The BOERDIJK–COXETER HELIX, named after
H. S. M. Coxeter and A. H.
Boerdijk , is a linear stacking of regular tetrahedra , arranged so
that the edges of the complex that belong to only one tetrahedron form
three intertwined helices . There are two chiral forms, with either
clockwise or counterclockwise windings. Contrary to any other stacking
Platonic solids , the
* 1 Architecture * 2 Higher-dimensional geometry * 3 Related polyhedral helixes * 4 See also * 5 Notes * 6 References * 7 External links
See the Art Tower Mito .
30 tetrahedral ring from 600-cell projection
The 600-cell partitions into 20 rings of 30 tetrahedra , each a Boerdijk–Coxeter helix. When superimposed onto the 3-sphere curvature it becomes periodic, with a period of ten vertices, encompassing all 30 cells. The collective of such helices in the 600-cell represent a discrete Hopf fibration . While in 3 dimensions the edges are helices, in the imposed 3-sphere topology they are geodesics and have no torsion . They spiral around each other naturally due to the Hopf fibration.
In addition, the 16-cell