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 a single tetrahedron form
three intertwined helices . There are two chiral forms, with either
clockwise or counterclockwise windings. Contrary to any other stacking
of
**Platonic solids** , the
**Boerdijk–Coxeter helix**

Boerdijk–Coxeter helix is not rotationally
repetitive. Even in an infinite string of stacked tetrahedra, no two
tetrahedra will have the same orientation. This is because the helical
pitch per cell is not a rational fraction of the circle.

**Buckminster Fuller**

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

CONTENTS

* 1 Architecture
* 2 Higher-dimensional geometry
* 3 Related polyhedral helixes
* 4 See also
* 5 Notes
* 6 References
* 7 External links

ARCHITECTURE

See the
**Art Tower Mito** .

HIGHER-DIMENSIONAL GEOMETRY

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** partitions into two 8-tetrahedron rings,
four edges long, and the
**5-cell**

5-cell partitions into a single degenerate
5