tetrahelix

a tetrahelix is a linear stacking of regular tetrahedra, which on stacking form a helix by default. the helix which is formed rotates by an irrational angle.



"Leave the beaten track behind occasionally and dive into the woods. Every time you do, you will be certain to find something you have never seen before."  Alexander Graham Bell


the tetrahelix also known as "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"  wikipedia

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



the following pages illustrate some of the ideas that i have been working on through the study of tetrahelix. 

i like to think the work illustrated here is original. if you have developed similar ideas or seen similar work else where, i would appreciate if you could send me an email so that i can check it out.

the initial driver for this study was not the tetrahelix at all but rather an attempted to find other possibly unrelated helical forms which could be constructed from congruent triangles to create an infinite helix.

it was not until i had pursued this notion for quite sometime (without any success ) that i came to the conclusion that i should use the tetrahelix as a starting point, only then did the many forms illustrated here began to show themselves.
the forms here have been generated from trial and error, sketching and model making and not from maths.

most of the images on this site were modeled and rendered in AutoCAD.  copyright obviously applies to all of the images. if you would like to use any of the images please send me a note to let me know.

this site also contains a lot of ideas on related helices, tiling and tensegrity, which is now my current preoccupation.

new work will be posted to a blog page:

http://tetrahelix.blogspot.com/

i can be contacted at urbanabkk@gmail.com




Acknowledgments

James Reid, a 3D CAD expert, for his assistance and advice in
generating my first tetrahelix CAD models.