• Some references to gluing together tetrahedra.

J. H. Mason, Can regular tetrahedra be glued together face to face to form a ring? Math. Gaz., 56 (1972), 194-197.

S. K. Stein, The Planes Obtainable by Gluing Regular Tetrahedra. The American Mathematical Monthly, Vol. 85, No. 6 (1978), 477-479.

  • I have print-outs of two articles:

Lagarias, Jeffrey C., and Chuanming Zong. 2012. Mysteries in packing regular tetrahedra. Notices of the American Mathematical Society 59(11):1540-1549.

Zheng, Chong, Roald Hoffmann, and David R. Nelson. 1990. A helical face-sharing tetrahedron chain with irrational twist, stella quadrangula, and related matters. Journal of the American Chemical Society 112:3784-3791.

  • This paper mentions a connection between a chain of tetrahedra and a chain of triangle-prisms (as found in Rubik’s Snake).

Rubik’s Snake or Rubik’s Twist can twisted to form a straight stick or other forms.

https://en.wikipedia.org/wiki/Rubik%27s_Snake rubik’s snake or twist
http://www.wikiwand.com/en/Rubik%27s_Snake

A link to other twistable toys  https://fidgetclub.com/collections/tangles

  • Additionally, here are some links:

http://bit-player.org/2013/tetrahedra-with-a-twist

http://www.rwgrayprojects.com/rbfnotes/helix/helix01.html