Periodic arrangements of tetrahedra having appearances similar to that of the Boerdijk-Coxeter helix

The Boerdijk-Coxeter helix (BC helix or tetrahelix) is a linear stacking of regular tetrahedra. Although the BC helix exhibits an aperiodic nature, structures resembling the BC helix with periodicity are found in materials. To understand such structures, we considered a modification of the BC helix to introduce periodicity. By adjusting the relative rotation of adjacent tetrahedra, we demonstrated that periodic arrangements consisting of 8, 11, and 14 tetrahedra have appearances similar to that of the BC helix.