The 30-tetrahedron ring is not a 3D structure, but a 4D structure: It is a piece of the surface of a 4D shape. In its true 4D form, every vertex has the same distance from the center, as does every edge. It is obtained from the Boerdijk-Coxeter helix by folding the chain along each of its touching faces in the fourth dimension.
The three-dimensional projection in the picture you've shown is distorted, because distortion is necessary to project the true 4D shape into 3D space. For that reason, the tetrahedra the projection is made of are all differently shaped, so there is no basic symmetry you can follow
If you want to recreate this pattern, you'll need to measure out a 3D model of this mesh and construct it like you would construct any other mesh. If you want to build it using interlocking tetrahedra, you'll have to make each one of your tetrahedra have a different, customized shape. There are no shortcuts, I'm afraid.