This figure is a chain of 8 octahedra, and has 48 triangles in total. You can find more information about this toroidal polyhedron in wikipedia.
With flexible diamond pieces you can also construct the 8 convex deltahedra http://www.ac-noumea.nc/maths/polyhedr/p_delta_.htm as well as many beaitiful non convex deltahedra http://www.ac-noumea.nc/maths/polyhedr/index2_.htm, and of course many other curved three-dimensional figures, which are not possible with plastic or wood pieces.
The adventure of flexible deltahedra with 3D Polyfelt just started. We will publish more pictures here very soon.