Yesterday I began covering enough equilateral triangles to make 4 tetrahedrons, and I just finished #16 this afternoon. As I tidied the work area gathering up the threads and snippets, I heaped the triangles into a neat pile,  and it struck me how much these cream triangles looked like sandwiches or cut bread!  So I set them on a plate for a pic or two – 

Starting from the lower RH corner, the next pic shows template plastic with cream fabric machine sewn to one side and trimmed;  heat activated batting triangles glued to triangular shapes of cream fabric; and finally the edges hand sewn in place all round a triangle shape.

So if you want to try them yourself, you have all the knowledge you need, except to practice slip stitching the edges together in such a way that very little stitching shows – use matching thread+skill.  OR one could make the stitching up each join part of the surface decoration.