Making a regular tetrahedron out of concrete I'm trying to make the following tetrahedron made of concrete just for fun:

Each edge is a beam with a triangular cross section.
I imagine the easiest way is to make 6 identical truncated triangular prisms and glue them. Identical because I would need to make only one mold.
The problem I'm having is figuring out the angles to make the mold. Currently I have the following equilateral triangle prism I made just for testing: 
Equilateral because it could be rotated to whatever edge it would be placed, but I tried recreating it on Autocad and the pieces wouldn't fit together. 
What I want is to find out what are the angles I need at the end of each prism and build a wooden piece to put into the mold to make the final piece.

I think you are after the dihedral angle of the regular tetrahedron
which is $\cos^{-1}(1/3)$ or about 70.53 degrees.
