TITLE: Making a regular tetrahedron out of concrete
QUESTION [9 upvotes]: 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.

REPLY [2 votes]: With your help I was able to make a 3D model. Here are the results for a tetrahedron inside a cube of side 10 and height of the triangular cross section = 2.
First slicing the planes through the solid.

The final piece is this



Now subtracted the piece from a triangular prism.

Thank you all!