In this build I made a jig which fits onto the table saw sledge with the intent of cutting sides to form a regular tetrahedrons and pyramids of various sizes. I have to admit that the final jig in the video quickly left the realms of functionality because I based the design on the angles of a two dimensional triangle and needless to say I have now re-discovered Euclidean geometry. That is to say, the dihedral angle of a three dimensional, regular tetrahedron is not the same as the angle of a two dimensional equilateral triangle. While all the angles of a triangle equal to 180 degrees and that an equilateral triangle individual angle are 60, the angle between two faces of a tetrahedron is actually 70.5 degrees. For a pyramid this would be 109.5 degrees.
I haven't had to use pure mathematics for quite a while and we probably all know that in fabrication and woodworking there are many tricks to avoiding sums. Had my table saw been one which allowed the blade to tilt, I could have compensated for my error but as it stands the gap left inside the tetrahedron is too wide and would probably require hot glue to join.
When I have time I will add a link to a correct sketch up model and write up a step by step with accurate angles.
In the short term, if you have the time to make one and don't fancy the maths, use an online calculator to work out your angles such as the one in the link bellow! http://www.slyman.org/m_projects_mathematics_pyramids_polyhedra_intersurface_angle.php?alpha=60&n=4&p=45&submit_pyramid_parameter_calculator=Calculate