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The Magic Tetrahedron was independently invented by four inventors, Benjamin R Halpern , Kersten Meier and Marko van Eekelen together with Bernard van Houtum . The Magic Tetrahedron is also know as the Halpern-Meier Pyramid.  Marko van Eekelen & Bernard van Houtum wrote a paper for there graduation in September 1981, its describes drawings and solutions and mathematical description of the puzzle. 

This puzzle was build using a skewb as the internal mechanism, this puzzle was transformed into a Magic Tetrahedron. This rebuild of the  Halpern-Meier Pyramid the corners tops are the centers instead of the little triangle, this improves stability. This time I used the plastic of a Pyrix puzzle for the edges  a Pyramorphix keychains for the corners and a keychain skewb for the kernel. In addition I used 1 bar of black milliput in total about $35 for material. -the Pyrix puzzle is a take-apart puzzle connected with a string-

Material:  I prefer to use plastic of other puzzles with the correct angle, this is easy and the pieces are not that heavy when using only milliput.

This will be the rough form of the edge, the piece is 42mm long.

Now sand down the bottom at at a 30º angle

The skewb center (square part) is 22mm, make the base is also 22 mm.  The side is 20mm

We use the skewb as the kernel, disassemble and remove the caps from the centers. These will become our corners.

Now test glue the edges using a little drop of super glue, use only a tiny drop we must take it a part again! And assemble

For the corners (tops) we use the Pyramorphix pieces, these have a nice rounded top, but you could use an other Pyrix for this.

Sand down the edges at a 15º angle

Sand down a bit and test fit, like this:

Now we have four corners

Some more part of the top  we remove the center cap of the skewb

And spilt the Pyramorphix triangles in three:

We use this for the tip of the corner piece like:

We mold with black milliput this top piece. Use a lot of water during the molding process, and use a flat knife or molding tools to get a smooth surface. This is the first phase of this piece.

Use the edges and as mold, tape the edges.

And mold, push the little triangle in the milliput

We test fit and use the edge pieces as mold. You must clean the part with water after building!

After you fill the edges, we have the rough form of the pieces

This is the rough form what it looks like, we have done 25% of the basic construction, the next step is fit and finish every piece

The center part, sand down the old skewb corner, this will be our center part. The triangle is 19 mm. Use the kernel as support for the sanding of the main part, set the dremel at a 15º angle

Please note that must stop at the exact position this is the side view

Please note that you have to remove the screw and glue the triangle on!

We have to fill the center with some milliput 

The last mm needs some delicate manual sanding if you want it perfectly flat. 

Next step

Polished

Now make the stickers

And apply them, result

I also made a packing !