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Of this 3x3x3-variant only few examples were produced and sold in the eighties.
This is one of the shape-variants of the original 3x3x3 which were produced but only for a very limited time with a equally limited number of samples. The original samples (which weigh 94 grams) are highly valuable collectors items.
The images of this entry show one of these few existing production samples. Compared with the original 3x3x3 the corners not longer need to be oriented but the faces now have a visible orientation.
David Singmasters Cubic Circular (issue #3) confirms that the puzzle was produced no later than 1982.
Around and after the year 2000 this modification was a popular hand-built modification. To make one requires a lot of work. The triangles are the original "corners" on the 3x3x3 cube. The 4-sectioned pieces are the "centers" on the 3x3x3. The 2-sectioned pieces are the "edges" on the 3x3x3. It is a simple mod, but every single piece needs modification.
About one additional decade later this variant went again into mass production. Therefore nobody has to built one or pay a fortune on ebay to get one.
The fourth image shows a version from the early eighties which calls this puzzle "Double Triangle Puzzle"
In 1984 Aleksandr Ordynets filed a patent which covers Halpern-Meier-Tetrahedron and Trajbers Octahedron. It is assumed that this is a case of parallel invention.
If you're looking to buy, eBay is the one place you can find almost anything... if you're willing to wait for it, then pay the price!
Thank you to the following people for their assistance in helping collect the information on this page: Tyler Robbins, Geert Hellings.
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