Here’s some video of a new interlocking puzzle I designed and had 3D printed. I say “I designed” it but actually found it by combinatorial search similar to the one I did to find my Rhombo puzzle a year ago. I’m calling this one “Octet-1”, short for octahedron-tetrahedron because it is uses the octahedron-tetrahedron honeycomb as its lattice.

The structure of the completed puzzle can be viewed as a continuation of a simple process in which you add neighbors to a cell in the oct-tet honeycomb. If you start with an octahedron and then add all of its tetrahedral neighbors you get a stella octangula. If you then add all the octahedral neighbors to the stella octangula you get the shape of the completed Octet-1 which looks like the following

The above can be viewed as a compound of six bars formed by connecting a row of three octahedra with four tetrahedra. Below is a higher order model of one of these bars, “higher order” in that each of the three octahedron in the bar is composed of multiple cells from the oct-tet lattice. This is size in terms of fundamental cells that the puzzle uses.

To find the puzzle I searched the intersection of six of the above allowing octahedron cells to be split into square pyramids (because this turned out to be necessary). The intersection is shaped like a stella octangula. I searched for six non-intersecting paths connecting the octahedra ends of the bars. Ultimately to make the puzzle constructible I had to also split one of the bars into “key” piece in which a single bar is formed from two half pieces. You can see me inserting those at the end in the video above. I believe there is no constructible puzzle of this kind that does not use some kind of key piece like this.

Below is a model of the assembled puzzled that I have “buffered” to make its internal structure somewhat visible.

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