We are in 3-D. Here the polytoothpick is a K-toothpick. The K-toothpick has 4 components or line segments, a central point and 4 endpoints, as a tetrapod but without volume. The K-toothpick endpoints coincide with the vertices of a regular tetrahedron.
It appears that this is a three-dimensional version of A160120, but with K-toothpicks, not with Y-toothpick.
The first differences are in the entry A177241.
For the toothpick mechanism see A139250 and A160120.
Question: Is this the same as A116520? (To answer the question we need a program because the structure is hard to visualize).