The dual of a convex geometric solid is obtained by taking the center of gravity for all faces as vertices. The faces of the dual are associated with the original vertices: for each vertex consider the center of adjacent faces and use them to generate a face of the dual. Obviously, the convex hull of these vertices will be used (not the star polygons).

**Theorem of Dual Tetrahedron**

The dual of a regular tetrahedron has the side length equal to 1/3 of the side length of the original tetrahedron.

**Solution**

Of course, we prefer a visual solution.

First, we construct the dual (red) of a tetrahedron (green).

Secondly, we truncate the green tetrahedron (cutting edges at 1/3 from each vertex). To convert this into a hull body, we have to generate its convex hull and to compact the faces of the resulting object.

And last, we promote the dual to the default **Build **module and add copies of it to all missing corners of the previously constructed object, thus obtaining a shape similar to the original.