Compound of Truncated Tetrahedron and Dual
This is a compound of the truncated tetrahedron
and its dual, the triakistetrahedron. Notice how
each vertex of one sits above a face of the other, and that edges from each
cross at right-angles in pairs. The points where they cross lie on the shared
midsphere of the two polyhedra, i.e. the edges are tangent to the midsphere at
The model may be constructed in
by adding the truncated tetrahedron to its dual via the menu item
"Poly>Add Base Model and Dual", or equivalently by going to the
compound of base & dual view, and clicking the left-and-down button
at the top of that view to use this compound as the new base model. Nets may
then be displayed and printed.
Here's a clever way to build a paper model, based on advice from Fr.
Magnus Wenninger's book Polyhedron Models. Firstly, just
sticking pyramid tips onto the faces of either the truncated
tetrahedron or its dual won't lead to the cleanest result. But pieces
may be made as shown, with long tabs to hold parts together that only
touch at a point in the final model. These tabs span across potential
weak points in the model where edges of the two polyhedra cross,
keeping them in alignment and strengthening the model.
To print these hollow faces, start with the truncated tetrahedron and
use "Poly→Subdivide Faces" with a value of 2 so that points are
printed half way along each edge.
I also printed smaller hexagons to fit inside and add further strength.
But glue the dual's pyramidal peak in first.
Finally just attach the sections together like faces of a truncated