Compound of Cuboctahedron and Dual
This is a compound of the cuboctahedron and its
dual, the rhombic dodecahedron. 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 cuboctahedron 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.
It's a compound of these two polyhedra.
Just sticking pyramid tips onto the faces of either the cuboctahedron
or its dual won't lead to the cleanest result. But here's
a clever way to build a paper model, based on advice from Fr. Magnus
Wenninger's book Polyhedron Models. 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 cuboctahedron and
use "Poly→Subdivide Faces" with a value of 2 so that points are
printed half way along each edge. I also printed smaller squares and
triangles to fit inside and add further strength.
Attach the sections together like faces of a cuboctahedron.
Another photo of the finished model.