Here are three Christmas ornaments made from compounds of dodecahedrons and icosahedrons. The polyhedra were generated so that the principal axes of the coordinate system, x,y, and z, coincided with 3 of their 2 fold axes. Before combining one of the polyhedrons was rotated by 90 degrees around the x axis.
ornament_1.stl - two dodecahedrons - the result has octahedral symmetry
ornament_2.stl - one dodecahedron and one icosahedron - this is the dual compound - it has icosahedral symmetry
ornament_3.stl - two copies of ornament_2 - the result has octahedral symmetry
OpenSCAD code is included.
George Hart's Virtual Polyhedra Site has some information about compound polyhedra - See
The ornaments were printed on a raft with external support. On my Replicator they took about 3 hours to print using 2 shells and 5% infill.
When first generated by openSCAD the stl files had multiple shells and were not closed. Netfabb Studio was used to repair the files.