 Compounds 
Great Stella(and Stella4D)
can create various compounds of polyhedra. A compound is two or more
polyhedra intersecting in interesting ways. Depending on the compound, these
can be made via stellation, faceting, augmentation, or a combination of
methods. But you don't have to figure out how, as a great many compounds are
included in the polyhedron library and ready to go.
Click on the images below to see a bigger picture and get more information
about how they were built.
 Dual Compounds 
A nice compound can often be made by combining a polyhedron with its dual.
These are easily made in
Great Stellaand Stella4D.
Notice that a vertex of either shape sits above a face of the other, and for
uniform polyhedra, an edge of one will intersect an edge of the other at right
angles. If regular, these edges will also bisect each other.
 Symmetric Compounds 
The most common compounds of interest are ones where the polyhedra involved are
all the same, and each fit into the whole in the same way. See if you can
recognise what polyhedra is making up each compound below before clicking on
them to see if you're right.
 Cuboid Compounds 
Here's an interesting subset of symmetric compounds, each consisting of 15
cuboids. These are kind of a generalisation of the well known compound of 5
cubes, where each is split into three cuboids (see final paper model below). A
different compound of 15 cuboids can be created based on any seed point placed
within icosahedral symmetry. The ones below were all created as facetings of
various Archimedean solids. These and more
examples can be found in Stella's polyhedron library.
 Miscellaneous Compounds 
And why not just put miscellaneous polyhedra together in a compound?
