software3d.com

Some years ago I constructed a model using this software but now after a few attempts I cannot seem to find it on Stella.
It is almost identical to a Rhombicosahedron but with rectangles rather than squares,

It is basically a non-uniform morph of the rhombicosahedron. One way of making it would be to create a compound of the regular icosahedron and the rhombic triacontahedron, as a new compound polyhedron (I assume Great Stella can do that), and then explore its stellations.

Here's the rhombicosahedron:



Take the convex hull with "Poly->Create Convex Hull" and you'll see the hull is a non-uniform truncated icosahedron:



So try starting with a uniform truncated icosahedron and go the other way. Use Faceting Mode to connect the vertices up to form the new rectangle and irregular hexagon required for the faces:



Is that what you were after?