The Eleventh Stellation of the Truncated Octahedron Is an Interesting Polyhedral Compound

This compound has three parts: two tetrahedra, plus one smaller cube. I made it using Stella 4d: Polyhedron Navigator, which you can try for free at http://www.software3d.com/Stella.php.

A Compound of the Great Stellated Dodecahedron and the Great Dodecahedron

Compound of Great Stellated Dodeca and Great Dodeca.gif

In the picture above, each component of this compound has its own color. In the one below, each set of parallel faces is given a color of its own.

Compound of Great Stellated Dodeca and Great Dodeca 2

These images were made using Stella 4d, software you may try for yourself at this website.

A Compound of Three Trapezohedra

I came across this little beauty while exploring stellations of the triakis octahedron, which is the dual of the truncated cube. Its three components are each eight-faced trapezohedra, and it showed up as the sixth in that stellation-series.

compound of three trapezohedra.gif

Stella 4d: Polyhedron Navigator was used to make this rotating image. You may try it for free right here.

The Eighteenth Stellation of the Rhombicosidodecahedron Is an Interesting Polyhedral Compound

Rhombicosidodeca 18th stellation and an interesting compound

The 18th stellation of the rhombicosidodecahedron, shown above, is also an interesting compound. The yellow component of this compound is the rhombic triacontahedron, and the blue-and-red component is a “stretched” form of the truncated icosahedron. 

This was made using Stella 4d, which you can try for free right here.

The Compound of the Truncated Isocahedron and the Pentakis Dodecahedron, with Related Polyhedra

The yellow-and-red polyhedron in the compound below is the truncated icosahedron, one of the Archimedean solids. The blue figure is its dual, the pentakis dodecahedron, which is one of the Catalan solids.

Pentakis dodecahedron and truncated icosahedron

The next image shows the convex hull of this base/dual compound. Its faces are kites and rhombi.

Convex hull of trunctaed icosahedron slash pentakis dodecahedron compound

Shown next is the dual of this convex hull, which features regular hexagons, regular pentagons, and isosceles triangles.

dual of Convex hull of trunctaed icosahedron slash pentakis dodecahedron compound

Next, here is the compound of the last two polyhedra shown.

dual and base compound of Convex hull of trunctaed icosahedron slash pentakis dodecahedron compound

Continuing this process, here is the convex hull of the compound shown immediately above.

Convex hull

This latest convex hull has an interesting dual, which is shown below. It blends characteristics of several Archimedean solids, including the rhombicosidodecahedron, the truncated icosahedron, and the great rhombicosidodecahedron.

Dual of Convex hull

This process could be continued indefinitely — making a compound of the last two polyhedra shown, then forming its convex hull, then creating that convex hull’s dual, and so on.

All these polyhedra were made using Stella 4d: Polyhedron Navigator, which you can purchase (or try for free) at http://www.software3d.com/Stella.php