This 122-faced solid is the dual of the convex hull of the compound of the rhombicosidodecahedron and its dual, the strombic hexecontahedron. Its regular faces are 20 triangles, 12 pentagons, and 30 squares. It also has 60 faces which are isosceles trapezoids.
I made this using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php.
This is the compound of five dodecahedra, a shape which is included in the built-in polyhedral library of Stella 4d, a program you can try for yourself, free, right here.
I wanted to see what I could make, starting from this compound. My first modification to it was to create its convex hull, which is shown below.
The next move was to use Stella‘s “Try to Make Faces Regular” function, which produced this:
Next, I augmented this figure’s thirty yellow rhombi with prisms.
I then created the convex hull of this augmented polyhedron.
Next, I used the “Try to Make Faces Regular” function again, producing a solid that looks, to me, like a hybrid of the rhombicosidodecahedron and the rhombic triacontahedron.
This polyhedron has yellow faces that are almost squares. Careful inspection reveals that they are actually isosceles trapezoids. The next thing I did was to augment each of these trapezoids with a tall prism.
The next step was to, again, create the convex hull.
That was the end of this polyhedral journey, but I am confident there will be others.
The stars on the pentagonal faces were drawn using Geometer’s Sketchpad and MS-Paint. The icosidodecahedron itself was created using Stella 4d: Polyhedron Navigator, which you can try for free at http://www.software3d.com/Stella.php.
Polyhedral excavation is the opposite of augmentation. In this excavated tetrahedron, short pyramids have been removed from each face. I made this using Stella 4d, which can be tried for free at this website.
I made this using Stella 4d, a program you can try for free at http://www.software3d.com/Stella.php.
There’s a tetrahedron in the center of this figure, but you can’t see it because it is covered on all sides by octahedra. I made this using Stella 4d, which you can try for free at this website.
Here’s another version, with a different coloring-scheme.
I made this variation of Kepler’s Stella Octangula, using Stella 4d, software you can try for free at this website.
The first version of this polyhedron was created by zonohedrification of a tetrahedron, based on that solid’s faces, edges, and vertices. All of its faces are regular polygons, except for the red hexagons.
I used Stella 4d: Polyhedron Navigator to make these (and you can try that program for free at this website). The next thing I did was to apply Stella‘s “try to make faces regular” function to the solid above, producing the one shown below. In this second version, the only irregular faces are the yellow isosceles trapezoids.
The blue figure above is an octahedron. The next image shows what happens if red octahedra are used to augment each of the blue octahedron’s faces.
The third image shows what happens if yellow octahedra are used to augment each red face in the second figure.
These polyhedral images were created using Stella 4d: Polyhedron Navigator, which you can try for free at http://www.software3d.com/Stella.php.
To make this polyhedron, I started with a great dodecahedron, and then augmented each of its facelets with a prism, using a program called Stella 4d. You can try this program for free at this website.
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