To make this cluster, start with a cuboctahedron, then augment each of its square faces with rhombicosidodecahedra. Although the cuboctahedron has cuboctahedral symmetry, this cluster does not — rather, it has tetrahedral symmetry. I created this using Stella 4d, which is available here.
Software used — Stella 4d: Polyhedral Navigator, available as a free trial download at http://www.software3d.com/Stella.php.
The polyhedron above reminded me of the snub dodecahedron, which is shown below. Both rotating images were made using Stella 4d, which you can try for yourself — with a free trial download available — right here.
This was made using Stella 4d: Polyhedron Navigator, a program available here.
Zonohedra are a subset of polyhedra. In a zonohedron, all the faces are zonogons. A zonogon is a polygon with an even number of sides, as well as having opposite sides both congruent and parallel. This small collection of rotating zonohedra was made using Stella 4d, a program you can try for yourself at this website.
Also, if you want to see a larger version of any one of these zonohedra, simply click on it.
In addition to the 42 regular decagons, the faces of this polyhedron include twenty equilateral triangles, sixty yellow trapezoids, and sixty blue trapezoids. That’s 182 faces in all.
The next picture shows what happens if all of the decagons have the same color, the triangles have another, and the trapezoids are hidden from view.
Both images were created using Stella 4d, software you can try for yourself at this website.
Images obtained by NASA’s New Horizons space probe. Geometrical rendering done using Stella 4d, available at http://www.software3d.com/Stella.php.
Software used: Stella 4d, available at www.software3d.com/Stella.php.
I made this using Stella 4d, software you can try for free at http://www.software3d.com/Stella.php.
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