To make this using Stella 4d (available here), I started with an octahedron, and then performed a face-based zonohedrification on it — six times.
I created this symmetrohedron as the zonohedron based on the faces, edges, and vertices of the tetrahedron. It has fifty faces: thirty squares, plus eight regular hexagons, and twelve merely-equilateral hexagons. I made it using Stella 4d, which you can try for free at this website.
This zonohedron has 432 faces, and is shown here with two different coloring-schemes — coloring faces by number of sides (above) and rainbow color mode (below). I made these using Stella 4d, which you can try for yourself, for free, at this website: http://www.software3d.com/Stella.php.
The one below is in “rainbow color mode.”
I made this using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php.
This version colors the faces by number of sides.
This one is in “rainbow color mode.”
I made these images using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php.
I made this polyhedron by creating a zonohedron based on the edges and faces of the truncated tetrahedron. Only the blue hexagons are irregular. Stella 4d was used in its creation, and you may try this program for free at http://www.software3d.com/Stella.php.
This zonohedron was made using the edges and vertices of the truncated tetrahedron.
I made this using Stella 4d: Polyhedron Navigator, which you can try for free right here.
I made this by zonohedrificaton of an octahedron, using its faces, edges, and vertices, and software called Stella 4d, which you can try for free right here.
This polyhedron has six regular octagons (red), a dozen octagons which are merely equilateral (yellow), eight regular hexagons, and 24 squares.
To make this zonohedron with Stella 4d (available as a free trial download here), start with a dodecahedron, and then perform a zonohedrification based on both faces and vertices. It is similar to the rhombic enneacontahedron, with thirty equilateral octagons replacing the thirty narrow rhombic faces of that polyhedron.
I’ve run into this polyhedron from time to time, and have also had students make it. It is the largest zonohedron which can be built using only red and yellow Zome (available here) of a single strut-length (short, medium, or long). I thought it needed a name, so I made one up.
If one starts with a dodecahedron, and then creates a zonohedron based on that solid’s vertices, the result is a rhombic enneacontahedron.
If, in turn, one then creates a new zonohedron based on the vertices of this rhombic enneacontahedron, the result is this 1230-faced polyhedron — a twice-zonohedrified dodecahedron. Included in its faces are thirty dodecagons, sixty hexagons, and sixty octagons, all of them equilateral.
Stella 4d: Polyhedron Navigator was used to perform these transformations, and to create the rotating images above. You can try this program for yourself, free, at http://www.software3d.com/Stella.php.