This is the compound of five rhombic dodecahedra, with each component shown in a different color. This is one of the few well-known polyhedral compounds which is actually more attractive with the faces hidden, and that’s what’s shown in the next image.
I made these images using Stella 4d: Polyehdron Navigator, which you can try for free at http://www.software3d.com/Stella.php.
Symmetrohedra are symmetrical polyhedra which have many (but not necessarily all) faces regular. The only irregular faces in this polyhedron are the blue isosceles trapezoids.
I made this using Stella 4d: Polyhedron Navigator. You can try this program yourself, for free, at http://www.software3d.com/Stella.php.
The tessellations of the faces of this rhombic triacontahedron first appeared in my last post here. For putting the whole thing together and creating this rotating .gif, I used a program called Stella 4d. If you want to, you can try Stella for free at this website.
Stella 4d: Polyhedron Navigator is selling at 25% off to help cure the boredom of people in isolation because of COVID-19. This software is used to make almost all of the polyhedral images on this blog. Trying the program to see if you like it is free. The website to visit to try Stella is http://www.software3d.com/Stella.php.
The patterns on the faces are from the last post here, immediately before this one. I used Stella 4d: Polyhedron Navigator to make this, and you can try this software for free at this website.
To get started packing space with cuboctahedra and octahedra, I started with a single octahedron, then augmented its square faces with additional cuboctahedra.
Next, I augmented each triangular face with a blue octahedron.
Next, I augmented each square face with a cuboctahedron.
Next, I added still more cuboctahedra.
The next step was to augment the yellow triangular faces with blue octahedra.
I next added more cuboctahedra.
This process may be continued without limit. I used a program called Stella 4d to make these models, and you can try this software yourself, for free, at this website.
This compound is the 16th stellation of the tetrakis hexahedron, the Catalan solid which is the dual of the Archimedean truncated octahedron. I made it using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php.
To make the polyhedron shown above, I started with an icosahedron . . .
. . . and then I augmented each face with a triangular cupola, with this polyhedron’s hexagonal faces pointed outward.
I made these images using Stella 4d, which you can try for free at this website.
The first image shows a central yellow rhombic triacontahedron, with smaller, blue rhombic triacontahedra attached to each of its thirty-two vertices. The second polyhedron shown is the dual of the first one, with colors chosen by the number of sides per face in the second image — pentagons red, and triangles yellow. The convex hull of this second polyhedral complex shown would be an icosidodecahedron, itself the dual of the rhombic triacontahedron.
I use software called Stella 4d: Polyhedron Navigator to make the rotating polyhedral images on this blog. You can try Stella for yourself, for free, at http://www.software3d.com/Stella.php.
I made this by augmentation (with prisms) of the faces of a small stellated dodecahedron, using Stella 4d, which you can try for free at this website.
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