If the isosceles triangles in this polyhedron were close enough to being equilateral that close inspection would be required to tell the difference, this would be a near-miss to the Johnson Solids. However, in my opinion, this doesn’t meet that test — so I’m calling this a “near-near-miss,” instead.
Software credit: visit this website if you would like to try a free trial download of Stella 4d, the program I used to create this image.
Software used: Stella 4d, available at http://www.software3d.com/Stella.php (including a free “try it before you buy it” trial download).
In this polyhedron, the twelve rhombic faces are in the same position as the faces of a rhombic dodecahedron — but narrowed, so as to make room for the kites. As for the kites, there are 24 of them — in eight sets of three. These set-of-threes’ positions correspond to those of the faces of an octahedron.
Software credit: I made this with polyhedron-manipulation software called Stella 4d. If you wish to purchase it, or try the free trial download, here’s the site to visit:
Software credit: I made this image using Stella 4d, available at http://www.software3d.com/Stella.php (free trial download available).
Software credit: I made this image using Stella 4d, available at http://www.software3d.com/Stella.php (free trial download available).
Software credit: I made this image using Stella 4d, available at http://www.software3d.com/Stella.php (free trial download available).
When adding icosakaipentagonal prisms (those where the bases have 25 sides) to the thirty square faces of a rhombicosidodecahedron, the prisms can have one of two orientations. One is above, and here is the other one (click to enlarge):
Software credit: I made these images using Stella 4d, available at http://www.software3d.com/Stella.php (free trial download available).
Software credit: I made this using Stella 4d, available at http://www.software3d.com/Stella.php (free trial download available).
This compound is unusual in that it is most attractive as a ball-and-stick model, with the faces rendered invisible, rather than the traditional coloring for compounds. In the traditional coloring, no faces are hidden, and each component of the compound is given faces of a different color. Here’s the same compound, rendered in the traditional manner:
Of course, matters of aesthetics are not subject to mathematical proof. Some might prefer the second version to the first.
Software credit: please see www.software3d.com/Stella.php to try or buy Stella 4d, the software I use to make these polyhedral images.
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