This is like a tessellation, but in three dimensions, rather than two. The pattern can be repeated to fill all of space, using cubes (yellow), truncated octahedra (blue), and great rhombcuboctahedra, also known as truncated cuboctahedra (red).
Software credit: see www.software3d.com/stella.php to try or buy Stella 4d, the software I used to create this image.
This was made by the augmentation of an icosahedron, using snub dodecahedra on each of its twenty faces. I used software available at http://www.software3d.com/stella.php.
I made this, using Stella 4d, by augmenting the thirty square faces of a great rhombicosidodecahedron with additional great rhombicosidodecahedra. The result has one of these polyhedra located in each position which corresponds to a vertex of an icosidodecahedron.
You can give this program a try yourself, for free, at http://www.software3d.com/stella.php.
The 122 faces are twenty blue, irregular hexagons; thirty red, irregular hexagons; 60 rectangles, and twelve regular pentagons.
Software credit: just visit http://www.software3d.com.Stella.php, and look for the free trial download of Stella 4d, the program I used to make this rotating image.
Software credit: see http://www.software3d.com/stella.php for a free trial download of Stella 4d, the software I used to construct this cluster, three deep, of octahedra.
Software credit: you can try the software I used to make this at http://www.software3d.com/stella.php.
To create this, a central rhombicosidodecahedron had each of its faces augmented by pyramids, each of which uses only equilateral triangles for lateral faces.
Software credit: The program used to make this image, Stella 4d, may be tried for free at http://www.software3d.com/stella.php.
The great icosahedron has 20 faces which are interpenetrating equilateral triangles, most of which are hidden in the interior of that polyhedron. The non-hidden, and therefore visible, parts are called “facelets” — and there are 180 of them: 120 scalene, and 60 isosceles.
In this variant of the great icosahedron, the sixty isosceles facelets are simply missing, which changes the shape of the remaining 120, still-scalene facelets. The color scheme is one which gives each facelet a different color — except for coplanar or parallel facelets, which are the same color, making them easier to spot.
Software credit: see http://www.software3d.com/stella.php — with a free trial download available there.
Software credit: see http://www.software3d.com/stella.php — free trial download available.
What exactly did I stellate to get this polyehdron? Well, it took a long time, was based on polyhedra previously posted tonight, and was complicated. To retrace my steps, and find the exact “recipe” for this polyhedron, would require work I am simply not in the mood to do.
I like it, and am therefore blogging it, for purely aesthetic reasons.
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