Since rhombic triacontahedra can form pentagonal rings, triangular rings, and square rings, I wanted to find out if a rhombicosidodecahedron could be built out of these building blocks. As you can see here, the attempt was a success. Each rhombic triacontahedron which appears here is located at the vertex of a rhombicosidodecahedron.
Software credit: see 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.
The dodecagons are in the same planes as a cube’s faces, so there are six of them. Also, this could be constructed via an unusual truncation of the cube, using three different truncation-planes at each vertex. This polyhedron has thirty faces: the six dodecagons, and twenty-four kites (in eight sets of three).
Software credit: see http://www.software3d.com/stella.php for a free trial download of Stella 4d, the software I used to construct this polyhedron.
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 152 faces of this polyhedron are:
This software used to make this image, Stella 4d, may be tried for free at http://www.software3d.com/stella.php.
This software used to make this image, Stella 4d, may be tried for free at http://www.software3d.com/stella.php. The “breathing” effect is optional with this program, and is created by having the software use a tight fit-to-frame in each still pic that composes this .gif file.
We’re out of school today because of an ice storm, and I wanted to make a snowman. However, we got very little snow — mostly freezing rain and sleet fell — so I can’t make a traditional snowman. Also, it’s really cold outside. So, instead, I stayed inside, where it’s warm, and made a polyhedral snowman out of (from top to bottom) an icosahedron, an icosidodecahedron, and a rhombicosidodecahedron.
Software credit: see http://www.software3d.com/stella.php for a free trial download of Stella 4d, the software used to make this image.
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