The faces of this polyhedron are twelve yellow regular star pentagons, twenty blue equilateral triangles, and thirty golden rectangles, shown in red. I used Stella 4d to make this, and you can try this program for free, at http://www.software3d.com/Stella.php.
I made this with Stella 4d, which you can try for free here.
In the image above, the icosidodecahedron’s final stellation is colored by face type. In the one below, I used “rainbow color mode.” Both were made using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php.
I created this using Stella 4d, software you can try right here.
The polyhedral compound above contains an icosidodecahedron (blue) and a rhombic triacontahedron (red). In this compound, the icosidodecahedron’s edges are bisected, while the rhombic triacontahedron’s edges are split into segments with lengths in the square of the golden ratio (~2.618 to 1).
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Here’s an icosidodecahedron, one of the thirteen Archimedean solids.
Using a computer program called Stella 4d (available here), I augmented each face of this solid with a pyramid. Here’s the result.
Also interesting is the dual of this pyramid-augmented icosidodecahedron:
The stars on the pentagonal faces were drawn using Geometer’s Sketchpad and MS-Paint. The icosidodecahedron itself was created using Stella 4d: Polyhedron Navigator, which you can try for free at http://www.software3d.com/Stella.php.
This polyhedron combines the faces of an icosidodecahedron (red and blue) with the those of a rhombic triacontahedron (green). The gaps between those two sets of polygons are the yellow rectangles. I made this using the “morph duals by expansion” function of Stella 4d: Polyhedron Navigator. You can try this program for yourself, free of charge, at http://www.software3d.com/Stella.php.
This is the icosidodecahedron. It’s one of the thirteen Archimedean solids. To make an expanded version of it, I first augmented each of its faces with a prism.
Next, I formed the augmented icosidodecahedron’s convex hull.
This expanded icosidodecahedron has the twelve pentagonal faces (shown in red) and twenty triangular faces (shown in blue) of the original icosidodechedron. It also has sixty rectangular faces (yellow), and sixty isosceles triangles (shown in green). That’s a total of 152 faces.
To do all of this, I used a program called Stella 4d. If you’d like to try Stella for yourself, for free, just visit this website: http://www.software3d.com/Stella.php.
There’s one icosidodecahedron at the center of this cluster, with more icosidodecahedra attached to each of the central figure’s 32 faces. In the first version, the coloring is simply based as the number of sides for each face.
In the next picture, the coloring is by face-type (position in the overall cluster).
The last image shown here has the cluster in “rainbow color mode.”
I used Stella 4d to make these — a program you may try for free right here.
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