I found this using software you can try for free at http://www.software3d.com/stella.php. It’s one of the many stellations of the dual of the truncated octahedron.
Compound of Four Triangular Dipyramids
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Tag Archives: Mathematics
A Radial Tessellation Featuring Regular Decagons, Regular Pentagons, and Golden Hexagons
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As you can see, this can be continued indefinitely from the center.
Op Art On a Rhombic Enneacontahedron
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The rhombic enneacontahedron has 90 faces; 30 are narrow rhombi (hidden here), and 60 are wider rhombi (decorated with the op art piece from two posts ago).
Software credit: see the polyhedral software I used at http://www.software3d.com/stella.php — free trial download available.
The Great Rhombcuboctahedron
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The images on the faces are colorized versions of my last post here. This transfer was accomplished using software you can find at http://www.software3d.com/stella.php.
Tessellation Featuring Dodecagons II
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Tessellation Featuring Dodecagons
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Rhombic TriacontaSaturn
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One of many photographs of Saturn provided by the Cassini spacecraft, and then projected onto the faces of a rhombic triacontahedron with the software available at http://www.software3d.com/stella.php.
Sol, Terra, and Luna On a Rhombicosidodecahedron
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Projecting images on the sun, earth, and moon onto the faces of a rhombicosidodecahedron was accomplished with Stella 4d, software you may try for free at http://www.software3d.com/Stella.php.
Conjucture About the Rhombic Penrose Tiling
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Roger Penrose is famous for many things, including the discovery of aperiodic tilings, the most familiar of which involves two types of rhombus:
I think I have made a minor discovery about this Penrose tiling, and that is that one can add regular pentagons to it, in varying levels of pentagon-density, as shown in the first image, without it losing its aperiodicity. (I created only the first image, not the second.) I have not, however, proven this, and doubt I will.
Is this conjecture provable? I think so, but I lack the ability to write such a proof myself.
Compound of Three Cubes and an Octahedron
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Software used: see http://www.software3d.com/stella.php.
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