To make this “cube,” I started with an octahedron, and then augmented all eight of its faces with rhombicosidodecahedra. Such polyhedral manipulations are quick and easy with Stella 4d, available at http://www.software3d.com/stella.php.
This polyhedral compound was found by repeatedly-stellating the 38-faced polyhedron featured in the last post.
Software credit: http://www.software3d.com/stella.php
The 38 faces are:
This polyhedron also has an interesting dual, which features 24 kites and twelve rhombi as faces (click on it to see it rotate):
I discovered these while “surfing” the universe of polyhedra using software called Stella 4d. You may try this software as a free trial download at http://www.software3d.com/stella.php.
Update: It turns out that this was previously found by the formidable polyhedra-researching team of Craig S. Kaplan and George W. Hart, as you can see at http://www.cgl.uwaterloo.ca/~csk/papers/kaplan_hart_bridges2001.pdf. Finding polyhedra no one has found before is no easy task, and, often, one thinks it has been done, only to find out later that one has already been beaten to the proverbial punch. When I discover that I’ve merely re-discovered what others have found before me, I always give credit to the previous researchers. That’s part of the prevailing etiquette within the polyhedra-research community, and I think it’s an important principle, on ethical grounds.
Software credit: http://www.software3d.com/stella.php
Software credit: http://www.software3d.com/stella.php
The decorations on the faces are based on the last post, and were made with Geometer’s Sketchpad and MS-Paint. Putting them on the faces and making this rotating .gif file was done with another program, Stella 4d, available at http://www.software3d.com/stella.php.
The “snowflake” dodecagons are equilateral, and resemble star hexagons — but the resemblance is close, not exact.
Created using Stella 4d, software you can try at http://www.software3d.com/stella.php.
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