This rhombic triacontahedron is decorated with the image found in the last post, which I made using Geometer’s Sketchpad and MS-Paint. Projecting it on the faces, colorizing them, and making this rotating .gif were all done using another program, Stella 4d, which can be found here — http://www.software3d.com/stella.php — with a free trial download available.
I don’t usually post nets for the polyhedra I make, but I’m making an exception for this one:
. . . Brought me to this stellation of a convex hull of something or another . . . and it looks much like the polyhedral tattoo on my left wrist.
They aren’t a precise match, though. Here’s the tattoo for comparison:
The tattoo’s polyhedral design was also originally generated with Stella 4d (see http://www.software3d.com/stella.php), by multiple stellation of the dual of the rhombicosidodecahedron, and then turned into my tattoo by Nicholas Pierce at The Golden Lotus in Sherwood, Arkansas, USA. Their website is at http://goldenlotustattoos.com/.
It took some time for me to find the significant difference in the two polyhedra. Can you spot it? (Stop reading now if you want to solve this yourself.)
* * *
To find the difference, look at a single facelet — any of them. They are all non-convex pentagons, with larger and smaller “wings,” and, in one of them, the smaller wing has a triangular shape (rotating above), while in the other (the tattoo), it comes to an edge, rather than a point — more resembling a convex quadrilateral than a triangle. That’s the major difference I have spotted.
Software credit: see http://www.software3d.com/stella.php
To form this polyhedron, I took a rhombic dodecahedron, and augmented each of its twelve sides with additional rhombic dodecahedra, forming a cluster of thirteen of these space-filling polyhedra. I then stellated this cluster thirty-four times, and this was the unexpected result.
The software I used to do this may be found (and tried for free) at http://www.software3d.com/stella.php.
Software credit: http://www.software3d.com/stella.php
Software credit: http://www.software3d.com/stella.php
Software credit: www.software3d.com/stella.php.
The design on the hexagons appeared in the last post here, and was created using Geometer’s Sketchpad and MS-Paint. After that, I used another program, Stella 4d, to place these images on the hexagons of a truncated icosahedron, render the pentagons invisible, and create this rotating .gif file.
Stella 4d may be tried and/or purchased at http://www.software3d.com/stella.php.
The great dodecahedron here is red, and the yellow polyhedron is the sixth stellation of the icosahedron.
Software credit: http://www.software3d.com/stella.php
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