The Latest Step In My Long Polyhedral Journey Brought Me Back To My Own Tattoo

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The Latest Step In My Long Polyhedral Journey...

. . . 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:

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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.)

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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.

The Compound of the Rhombic Dodecahedron and Its Own Third Stellation

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The Compound of the Rhombic Dodecahedron and Its Own Third Stellation

Software credit: see http://www.software3d.com/stella.php

A Non-Convex “Bowtie” Polyhedron

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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.