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Zometool ? Rhombic Hexecontahedron, the Wolfram|Alpha‘s logo ?

Posted 10 years ago
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Last week, I participated in the Zometool Workshop organized by Paul Hildebrandt for the Simmetry Festival 2013, Delft. This was my first Zometool experience but it was like playing again with my favorite childhood toy emoticon. My first idea was to build up a self-similar object with icosahedral symmetry, and then fill the remaining gaps in between:

I had plenty of other ideas for new designs so I took the resulting sculpture back home. First I constructed a Golden Fractal Tree, then a Fullerene or a "soccer ball", and finally I ended up constructing a Rhombic Triacontahedron and its closely related Rhombic Hexecontahedron. To my surprise this last polyhedron appeared effortless in my hands, well, I suspect that the Wolfram|Alpha's logo has something to say about that ;-)

(The beautiful x-ray image of quasicrystals was taken from the following blog post )

To conclude, the main idea to share with the Zometool enthusiasts is that PolyhedronData in Mathematica or Wolfram|Alpha can be used wisely to gather the exact number of building blocks needed to construct your favorite polyhedron. For example the query 

Rhombic Hexecontahedron number of vertices and edges

tells us that we need 62 white balls and 120 red struts.

Finally, if you don't have access to Zometool you have still a chance to play with Rhombic Hexecontahedrons exploring the wonderful demonstrations submitted by Sándor Kabai:

P.S. I strongly recommend to read the fascinating WolframAlpha blog post by Eric W. Weisstein, WHAT’S IN THE LOGO? THAT WHICH WE CALL A RHOMBIC HEXECONTAHEDRON and his MathWorld related entries Golden Rhombus, Rhombic TriacontahedronRhombic Hexecontahedron and the famous Spikey
POSTED BY: Bernat Espigulé
Great, Bernat, I hope you had fun at that conference and I am glad people showed interest in CDF and Mathematica there - I hope you can tell us more about that in a separate post. And, yes, you are right, here is the Mathemtica point of view on the Rhombic Hexecontahedron:
Grid[{#, PolyhedronData[
     "RhombicHexecontahedron", #]} & /@ {"EdgeCount", "FaceCount",
   "Image", "Name", "NetGraph", "NetImage", "SkeletonGraph",
   "SkeletonGraphName", "Stellation", "SurfaceArea", "VertexCount",
   "Volume"}, Alignment -> Left, Frame -> All,
FrameStyle -> Opacity[.3]]

POSTED BY: Vitaliy Kaurov
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