Golden Rhombic Polyhedron made from Dodecahedra

For general discussion of polyhedra, not necessarily Stella-specific.
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Golden Rhombic Polyhedron made from Dodecahedra

Post by Wagyx » Sat Aug 26, 2023 3:02 pm

Hello there,

I have been playing with dodecahedra and found in the Stella database two Stewart's solids made only with dodecahedra:
a ring of 8 dodecahedra making a rhombus and a triacontahedron.
Based on the observation that this rhombus must be a golden rhombus (with its diagonal ratio being the golden number), I have derived other golden rhombic solids. This was very neat !

Then, playing with icosahedra I noticed that a ring of 8 icosahedra was amongst the Stewart's solid. From it I could make the (not golden) rhombic dodecahedron meaning that this time the rhombus has a diagonal ratio of square root of two. This was super neat !

If you want to see all the other shapes I have made please have look at this article.

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