Circumradii

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TomF
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Joined: Tue Dec 28, 2021 4:34 am

Circumradii

Post by TomF » Tue Dec 28, 2021 5:33 am

I'm rather new to polyhedron construction and have only made five of the basic stellations. Because of space considerations here at home, I've made all of them with the same circumradius, 34.5 cm. I made the calculations for the nets by hand, and the results have been just what I wanted. Now that I've discovered Great Stella, however, I'd like to use it to make the nets since the hand calculations are becoming increasingly difficult.
I'm not sure how to do this, however. Using the Shortest Edge Length function in GS requires knowing the ratio between the shortest edge length and the circumradius, something which doesn't seem obvious. I tried using using the Stellation Radius option but I must be misinterpreting the meaning of stellation radius. I was hoping that it would be the same as the circumradius of the stellated polyhedron in the case of a stellation, but the numbers that GS produces do not match the ratios in the figures I have already constructed. For example, in my Small Stellated Dodecahedron, with its 34.5 cm circumradius, the long edge of a a net triangle is 14.7 cm. If I put in 17.25 as the stellation radius, however, GS gives me a net edge length of 11.2. Clearly stellation radius means something other than what I had hoped.
Does anyone have any suggestions on the easiest way to achieve the uniform circumradius result I'm looking for?

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robertw
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Re: Circumradii

Post by robertw » Tue Dec 28, 2021 12:37 pm

I think you're looking at the wrong thing somehow. If you have the small stellated dodecahedron opened as the base model, then "Base Polyhedron Radius" and "Stellation Radius" (from the Scale menu) will be the same and you can set either. If you have a dodecahedron loaded and go to the SSD as a stellation of it, then "Base Polyhedron Radius" will give the radius of the dodecahedron, which is still the base model, and "Stellation Radius" will give the radius of the current stellation of that base model, in this case the SSD. Your 11.2 figure matches, but I don't know where you got the other figure.
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TomF
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Joined: Tue Dec 28, 2021 4:34 am

Re: Circumradii

Post by TomF » Tue Dec 28, 2021 8:16 pm

Thanks so much for this information, Robert. I’m afraid I have a lot of egg on my face with this one.
I’ve made two of each of my polyhedra, one for myself and one for my granddaughter, age two. She is fascinated by them and has them hanging from the ceiling in her bedroom. (She refers to all six of them generically as her ‘shapes,’ but knows that this one comes from the dodecahedron. She refers to it as the little dodecahedron star and its counterpart as the big dodecahedron star.) I scaled all of her polyhedra to have a circumradius of 42 cm so that their details would be easily visible even though she isn’t able to get near them. Mine were made to the smaller 34.5 cm scale to make them fit on a shelf at my house. The numerical discrepancy in my original post came about because I was using the physical dimensions of her SSD but input the numbers for my SSD into Stella to get the information for its net. Once I used the correct circumradius, the numbers matched perfectly.
I’ll try to research my issues more carefully in the future before asking for help.

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robertw
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Re: Circumradii

Post by robertw » Wed Dec 29, 2021 2:58 am

Hey no problem, glad you got it sorted.

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