Circumradii
Posted: 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?
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?