Is it possible to derive the three inradii of the rhombicosidodecahedron with synthetic geometry, or is analytic geometry required?
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Let each edge of the polyhedron have a length of 1. I was attempting to find the volume of each pyramid synthetically by calculating the central angles of the dodecagon cross section,
which would allow me to find the inradii, but got stuck. Is there a way this could work synthetically? I know I can use analytic geometry if I have to but prefer the former.
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