What is circumradius $R$ of the great disnub dirhombidodecahedron, or Skilling's figure?

The great disnub has identical vertices and edges as the Great dirhombicosidodecahedron, which has a circumradius of $\sqrt{2}/2$.

The Narayama cow sequence constant has a value of 0.325617..
The Pentagonal Prism Six Compound has diagonals of length 0.32492

Times 3 gets 0.97685 That's close to the lengths of the second and third longest diagonals in my caltrop. If the the 4 tetrahedral points are removed, a lot of balancing might be possible, and the second longest diagonals would be quite close to that. So, perhaps solve that figure for maximizing unit diagonals on 72 points and see if Narayana pops out. I used this shape to get excruciatingly close to a new solid of constant width, maybe this cow constant could be the key to making it work.