Great pentagrammic hexecontahedron

The great pentagrammic hexecontahedron is a uniform dual polyhedron. It consists of 60 mirror-symmetric pentagrams.

It is the dual of the great inverted retrosnub icosidodecahedron.

Each pentagram has three long and two short edges; the ratio between them is given by $$l = \frac{2-4\xi^2}{1-2\xi}\approx 1.77422$$, where $$\xi ≈ 0.94673$$, the largest positive root of the polynomial $$8x^3-8x^2+\phi^{-2}$$, and $$\phi$$ is the golden ratio. (The long edges' length is approximately 3.06368 or a root of the polynomial $$x^6-2x^5-4x^4+x^3+4x^2-1$$, and the short edges' length is approximately 1.72678 or a root of the polynomial $$31x^6-53x^5-26x^4+34x^3+17x^2-x-1$$.)

Each face has four equal angles of $$\arccos(\xi) ≈ 18.78563°$$, and one angle of $$\arccos(-\phi^{-1}+\phi^{-2}\xi) ≈ 104.85746°$$.

A dihedral angle is equal to $$\arccos\left(\frac{\xi}{\xi+1}\right) ≈ 60.90113°$$.

The inradius R ≈ 0.14897 of a great pentagrammic hexecontahedron with unit edge length is equal to the square root of a root of the polynomial $$856064x^6-3900416x^5+1443072x^4-149376x^3+6384x^2-128x+1$$.