where the first expression uses the basis of Conway et al. (1999). It can be dissected into the elongated
pentagonal orthobicupola, from which it differs only by a relative rotate of
top and bottom cupolas with repsect to one another.

Conway, J. H.; Radin, C.; and Sadun, L. "On Angles Whose Squared Trigonometric Functions Are Rational." Discr. Computat. Geom.22,
321-332, 1999.Johnson, N. W. "Convex Polyhedra with Regular
Faces." Canad. J. Math.18, 169-200, 1966.