where the first expression uses the basis of Conway et al. (1999). It can be dissected into the pentagonal
orthocupolarotunda, from which it differs only by the relative rotation of the
top and bottom cupola and rotunda.
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.