where the first expression uses the basis of Conway et al. (1999). It can be dissected into the elongated
triangular gyrobicupola, from which it differs only by relative rotation of the
top and bottom cupolas.

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.