where the first expression uses the basis of Conway et al. (1999). It can be dissected into the metabiaugmented
truncated dodecahedron, from which it differs only by the relative positions
of the two augmented 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.