Study Model 2: Inscribed Antiprisms

Guessed on the geometry of the outer antiprism. The triangle base is 2^1/2 of the inner antiprism triangle, but the apothem (altitude) needs to be taller but not by the same proportion. Dihedral angle becomes more acute as the triangle becomes more obtuse (flatter)....

 

see also: polyhedramath.com/prisms-and-antiprisms/ for the actual math.

Done