This beautiful solution to the 7-7-3 acron (above left) was discovered by Mason Green in 2005. The solution is re-entrant. Mason also discovered a 'great' isomorph (above right) which solves the starred 7/2-7/2-3 acron. Mason is currently exploring solutions to other starred acrons. Mason also describes these polyhedra on his own website.
Mason terms the two polyhedra the small supersemicupola and great supersemicupola respectively