These polyhedra are also presented as 'Stress Maps', a bespoke form of VRML model for showing distortion in such models. More information on Stress Maps and distortion is available here.
Alex Doskey discovered this fascinating polyhedron with a tetrahedral symmetry. All sides contain distortion, although I have minimised the distortion to the dodecagonal faces (stress map). Distortion: (E=0.142, P=5.19, A=118º)
Mason Green discovered this tantalisingly close crown shaped object, which he terms a 'hexacastle'. The distortion is limited to the triangles with the triangle -triangle edges extended by some 1% (stress map). Distortion: (E=0.09, P=0, A=24º)