If I'm not mistaken, both large faces above belongs to ...
Description: If I'm not mistaken, both large faces above belongs to tristetrahedron but in fact the third face of both triads which should be in contact with (111) are missing (marked in blue). Is curious that the edges in red are more or less parallel when they should be divergent, but contrary to the divergence of the edges at right in picture. Face between red edges seems to belong to a tetrahedron, not modified.