The truncations (cuttings of regular pyramids on each vertex) of two regular dual polyhedra P and P' give the same polyhedron tP. Their extensions (assemblings of regular pyramids on each face) give the same polyhedron eP.
tP and eP are dual; the same holds for P1 and P1' and for P2 and P2'. 
The snub cube and the snub dodecahedron  which can't be obtained by truncations  and their duals are absent.
The tetrahedron is its own dual, thus its sequences are very poor (and the snub tetrahedron is the regular icosahedron).
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