sequences of truncations and extensions of the regular polyhedra

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'.
cube sequences

dodecahedron sequences

The snub cube and the snub dodecahedron - which can't be obtained by truncations - and their duals are absent.

tetrahedron sequences

The tetrahedron is its own dual, thus its sequences are very poor (and the snub tetrahedron is the regular icosahedron).

The idea for this page came to me during dinner with John Conway during which we discussed at length after a conference he had just devoted to polyhedra (Melbourne 2002). This great mathematician (Cambridge then Princeton) died of CoViD-19 on April 11, 2020, in New Jersey. Its number of Erdös is 1.

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convex polyhedra - non convex polyhedra - interesting polyhedra - related subjects August 2002
updated 13-06-2020