# The Rhombicosidodecahedron and the Deltoidal Hexecontahedron

The Rhombicosidodecahedron and the Deltoidal Hexecontahedron

Conway polyhedron notation can be used to describe polyhedra of arbitrary complexity. As noted by Eric Weisstein, "midpoint cumulation" can be used to create compositions of some shapes and their duals. In Conway's notation, represents a midpoint cumulation or "cumulated rectification" of shape ( is the icosahedron and is the dodecahedron), and can be used to create compositions of Platonic, Archimedean, and Catalan solids with their duals. Since the rectification operator has the property , the final form of these compositions can depend on the symmetry group of rather than upon itself. Dual compositions that can be made by cumulated rectification include but may not be limited to: , , , . Does the pattern continue?

kaX

X

I

D

a

aX=adX

X

X

katX=tX+dtX

kaX=X+dX

kaaX=aX+daX

kaaaX=aaX+daaX