WOLFRAM|DEMONSTRATIONS PROJECT

The Rhombicosidodecahedron and the Deltoidal Hexecontahedron

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rhombicosidodecahedron
1
pentagon
corners
1
centroid
1
triangle
centroid
1
corners
1
square centroid
1
opacity
1
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,
kaX
represents a midpoint cumulation or "cumulated rectification" of shape
X
(
I
is the icosahedron and
D
is the dodecahedron), and can be used to create compositions of Platonic, Archimedean, and Catalan solids with their duals. Since the rectification operator
a
has the property
aX=adX
, the final form of these compositions can depend on the symmetry group of
X
rather than upon
X
itself. Dual compositions that can be made by cumulated rectification include but may not be limited to:
katX=tX+dtX
,
kaX=X+dX
,
kaaX=aX+daX
,
kaaaX=aaX+daaX
. Does the pattern continue?