## Rhombicosidodecahedron

Even with two views, this model is much easier to fathom
if you see it in person.
Unfortunately, it requires more
Zometool pieces than a sane person is likely to have
(180 blue, 60 yellow, 60 red, 92 vertices). The outer blue solid is the
rhombicosidodecahedron. Inside it are a blue dodecahedron
and a blue icosahedron. You can imagine collapsing the
rhombicosidodecahedron onto either of the inner solids.
For instance, you can slide each of the twenty triangles
along the yellow edges down to the twenty triangular faces
of the icosahedron: the model contains twenty blue and yellow
triangular prisms corresponding to this motion, as well as
twelve blue and yellow pentagonal pyramids which show how each
pentagon in the rhombicosidodecahedron collapses to a vertex
of the icosahedron. The red edges give a similar collapse to
the dodecahedron, with a corresponding twelve pentagonal prisms
and twenty triangular pyramids.

If you prefer, you may instead focus on the thirty squares
in the rhombicosidodecahedron. There are two ways in which
to simultaneously collapse all of these squares into line
segments, and each is manifested in a family of triangular
prisms in the model. Following the red and blue triangular
prisms gives the edges of the dodecahedron, while following the
yellow and blue triangular prisms gives the edges of
the icosahedron.

Note that the icosahedron and dodecahedron are in the standard
dual-polyhedron configuration,
although the icosahedron is a little smaller than the one you get by
connecting the centers of the faces of the dodecahedron.

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