Rhombic Hexecontahedron in a Rhombohedron

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Find a point that divides the diagonal of a large rhombohedron in proportion to the golden ratio. Construct a small rhombohedron
around this point so that one of its vertices coincides with the center of
. Construct a rhombic hexecontahedron
so that one of its constituent 20 rhombohedra coincides with
. If you enlarge the
, then you will see two small dots on each face of
, which are actually vertices of the
. (Drag to rotate the graphic to see the dots.) Therefore,
vertices (out of 20) of the
are on the six faces of
. When 20 rhombohedra with
s inside them are assembled to form a large
, then the
s meet at their vertices, and a rhombic triacontahedron connected face-to-face can be inserted between them.
Contributed by: Sándor Kabai (October 2015)
With additional contribution by: István Muzsai
Open content licensed under CC BY-NC-SA
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"Rhombic Hexecontahedron in a Rhombohedron"
http://demonstrations.wolfram.com/RhombicHexecontahedronInARhombohedron/
Wolfram Demonstrations Project
Published: October 28 2015