Ring of 2n Rhombohedra

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Rings are formed by face-to-face connections of rhombohedra, where
. Each rhombohedron is made up of two congruent tetrahedral parts and one octahedral part at the center. The diagonal ratio of the faces of the rhombohedra is
, giving the series 0.707107, 1., 1.30656, 1.61803, 1.93185, 2.24698, …. If
, the ratio is
, producing an oblate silver rhombohedron. The first member of this family of rhombohedral rings is the rhombic dodecahedron, composed of
oblate silver rhombohedra. A cube and a prolate golden rhombohedron are obtained when
and
Contributed by: Sándor Kabai (April 2007)
Open content licensed under CC BY-NC-SA
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"Ring of 2n Rhombohedra"
http://demonstrations.wolfram.com/RingOf2nRhombohedra/
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Published: April 27 2007